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Kerbal Space Program The Missing Manual (updated for version 0.24.2) Volume I Author: Anthony de Araujo

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Disclaimer The information in this book is for informational purposes only.

Kerbal Space Program is a product developed by Squad. It is currently in the alpha stage, but has been available for early access purchase for around 2 years. I am not a lawyer or a rocket scientist, nor am I affiliated with the producers of the Kerbal Space Program game. Any advice that I give in this publication is my opinion based on my own experience with the game and research I have done about the subject. The material in this book may include information, products or services by third parties. Third Party Materials are comprised of the products and opinions expressed by their owners. As such, I do not assume responsibility or liability for any Third Party Material or opinions. The publication of such Third Party Materials does not constitute my guarantee of any information, instruction, opinion, products or services contained within the Third Party Material. Publication of such Third Party Material is simply a recommendation and an expression of my own opinion of that material. 3

4 No part of this publication shall be reproduced or transmitted, in whole or in part in any form, without the prior written consent of the author. All trademarks and registered trademarks appearing in this publication are the property of their respective owners. Readers of this book are advised to do their own due diligence when utilizing the information contained herein. By reading the information contained in this publication, you agree that the author is not responsible for the success or failure when utilizing any information presented.

Contents

1 About the Author

9

2 Introduction

11

2.1

What is Kerbal Space Program? . . . . . . . . . . . . . . . . . 11

2.2

About this book . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3

Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3.1

∆v (Delta-v) . . . . . . . . . . . . . . . . . . . . . . . 13

2.3.2

Isp - Specific Impulse . . . . . . . . . . . . . . . . . . . 18

2.3.3

TWR - Thrust to Weight Ratio . . . . . . . . . . . . . 20

2.3.4

Staging . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.3.5

Attitude . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.3.6

Prograde/Retrograde . . . . . . . . . . . . . . . . . . . 31

2.3.7

RCS - Reaction Control System . . . . . . . . . . . . . 33

2.3.8

SAS - Stability Augmentation System . . . . . . . . . . 34 5

6

CONTENTS 2.4

Orbital Mechanics - The ”Mathy” part . . . . . . . . . . . . . 35 2.4.1

What is an Orbit? . . . . . . . . . . . . . . . . . . . . 35

2.4.2

Periapsis . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.4.3

Apoapsis . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.4.4

Semimajor Axis . . . . . . . . . . . . . . . . . . . . . . 40

2.4.5

Eccentricity . . . . . . . . . . . . . . . . . . . . . . . . 43

2.4.6

Inclination . . . . . . . . . . . . . . . . . . . . . . . . . 44

2.4.7

LAN - Longitude of Ascending Node . . . . . . . . . . 47

2.4.8

Argument of Periapsis (ω) . . . . . . . . . . . . . . . . 50

2.4.9

Mean Anomaly . . . . . . . . . . . . . . . . . . . . . . 50

2.4.10 Orbital Stability . . . . . . . . . . . . . . . . . . . . . 51 2.4.11 Lagrange Points . . . . . . . . . . . . . . . . . . . . . . 54 2.4.12 Altitude vs. Velocity . . . . . . . . . . . . . . . . . . . 56 2.4.13 Oberth Effect . . . . . . . . . . . . . . . . . . . . . . . 57 3 The Navball 3.1

63

Navball Indicators . . . . . . . . . . . . . . . . . . . . . . . . 65 3.1.1

Prograde . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.1.2

Retrograde

3.1.3

Target Prograde . . . . . . . . . . . . . . . . . . . . . . 66

3.1.4

Target Retrograde . . . . . . . . . . . . . . . . . . . . 67

3.1.5

Maneuver Node . . . . . . . . . . . . . . . . . . . . . . 67

3.1.6

Level Indicator . . . . . . . . . . . . . . . . . . . . . . 67

3.1.7

Other Navball Indicators . . . . . . . . . . . . . . . . . 68

3.1.8

Using the Navball To Change Your Attitude . . . . . . 69

3.1.9

Maneuver Nodes . . . . . . . . . . . . . . . . . . . . . 73

. . . . . . . . . . . . . . . . . . . . . . . . 65

3.1.10 Executing Maneuvers . . . . . . . . . . . . . . . . . . . 81

CONTENTS

7

4 Orbital Maneuvers

85

4.1

Gravity Turn . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

4.2

Circularizing your Orbit . . . . . . . . . . . . . . . . . . . . . 87 4.2.1

Achieving Orbit . . . . . . . . . . . . . . . . . . . . . . 87

4.2.2

Circularization . . . . . . . . . . . . . . . . . . . . . . 88

4.3

Changing your Orbital Inclination . . . . . . . . . . . . . . . . 96

4.4

Aerobraking . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

4.5

Rendezvous . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

4.6

Docking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

4.7

Gravity Assist . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

4.8

Landing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

8

CONTENTS

Chapter 1 About the Author I am a software developer with 30+ years of experience. Over the course of my professional career, I have also been a big game enthusiast during my free time. I’ve played everything from Tetris, Breakout, Duke Nukem and Doom to Left 4 Dead, Portal, Space Engineers and, of course, Kerbal Space Program. I am not a rocket scientist. I am simply an enthusiast of the game with a knack for research. All the concepts and descriptions that I provide in this book are my own experiences with the game and are not guaranteed, in any way, to help you accomplish your own goals in the game. I strive to provide the technical content in a fashion that a layperson can easily understand. If you have suggestions about how I could better explain anything you see here in the book, I would appreciate it if you would drop me a note about it at [email protected]. For the real rocket scientists that might stumble upon this book, if I got anything wrong, please let me know so that I can fix it. I want to provide the most accurate information possible, but in trying to translate ”engineer-ese”, or ”rocket-scient-ese” to English I might have made some mistakes. Also bear in mind that some things I explain in this book might be ”wrong” in the real world, but may apply in the Kerbal universe, so be gentle. 9

10

CHAPTER 1. ABOUT THE AUTHOR

I thoroughly enjoyed writing this book, and I hope that anyone who is reading it can glean some useful information from it and have a better, more enjoyable, experience in the game.

Chapter 2 Introduction 2.1

What is Kerbal Space Program?

Kerbal Space Program is an extremely fun and educational game. Having always been interested in the space program, I thought I knew something about space. Turns out I was wrong. My firsts forays into space in Kerbal Space Program ended in disaster, multiple disasters. If that is what you are experiencing, do not fret. The learning curve is rather steep, but once you start to understand the concepts, that I describe in detail in this book, the game becomes something that is, well. . . indescribable. . . Without realizing it, you will be learning concepts about space travel that you never even imagined! The game comes with three distinct modes of play: sandbox, science and career. In sandbox mode, you have all of the parts available for use and can create some pretty impressive vehicles. 11

12

CHAPTER 2. INTRODUCTION

In science mode, you start with a few, basic parts, and you must do research to gain ”science points” which you use to unlock more advanced parts. While science mode might seem intimidating, it is a very good way to start learning the game. Since you have access to a limited set of parts, you can use, and understand, those parts, naturally progressing to more advanced parts as they are unlocked. In career mode, you start with a few, basic parts just like in science mode. You still must do research to gain ”science points” which you can use to unlock more advanced parts. Besides the science aspect of career mode, version 0.24 introduced contracts, funds and reputation. These three resources must be acquired/used over the course of your career. Like science mode, it might seem intimidating but is also a very good way to start learning the game. The contract aspect of career mode forces you to use parts in some interesting ways that you might not have thought of otherwise. If you start playing in sandbox mode, the sheer number of parts can be a little overwhelming, which makes the game a little harder to learn.

2.2

About this book

When I first started playing Kerbal Space Program, it was very difficult to find any type of reference material online. I followed the advice of fellow players (shout out to http://reddit.com/r/kerbalspaceprogram) and watched all the mandatory videos (that mean’s YOU, Scott Manley! https: //www.youtube.com/user/szyzyg) I still found it very hard to gain any real knowledge about the concepts that you need to understand to play the game effectively. So I decided I was going to figure this stuff out for myself, and publish what I had learned on a blog. So I created http://mykspcareer.com, hoping to share my ”knowledge”. The response to the blog was, well, underwhelming. So here I am again, trying to get this information out there. So I decided to write this book.

2.3. CONCEPTS

13

A lot of the content in this book can be found on the blog mentioned above, including some features that I, obviously, can’t include in the book, like .craft files. As I mentioned in the disclaimer above, I’m not a rocket scientist, just an enthusiast of the game with a knack for research, so I hope this book helps old and new players alike in accomplishing their goals within the game. If you happen to be a rocket scientist, or just someone smarter than me (probably not rare), and you see anything in this publication that is wrong, could be explained better or missing entirely, I would appreciate it if you dropped me a note at [email protected]. Any contributions made by third parties will be fully credited in subsequent editions of the book. The fact that you are even taking the time to read this book, makes me happy to have invested the time to produce it.

2.3

Concepts

There are a myriad of concepts related to orbital mechanics, terminology, etc. that will help you immensely in learning the game. In this section I will go over SOME of the ones I think are more important.

2.3.1

∆v (Delta-v)

delta-v means, literally, change (∆) in velocity (v), and is simply short-hand used by personnel involved in astrodynamics. Think of your car: it has a gas tank of finite size; it has an engine of a specific power (in the case of cars, horsepower), and it has a certain ”drymass” (how much the car weighs, without fuel).

14

CHAPTER 2. INTRODUCTION

The equivalent of your car’s ∆v is not its MPG rating, nor is it the power of your engine. Imagine that your car doesn’t have an upper speed limit. So we put you in your car, with a full tank on the salt flats of Utah. You step on the gas, and hold it down, constantly accelerating, until you run out of fuel. If your speed, when you ran out of fuel was, let’s say, 2237 mph, then that is your ∆v. Your car has the capacity to change its speed, from a dead stop with a full tank, by 2237 mph until it runs out of fuel. I’ll take this opportunity to say that when dealing with astrodynamics, we use the metric system almost universally. So instead of miles per hour, we use kilometers per hour, or even more frequently, meters per second. 2237 mph works out, in metric, to be almost exactly 1000 m/s. In your car above, the overwhelming majority of mass of the fully fueled vehicle is the vehicle itself, the mass of the fuel in your car, when compared to the total mass of the car is minuscule. In the rocket world, the majority of mass is the fuel. As an example, I’ll show you the specifications for the Space Shuttle: The Shuttle itself, just the orbiter, without the big orange tank or the solid boosters, has a gross liftoff mass of 110,000 kg (this includes payload, crew, consumables, fuel for the shuttle to use in space, etc). To launch the shuttle, we add the big orange external tank, and the two solid rocket boosters which weigh in, fueled, at 756,000 kg and 1,142,000 kg (each booster is 571,000 kg), respectively. 1,000 kg per ton is a fair approximation for our purposes, so let’s just call the entire shuttle assembly 2,000 tons. Bear in mind that we burn through the solid rocket boosters in the first 2 minutes of the flight and the external tank runs the shuttle’s main engines for a grand total of 8 minutes before being jettisoned, so we use 1,898 tons of hardware and fuel to launch 110 tons of spacecraft into space. So only 5.8% of our spacecraft is actual spacecraft, the remaining 94.2% of our spacecraft is launch hardware and fuel.

2.3. CONCEPTS

15

In comparison, a 2010 Chevy Camaro weighs in at about 1720 kg and has a fuel tank capacity of about 20 gallons (19 actually, but 20 makes our calculations easier). Those 20 gallons of gas weigh 55 kg. So our Camaro, at ∼1.8 tons, is 96.9% vehicle and only 3.1% fuel. But our Camaro can’t go straight up in the air either. This Camaro can also accelerate from 0 to 60 mph in 6 seconds, which gives us a very convenient 10 mph/s (4.5 m/s2 ) of acceleration. Everyone knows that a heavier vehicle gets worse gas mileage. But the 97/3 ratio for our Camaro is pretty negligible. In our example above, of 1000 m/s, the car was heavier when it started to accelerate than at the end when it was running out of gas. So of those 1000 m/s of ”∆v” slightly more of it came from the second half of the tank versus the first half of the tank. With our space shuttle, however, after 2 minutes of flight, the vehicle drops the two solid boosters which accounted for 1,142 tons: more than HALF of the total mass of the vehicle when it was sitting on the launchpad. So in our example, 20 gallons of gas got us from 0 to 1000 m/s. And the mass of the vehicle only changed by 3%. In the case of the shuttle, at liftoff we are pushing 2,000 tons, the total burn time for the shuttle is 8 minutes. After 41 of the burn time (2 minutes), we shed more than half the mass of the vehicle. So that last 34 of burn time, theoretically, we are accelerating more quickly than during the first 14 (not necessarily true, since during that first 14 we also have two additional engines - the two solid boosters - burning). The point I’m trying to make is that the mass of the shuttle changes VERY rapidly over the course of the launch (8 minutes). In the case of our Camaro, you can use Newton’s Second Law of Motion to analyze the vehicle since, for all intents and purposes, we can consider the mass of the vehicle to be constant (it only varies by 3%, slowly decreasing as the fuel tank empties).

16

CHAPTER 2. INTRODUCTION When it comes to the shuttle, we cannot use Newton’s Second Law of Motion to analyze the system because the mass is not even close to constant (it varies by 94.2% over the course of 8 minutes!). Where the Space Shuttle’s Main Engines (SSMEs the three engines we see right below the vertical stabilizer) could not even budge the shuttle off the pad at its full 2,000 ton liftoff mass, once the shuttle is already moving at a good clip, and having dumped the extra 1,142 tons of solid booster mass, they are more than sufficient to propel the vehicle into orbit over those last 6 minutes of the launch burn.

Due to this inability to analyze the shuttle system performance using Newton’s Second Law of Motion, we need a different mechanism. That mechanism is the ”Tsiolkovsky rocket equation”.

m0 ∆v = Isp · g · ln m 1 where: m0 is the total initial mass of the vehicle, including propellant; m1 is the total final mass of the vehicle (after burning all of the propellant) Isp is the specific impulse for the engine(s) g is Standard Gravity (9.8 m/s2 ) This equation takes into consideration the rapidly changing mass of the vehicle and allows us to calculate how much change in velocity the vehicle is capable of applying to itself. As you can see above, the equation needs the Isp of the engine to calculate the ∆v. For now, just accept that rocket engines have Isp values (kind of

2.3. CONCEPTS

17

like the horsepower values you get for car engines, we’ll be discussing those next). Now we know what ∆v is and how to calculate it, but why should we care? Every maneuver, performed by a rocket, has a specific amount of ∆v that is required to perform the maneuver. For example: to launch, from the Kennedy Space Center and achieve a Low Earth Orbit (LEO), it takes anywhere from 9,300 to 10,000 m/s of ∆v. Once in an LEO, to transfer to a Low Lunar Orbit (LLO), it takes an additional 4,000 m/s of ∆v. Since we don’t want to just leave our poor astronauts there, we need 1,300 m/s of ∆v to transfer from LLO back to LEO and then another minuscule amount of ∆v necessary to deorbit (since atmospheric drag does most of the work). So a vehicle, tasked with launching to LEO, then transferring to LLO, then transferring back to LEO and landing, would require a total of 15,300 m/s of ∆v. From

To

∆v req’d

Low Earth Orbit (LEO)

Earth-Moon Lagrange 1 (EML-1)

3,770 m/s

Low Earth Orbit (LEO)

Geostationary Earth Orbit (GEO)

4,330 m/s

Low Earth Orbit (LEO)

Low Lunar Orbit (LLO)

4,040 m/s

Low Earth Orbit (LEO)

Earth-Moon Lagrange 2 (EML-2)

3,430 m/s

Low Earth Orbit (LEO)

Moon

5,930 m/s

Table listing approximate ∆v requirements within the Earth-Moon system

If you want to have an idea of how big of a rocket is needed to do that, think Saturn V, the one that went to the Moon: It was the length of a football field, at it’s base it was over half the width of a football field, and weighed, on the pad, ready to launch, 2,800 tons. Of that total, only 45 tons worth of spacecraft actually went to the Moon. 1.6% worth of spacecraft got

18

CHAPTER 2. INTRODUCTION

to the Moon, the other 98.4% of the spacecraft was either burned (as fuel) or jettisoned (as spent stages). Thankfully, the developers at Squad realized that making the Kerbal Solar System an exact replica of our own Solar System would make the game WAY too difficult to be enjoyable. If you think you have it tough getting into Kerbin orbit, which only requires ∼4500 m/s of ∆v, imagine if our flimsy, wobbly rockets had to be 4 times as big as they are!

2.3.2

Isp - Specific Impulse

Isp is, loosely, the rocket engine equivalent of an Earthbound car engine’s miles per gallon. It measures the efficiency of the engine (each engine has its own Isp). If you have one engine, with an Isp of 800, you might think that you could get more ∆v if you add a second engine of the same Isp. You won’t, you’ll get your ∆v faster, but not more of it. Isp defines how much ∆v you can, effectively, get out of a unit of fuel (a kg, for example). So if you have an engine with an Isp of 400 and 500 kg of propellant, in a 1,500 kg rocket (so 1,000 kg of rocket and engine, plus 500 kg of propellant) you would have a total ∆v of 1,590 m/s. Let’s say that your rocket takes 4 minutes to burn through those 500 kg of propellant. So if I was moving at 1,000 m/s when I started burning, when I ran out of propellant (4 minutes later), I would be moving at 2,590 m/s, a change (∆) in velocity (v) of 1,590 m/s. Too slow for me, I’m gonna add another engine on that rocket. So I put a second, identical, engine on the rocket. Do I get more ∆v? No. My rocket now will burn through my propellant twice as fast, since I have two identical engines sucking on the tank, so my burn will only last 2 minutes. And to top it all off, my final speed, when the burn ends, is now only 2366 m/s!. I got my ∆v faster (2 minutes versus 4 minutes), but I got less ∆v than with the single engine. You LOSE a small amount of ∆v because the engine you added increased the overall mass of the vehicle (dead weight once it stops burning).

2.3. CONCEPTS

19

Our 1,500 kg rocket had 500 kg of propellant and I said 1,000 kg of rocket and engine. Consider that the engine was 200 kg (so 800 kg of other ”stuff” that made up the rocket). I added an additional 200 kg of mass to the vehicle, so my rocket’s total fueled mass is now 1,700 kg, and after all the fuel is burned, 1,200 kg. All the propellant that I burned during my maneuver had to push 200 kg more of mass during the burn, therefore the ∆v produced was slightly less. From this we learn that if I want more ∆v, I have to increase the mass of propellant available to the engine (assuming the engine remains the same) *OR* keep the mass of propellant I currently have and increase the Isp of the engine I am using to burn it (effectively taking the 40 mpg engine out of the car and replacing it with a 50 mpg engine). So why don’t they just use something like miles per gallon to indicate efficiency? Because rockets aren’t cars. The mpg rating on your car is a rating calculated under specific conditions (usually conditions that benefit the manufacturer by maximizing said rating). For example: the 30 mpg rating on your car might be at a constant speed, on level ground, with no wind. Under these specific conditions, every, theoretically, 30 miles that you travel, your engine consumes one gallon of gas. If you then turn your engine off, your car, eventually, comes to a stop. THAT’S the difference. If I accelerate my rocket by burning, let’s say 200 kg of propellant, in space (outside of the atmosphere, with no gravity producing bodies nearby), from a standstill to 1,000 m/s, my speed will remain at 1000 m/s, theoretically, forever. So how far can I travel on 200 kg of propellant? An infinite distance (assuming I don’t run into anything that exerts force on the vehicle)! So there is no 1,000 miles/kg of propellant, or any other number related to a distance that we can use to indicate efficiency of the engine. What exists is velocity. With those 200 kg of propellant, I can accelerate my vessel by 1,000 m/s, and continue moving at that speed until I do another burn and change it (or run into something else that changes it). So in our example rocket, with 500 kg of propellant, if I double the amount of propellant, 1,000 kg, and leave the single engine, I double my ∆v, right? Nope, wrong again. Again, it’s close, but not quite double (2719 m/s), because at the start of the burn, the engine is pushing more mass (1,000 kg of fuel now versus the 500 kg it was pushing before), so it does it more slowly

20

CHAPTER 2. INTRODUCTION

(while expending the same amount of fuel). So after I burn the first half of my propellant (the first 500 kg), I’ve only increased my velocity by 1,129 m/s. That second half of propellant (the original 500 kg) will give me the same 1,590 m/s of ∆v that it gave me before, which added to the 1,129 m/s comes out to the 2,719 m/s total ∆v for the vehicle (these calculations are ignoring the mass of the tanks for simplicity’s sake)! Increasing the mass of propellant of the vehicle when you want more ∆v is a game of diminishing returns. Yes, more propellant gives you more ∆v. But every, let’s say, 1,000 kg of propellant that you add to your total, gives you less and less ∆v.

2.3.3

TWR - Thrust to Weight Ratio

One of the bigger issues when building vehicles in the game is finding out if you have enough engines/thrust to actually get your vehicle off the ground. The first thing we need to understand is that TWR is calculated by dividing the thrust of your vehicle by the weight of your vehicle. Both numbers should be in Newtons (N). Typically, engines have their thrust rated in kN (1000 N), but for the weight we need to do the conversion from kg to N. Contrary to popular belief, a kilogram (or a pound, for that matter) is NOT a unit of weight. It is a unit of mass1 . Weight does not exist, unless there is gravity. So the weight of an object is its mass multiplied by the force of gravity by which it is being affected. On the surface of Kerbin, the force of gravity is 9.81 m/s2 . 1,000 kg = 9,810 N on the surface of Kerbin. The main indicator of whether a vehicle will take off or not is the TWR. The TWR specifies a value, starting at 0, that indicates how much thrust you have on your vehicle, compared to the weight of the vehicle. So if your engines provide 220,000 Newtons of thrust (220 kN) and your vehicle weighs 1

Actually, while there are multiple variations on them out there, in the traditional English system of units, a pound is the unit of weight/force (there being no notion of a distinction between weight and mass when it was invented back in the day). The corresponding unit of mass is the slug - a mass that accelerates by 1 fs2t when a force of one pound is exerted upon it - Contributed by Alistair Y.

2.3. CONCEPTS

21

39,750 kg (389,948 N), you’re not going anywhere. Your engines need to provide more thrust than the weight of your vehicle to get off the ground. Our example above has a TWR of 0.56 (220,000 N/389,948 N). The lesson here is that we need a TWR greater than 1.0 if we want to get off the ground. If you want to build this vehicle in the vehicle assembly building, it’s a Mk1 Cockpit, 2 Rockomax X200-32 Fuel Tanks (one on top of the other), and a Rockomax ”Poodle” Liquid Engine. What the TWR is specifying is, in reality, the amount of g-force that the vehicle is capable of generating. So if our vehicle is generating less gforce than what is being exerted by the planet it is sitting on, it’s not taking off. On Kerbin, the force of gravity is the same as on earth, 1 G, or 9.81 m/s2 . If our vehicle cannot overcome the force of gravity, it will not lift off the launch pad. If we modify our vehicle, by adding more, or better, engines, to have 650,000 N of thrust, our TWR is now 1.61 (650,000 N/404,663 N). I replaced the ”Poodle” engine with a ”Mainsail” which weighs slightly more. Since we only have to overcome 1 G of surface gravity, this tells us that the vehicle will ascend, off the launch pad, at 0.61 G or 5.98 m/s2 . Figure 2.1: Our non-flying vehicle

22

CHAPTER 2. INTRODUCTION But, there are a couple of things that happen to a rocket as it launches. First off, as we discussed earlier, the vehicle loses mass VERY rapidly. As it loses mass, its weight goes down, as its weight goes down, its TWR goes UP !

Example: We start with our vehicle that has 650,000 N of thrust and weighs 404,663 N. Let’s assume, for this example, that the vehicle is 90,473 N of hardware and 313,920 N (32,000 kg) of fuel (remember that the shuttle was only 5.8% shuttle and 94.2% launch hardware and Figure 2.2: Our modified vehicle (that fuel). flies)

Our launch TWR is 1.61, so we lift off the launch pad at 5.98 m/s2 . At 1 minute into the flight, we’ve burned 39.4% of our fuel: 123,665 N (12,606 kg). So at the 1 minute mark our vehicle now weighs 280,998 N (28,644 kg) but it still has the same thrust: 650,000 N. Our TWR at 1 minute is: 2.31, so we are now accelerating a 1.31 Gs (12.85 m/s2 ). At the 2 minute mark, we’ve burned 75.2% of our fuel and our vehicle now weighs 168,506 N (17,177 kg), giving us a TWR of 3.86, or 2.86 Gs of acceleration (28.06 m/s2 ). The vehicle runs out of fuel at the 2 minutes and 42 second mark. Right before it runs out of fuel, it weighs 90,752 N (9,251 kg), giving us a TWR of 7.16, or 6.16 Gs of acceleration (60.43 m/s2 ) The second important thing about TWR that we need to understand is that, according to Newton’s Law of Universal Gravitation, masses attract

2.3. CONCEPTS

23

Figure 2.3: This chart shows the change in the TWR of your vehicle over time for the example vehicle described above (a vehicle that consumes all of its fuel over the course of a 2 minutes and 42 seconds burn)

each other and that the attraction is proportional to the product of the two masses and inversely proportional to the square of the distance between them. What does that mean to us? As our craft ascends from Kerbin, it loses mass quickly, since gravity is proportional to the product of the two masses (the planet Kerbin and our ship), the force of gravity reduces as the mass of our ship reduces. We are also flying (at least for a part of our flight) straight up, so we are increasing the distance between the two masses. Since the force of gravity is inversely proportional to the square of the distance between the two masses, it is reduced even more. Right above the previous chart, we discussed what the TWR was at the very end of our burn. We came up with the value of 7.16. I did this calculation so that you would understand the relationship between the weight of the vehicle and the TWR. But I slipped a white lie into those calculations. I was calculating the weight of the vehicle in N by always multiplying the mass in kg by the 9.81 m/s2 gravitational constant. In reality, the force of gravity is changing as the vehicle ascends. In our example, by the time the vehicle ran out of fuel, it was actually packing a TWR of 9.45.

24

CHAPTER 2. INTRODUCTION

Figure 2.4: As the vehicle increases its altitude the force of gravity diminishes. This graph shows the variation in gravity, by altitude, on Earth.)

2.3. CONCEPTS

25

To obtain information like ∆v, Isp and TWR for your vehicles, you can either do the math, or use one of the various mods that provide that type of information. As of this writing the most popular mods that provide this type of information are: MechJeb and Kerbal Engineer Redux. More information about these mods will be discussed in the chapter on Mods in a future volume.

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2.3.4

CHAPTER 2. INTRODUCTION

Staging

As we saw above, mass is a big factor. The more mass we have to push with our engines (for a given Isp), the less ∆v we get out of our propellant. The problem here is that, in our day-to-day lives, we are not used to thinking of things in the scale necessary for astrodynamics. In the Camaro example discussed, we carry 20 gallons of fuel that masses 55 kg. What we didn’t mention was the mass of the fuel tank. I have no idea how much a fuel tank for a Camaro would actually weigh, so let’s say 10 kg. Our Camaro’s mass, fueled, in total, is 1,775 kg. Of that total, 55 kg (fuel) plus 10 kg (fuel tank) is for our propellant. Only 0.56% of our vehicle is fuel tank (fuel itself, if you remember, was 3.1%). If we want to give our Camaro greater range, we could add another fuel tank (+10 kg) and fill it with gas (+55 kg). So we add an additional 65 kg of propellant and hardware (the tank) bringing our total mass to 1,840 kg. This way we extend the range of our vehicle, at the cost of increasing its mass. That first tank of gas isn’t going to get us as far as it used to because now it is hauling the second, additional, tank of gas with it. And even after the first tank is empty, the second tank will not take us as far as the single-tanked version of our vehicle, because it is still hauling that extra 10 kg of empty (first) tank with it. Ideally, once the first tank is empty, we drop it on the road, giving the second tank its full range (since after we’ve burned the fuel in the first tank, and dropped the empty first tank, our Camaro now masses 1,775 kg again). That is what staging is all about, getting rid of mass that is no longer needed: empty fuel tanks, dead engines (i.e. engines that have no more propellant to burn), contingency hardware (i.e. the Launch Escape System that sat on top of the Apollo command module in the Saturn V launch system), etc. We tend to think ”Empty tank? Only 10 kg? Not worth the hardware necessary to detach and jettison those 10 kg. . . ”, but that is car based thinking. In the shuttle’s case, the empty big orange tank has a mass of 26 tons. Each one of the empty, solid-rocket boosters on the shuttle has a mass of 91

2.3. CONCEPTS

27

tons. Remember that the shuttle itself (no external tank or boosters) has a mass of 110 tons. So the ”dead weight” on the shuttle, after all propellant is consumed, is 208 tons (26 tons + 91 tons + 91 tons). Almost TWICE the mass of the orbiter itself! The faster your vehicle sheds its dead mass, the more ∆v you will get from the engines and propellant that you still have, because there will be less mass to push. Your vehicle design can, theoretically, have as many stages as you see fit. Just remember that each stage requires additional hardware (a decoupler or a separator, at a minimum), which is more mass that you have to push. Also remember that, at least in game, stage boundaries tend to be the weakest structural points of your vessel. This means that you have to, typically, use struts to strengthen the link so it can withstand the stresses of a launch and maneuvers. The shuttle is a 3 stage launch system: 1. At liftoff, all three main engines on the orbiter are burning (being fed from the external tank) and the solid rocket boosters are also burning. Once the SRBs have exhausted their propellant, they are jettisoned. That is the first stage, the 2 minutes between ignition on the launch pad and the decoupling of the SRBs. 2. During the second stage, the orbiter continues burning its main engines using fuel from the external tank. At this point (2 minutes into the flight), the external tank has only been 14 depleted. So the second stage will last, approximately, another 6 minutes. At this point, the external tank is empty, so we get rid of it. That is the second stage, the 6 minutes between SRB separation and external tank separation. 3. This is the final stage of the system and includes the orbiter alone. Its main engines are still attached to the vehicle, however they are no longer used in the mission. In the real world, it is not an economically sound proposition to jettison 3 $40 million pieces of hardware that would, presumably, be burned up and destroyed upon reentry. So the shuttle hauls 10.5 tons (3.5 tons per engine) of hardware around space and brings it back when it lands.

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CHAPTER 2. INTRODUCTION

Fortunately for us, we don’t have (yet) congressional oversight committees or politicians breathing down our necks in Kerbal Space Program, so feel free to drop your ”Mainsail”s in the ocean or leave them in a degrading orbit once you no longer need them. Just for completeness sake, I’m going to mention here the shuttle’s Orbital Maneuvering System (OMS). Since once the orbiter is in orbit, it can no longer use the main engines, it needs some type of engine to do orbital injections, orbital corrections and deorbit burns. This is where the OM engines come in. Fairly lightweight (100 kg) engines, that provide about 300 m/s of ∆v (it uses about 21.5 tons of propellant to provide that amount of ∆v). Bear in mind that this OM system is separate from the RCS system (that we know and love so much in Kerbal Space Program) used by the shuttle. We currently don’t have OM engines/tanks in KSP. The strangest part about doing staging is that, in Kerbal Space Program, we have to build our vehicles from the top down. So if I were building a Saturn V equivalent, I would start with the Command Module (the capsule), would then add the Service Module, the third stage, the second stage and finally the first stage. The basics of staging are as follows: • To separate a stage, you should use a stack decoupler or a stack separator. A stack decoupler/separator is the type that was used in the Saturn V. Once the first stage is depleted it separates from the rest of the vehicle by ”dropping off” of the stack above it. • In Kerbal Space Program, fuel from tanks ”above” the stage boundary (above the decoupler/separator) will not feed ”through” the stage boundary to engines below the decoupler/separator. • The various stack decouplers, and stack separators, have different ”decoupling forces”. This means that they will push the separated stage (the one being discarded), away from the rest of the vehicle, with a certain force. In most cases, this force is negligible, since it is a ”small” force, typically, pushing a large piece of hardware. But in some cases, people use stack decouplers to ”launch” satellites from their main vehicle and don’t take that force into consideration and the satellite ends up in an orbit different from what they expected.

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• It does not matter if you have ”struts” crossing the stage boundary, since the struts will ”automagically” disappear when the stack decoupler/separator is triggered. You don’t have to worry about things not separating because they are strutted to other things. Obviously, this is only true in Kerbal Space Program. In real life, things would not work this way (actually they could, but it wouldn’t be a simple ”strut”). • If the part being separated (discarded) IS strutted across the stage boundary, the ”decoupling force” mentioned above, is affected by the struts. Despite the fact that the struts DO ”break” upon triggering the decoupler/separator, it seems they absorb some of the force being exerted by the decoupler/separator, resulting in the part being pushed away from the vehicle with less force than if the part had NOT been strutted. This is true for both stack decouplers/separators and radial decouplers/separators (see below). • The difference between a stack decoupler and a stack separator is that the decoupler only severs the connection on one side (the side that the ”arrow”, printed on the side of the decoupler, points to) and the decoupler will remain attached to the part being discarded. A stack separator, on the other hand, severs the connection on both sides. This means that with a separator, you end up with one vehicle, one discarded stage and a third part, the separator, floating freely around in space on its own. • Radial Decouplers function just like stack decouplers, except they are used ”radially” (sideways/on the side). Think of the solid rocket booster separation on the space shuttle: they are pushed off to the side as the shuttle (and external tank) continues to move forward.

2.3.5

Attitude

From here on, you will start seeing the ”Attitude” a lot. For those of you familiar with the aerospace industry, this isn’t a problem, but for those of us that are not familiar with it, I’m going to explain what is meant by ”Attitude”. From the Merriam-Webster, attitude is defined as:

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CHAPTER 2. INTRODUCTION the position of an aircraft or spacecraft determined by the relationship between its axes and a reference datum (such as the horizon or a particular star) So? Did that help? Didn’t think so. . .

Here’s the problem: a spacecraft doesn’t act like any other terrestrial vehicle with which you might be familiar. If you fire an engine in a spacecraft, that engine is going to push that spacecraft in a particular direction. Once you turn the engine off, the spacecraft will continue to move in that direction, at the same speed (i.e. inertia), unless something else influences that movement. So. . . if you accelerate your spacecraft in a certain direction, and then decide you want to stop moving in that direction, you have to ”turn around” and fire your engines again, to counteract the movement that you imparted on the vehicle when you fired them the first time. So it’s real easy for me to sit here and type ”turn around”, but in space how do you determine which way is forwards (and therefore, which ways is backwards)? Compasses don’t work. . . there’s no ”north” (magnetic or otherwise). . . I guess you could use the stars for orientation, but what if the particular celestial body you chose to use as guidance is no longer visible (on the other side of the planet, for example)? That’s what attitude is all about. . . rotating your vessel, using a myriad of different actuators, so that it is pointing in the direction that you need to point to execute whatever maneuver you want. The two main methods of adjusting attitude are discussed a little further below: RCS and SAS (or CMG, as it should really be called). Those are the mechanisms that are used to change the attitude of you vessel, but how do we figure out where we should be pointing? The answer to that is the next section: Prograde/Retrograde. . .

2.3. CONCEPTS

2.3.6

31

Prograde/Retrograde

Prograde is nothing more than the current direction of travel for your vehicle. There is no magic involved. There are actual sensors on real spacecraft that can determine which direction your vehicle is moving. In the game, the navball automatically shows you the information about prograde and retrograde, but that information IS available on real spacecraft. It might not be a pretty navball like the one we see in game (sometimes it is), but it’s there. But how does knowing what direction I am traveling help me in any way? Everything in space is about motion. If you want to slow down, you point in the direction opposite your direction of movement (retrograde) and fire your engines. If you want to speed up, you point in the same direction as your current direction of movement (prograde) and fire your engines. If you want to change the inclination of your orbit, you point in a particular direction, 90° from your current direction of movement, and fire your engines. And so on. . . But why would I want to do any of those things? Speed up? Slow down? You just said if I’m moving in a certain direction, I’ll keep moving in that direction, at that speed. So what difference does it make if I’m going 1,000 mph or 2,000 mph? Or 500 mph? Because as we will see when we get to the Orbital Mechanics part of this book, how fast you are going (or not) determines exactly where you are, and will stay (or not) in space. Remember what I said earlier, or even better, let’s look at Newton’s first law of motion:

When viewed in an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by an external force.

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One of the trickier words in there is ”velocity”. We tend to think of velocity as ”speed”, but velocity is in reality a ”vector” quantity that represents both speed and direction. We might apply a force to an object, like a spacecraft, that doesn’t modify it’s speed, but modifies it’s direction, therefore we ARE modifying it’s velocity. But your question still is: ”I’m not firing my engines, I’m out in space, so there’s no ’external force’ acting upon my ship, so who cares?” That’s where you are wrong. There ARE external forces acting on your ship. Dozens. . . hundreds. . . thousands of external forces acting on your ship ALL THE TIME. Some to a great extent, some to a lesser extent. Every single body, from the Sun and Jupiter, to the smallest of the asteroids, are all exerting a gravitational force on your ship. Even stars light-years away are exerting, however minute, gravitational forces on your ship! Think about it, it is gravity that maintains the solar system in it’s current configuration, the same way that it is gravity that maintains the Milky Way galaxy in it’s current configuration! All those teeny, tiny little gravitational forces combine to affect your ship, and every other body in the universe. In most cases, we can ”ignore” a lot of these forces, because of how small they are. Typically, you are under the influence of a ”main” body, which exerts a significant portion of the forces being applied to your ship. In real life we can’t ignore ALL of the forces except the ”main” one, but because of limitations in the capability of your computer to process these hugely complex calculations, in Kerbal Space Program, only ONE body ever exerts force on your ship at a time. But back to prograde/retrograde. . . Knowing which direction you are moving (prograde) is EXTREMELY important, because knowing that one direction, you can figure out all of the other directions that you will need to know to perform any maneuver.

2.3. CONCEPTS

2.3.7

33

RCS - Reaction Control System

Now that we understand what attitude of the vehicle means, let’s see what we use to adjust attitude. There are two different systems to adjust attitude. The first of these systems is the Reaction Control System. Most liquid fueled engines, in real life, have very limited duty-cycles (how many times they can be ”fired” without requiring a rebuild/refurbishing). For example, the space shuttle main engines, the 3 big ones on the back of the shuttle, are refurbished after every flight. They light up, once, during launch, and burn until their fuel is exhausted. They then return to Earth with the shuttle and are refurbished before being fired again. The shuttle’s OMS (Orbital Maneuvering System) engines, on the other hand, are built to be fired multiple times between refurbishings. An interesting scene to watch, in the movie Apollo 13, is the scene where the astronauts are tasked with firing the lunar module’s engine for a second time for a course correction. The representative, on screen, of the manufacturer of the engine (Grumman, I think) makes a comment along the lines of ”it wasn’t built to do this!” and the relief, after the successful firing is clearly visible on his face! This is exactly because the engine was designed to fire during the landing, and burn continuously until they reached the surface of the moon and stay behind when the ascent engine was used to return to orbit. It was never designed to be fired more than once. RCS thrusters, on the other hand are designed to be fired hundreds (if not thousands) of times, before needing to be rebuilt or refurbished. They provide very small amounts of thrust, compared to the SSME or even the OMS engines, but are more than sufficient to provide the necessary thrust for various types of maneuvers. These maneuvers include, but are not limited to: • attitude control during re-entry • station keeping (small maneuvers performed by orbiting craft to maintain its position in space since most orbits degrade slightly over long periods of time)

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CHAPTER 2. INTRODUCTION • docking maneuvers, that require multiple, very small, adjustments to complete • orientation, pointing the vehicle in a specific direction • deorbiting, in extreme situations, if the craft has lost its ability to deorbit due to a malfunction of the OMS engines or equivalent

In KSP, the RCS thrusters require a specific type of fuel, monopropellant, that you must provide for in your craft design. There are also two different types of RCS thrusters in game: the RCS block, which is a multi-directional thruster that can provide comprehensive maneuvering capability to a craft; and the Linear RCS thruster, which provides thrust in a single direction. The placement of the RCS thrusters on your vehicle is of paramount importance if you intend to do precise maneuvers such as docking. Also, if your craft is very large, multiple banks of RCS thrusters might be necessary, otherwise the craft will be ”sluggish” to respond to your maneuvers (which may be fine if you are the patient type). In the future I will go into more detail regarding RCS positioning and usage within the game.

2.3.8

SAS - Stability Augmentation System

The actual definition of what is an SAS system is a system that uses devices to STABILIZE the flight of a vehicle. The terminology in Kerbal Space Program gets confusing when they talk about capsules, cockpits and probes having SAS Torque. The SAS parts in Kerbal Space Program do indeed stabilize the vehicle, but the torque provided by the capsules/probes is NOT SAS torque. The torque generated by the capsules/probes is more aptly described as CMG (Control Moment Gyroscope) torque. SAS (Inline Advanced Stabilizer, Inline Reaction Wheel and Advanced SAS) can be used on your vehicles to reduce the vehicle’s tendency to ”wander” during flight. Most rockets will have some tendency to ”pull” to one

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side, or to rotate along it’s axis, etc., unless it is perfectly symmetrical. Once atmospheric drag is implemented in the game in a proper fashion, this tendency will most likely increase since, even the positioning of a part, such as a strut, will affect how the vehicle reacts to the atmosphere. The dampening effect of an SAS unit can be increased by placing multiple units on your vehicles. Placement of the SAS units will determine how effective they are in dampening any movement. An example of this would be a short, wide vehicle, where a significant amount of mass is ”around” the center of mass, and not lined up with the center of thrust (i.e. asparagus staging). If you were to place a single SAS unit along the center of thrust (i.e. on the nose of the capsule), it would not be able to, efficiently, counter movement imparted by the mass ”outside” of the center of thrust. It will work, just not as well. A solution in a case like this would be to place additional SAS units, in our asparagus staging case, on top of each stack in the asparagus ”bunch”.

2.4 2.4.1

Orbital Mechanics - The ”Mathy” part What is an Orbit?

An orbit is the ”gravitationally curved path of an object around a point in space”. This means that you are constantly falling toward that point in space, but you never reach it because your horizontal velocity pushes you away as you are falling. An example: a spacecraft in orbit around the Earth. The craft is constantly falling, however it is moving VERY fast horizontally, so as it falls it ”misses” the Earth, passing beyond the horizon and continues falling. It is because of this ”falling” that astronauts experience weightlessness. They are not weightless, but in relation to the vehicle that they are in, they feel weightless. They are, in reality, free falling around the planet.

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CHAPTER 2. INTRODUCTION

When I say VERY fast above, I mean VERY FAST! Orbital velocity for Earth, in a low Earth orbit (200 - 2,000 km altitude) is somewhere between 15,400 and 17,400 mph! But what we are going to discuss here are some components of an orbit so you can understand the terminology that you will see in game, on the wiki, in the forums and other places where Kerbal Space Program is discussed.

Apsides An apsis (plural: apsides) is the point of greatest or least distance of a body from one of the foci of an elliptical orbit. In Kerbal Space Program, we are acquainted with two of the apsides: periapsis and apoapsis. The reference focus, in our situation, is always the body that we are orbiting.

2.4.2

Periapsis

The periapsis of your orbit is the point in the orbit at which you will be at the least distance from the body you are orbiting. It is your closest approach to the body being orbited. When we discuss orbital maneuvers, you will see why it is important to know where this point of your orbit is located. Certain orbital maneuvers work especially well when performed at specific points in your orbit. Another important use for the periapsis is that, since it is the lowest point in your orbit, you can tell whether your orbit will degrade due to atmospheric effects. If at the lowest point in your orbit you are still above the atmosphere of the body you are orbiting (for Kerbin: ∼70km), then you know that your orbit is ”stable” since you will not encounter any atmospheric effects at any point in your orbit. You could, theoretically, leave your craft in that orbit, indefinitely, and it would never fall back to the body it is orbiting. Obviously, the previous paragraph only applies to bodies that have atmospheres. But even the bodies that don’t have atmospheres have a minimum

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periapsis of which you should be mindful. For example, on the Mun the highest mountain peak is 3,340 meters; on Minmus, 5,725 meters; and on Gilly, 6,400 meters. If you are establishing an orbit around any body, make sure you verify the highest elevation of that planet/moon, unless you want to plow into the face of a mountain.

All elevations, including the periapsis and apoapsis, in game are expressed in relation to sea level of the reference body. According to Kepler’s Second Law of Planetary Motion:

”A line joining a planet and the Sun sweeps out equal areas during equal intervals of time”

If we substitute ”planet” with ”vessel” and ”Sun” with ”orbited body”, the law still applies, since physical laws are not exclusive to stars and planets. We now have:

”A line joining a vessel and the orbited body sweeps out equal areas during equal intervals of time”

What this implies is that the vessel’s velocity is higher when it is closer to the orbited body, hence lower when it is farther away. Since the periapsis is the closest the vessel can come to the orbited body (in a given orbit), it is also the point in the orbit where the vessel has it’s highest velocity. In Kerbal Space Program, the periapsis of your orbit is indicated, while in map view, by a little blue marker with a ”Pe” inside of it. Below is a picture of what that looks like:

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CHAPTER 2. INTRODUCTION

If you hold your mouse over the ”Pe” marker, it will show you the altitude of your periapsis:

Additionally, if you click on the little marker, it will stay showing the periapsis altitude even if you move your mouse elsewhere. It is kind of tricky to click on the marker and not on the orbit at the same time, because when you click on the orbit, you get the popup asking you if you want to ”Add Maneuver”.

2.4. ORBITAL MECHANICS - THE ”MATHY” PART

2.4.3

39

Apoapsis

Similar to periapsis, above, the apoapsis defines the point, in your orbit, where your vessel is at the greatest distance from the body begin orbited. Also, as discussed about the periapsis, it is important to know where, on your orbit, your apoapsis is located, because there are particular orbital maneuvers that work especially well, when executed at this point.

According to Kepler’s Second Law of Planetary Motion, the apoapsis is the point, in your orbit, where your vessel has the lowest velocity.

Just like the periapsis, the apoapsis is indicated, in map view, by a little blue marker with ”Ap” inside:

You can mouse over the marker like you can with the periapsis to see the altitude:

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CHAPTER 2. INTRODUCTION

And you can click on it, to keep the apoapsis display showing regardless of whether you move the mouse or not. Another detail, that I didn’t mention in the periapsis explanation above, is that below both of the markers, when they show you the altitude, they also show you how much time until you reach the marker. This is important because sometimes you need to plan a maneuver at exactly that point in the orbit. This countdown tells you how long you have until you reach that marker, so make sure to create the maneuver and leave sufficient time for ship positioning and burn time before you actually hit the marker.

2.4.4

Semimajor Axis

The longest diameter, of an ellipse (and remember that orbits are, typically, elliptical; a perfectly circular orbit is, for our purposes, considered an ellipse with eccentricity of 0), is called the major axis. The shorter diameter is, as you would expect, the minor axis (just for completeness sake). The sum of your periapsis distance and your apoapsis distance is the major axis for your orbit. The semimajor axis is half of that. If you are in an orbit around Kerbin, and you have a periapsis of 281,969 meters and an apoapsis of 2,438,568 meters, the semimajor axis for your orbit is 1,960,268 meters

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(281,969+600,000)+(2,438,568+600,000) 2

(The 600,000 in the equation above is the radius of the planet Kerbin. In calculating the semimajor axis, we count the distance to the center of the body being orbited. Since periapsis and apoapsis are both given as an altitude from sea level, we need to add the radius of the planet for our calculations.) The closer your orbit is to a perfect circle, the closer the semimajor axis will be to the radius of your orbit (in a perfect circle, the semimajor axis IS the radius). The semimajor axis is important to determine the orbital period of your orbit (how long it takes for your vessel to complete one orbit). The formula is:

T = 2π

v u u a3 t

µ

where:

• a = the length of the semimajor axis of the orbit (in meters) • µ = the standard gravitational parameter of the body you are orbiting

When performing the calculation, if you are so inclined, remember to use meters and not kilometers for the semimajor axis. The gravitational parameter for the various bodies in the Kerbol System can be found in the Kerbal Space Program Wiki. In the description of each body in the system, you can find the gravitational parameter listed as shown in the screenshot below:

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In our example above, the orbit with a semimajor axis of 1,960,268 meters (around Kerbin in this example), the orbital period would be: 9,176 seconds (a little over 2 21 hours) An important thing to understand from this is that any orbits that have the same semimajor axis, have the same orbital period. In our example we used a semimajor axis of 1,960,268 meters (Pe=281,969 meters, Ap=2,438,568 meters), but any orbit that results in a semimajor axis of 1,960,268 meters (i.e. Pe=760,485 meters, Ap=760,051 meters) will have the same orbital period of ∼ 2 21 hours. Below is a picture of exactly the two orbits described above:

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The blue orbit is almost perfectly circular, with a periapsis of 760,051 meters and an apoapsis of 760,485 meters. The gray orbit has a periapsis of 281,969 meters and an apoapsis of 2,438,568 meters and is visibly elliptical. Both of these ships take the exact same time to complete one full orbit: the ∼ 2 21 hours I calculated above.

2.4.5

Eccentricity

Eccentricity of an orbit describes how elliptic an orbit is, compared to a perfect circle. A perfectly circular orbit is an orbit where the vehicle is at a constant reference altitude, in every point of its orbit. Perfectly circular orbits are uncommon. Most orbits are, at least, slightly elliptical in nature.

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CHAPTER 2. INTRODUCTION

In Kerbal Space Program, Kerbin, and both of its moons, have perfectly circular orbits (the former around the Sun, the latter around Kerbin itself). Duna, on the other hand has an orbital eccentricity of 0.05. This indicates that its orbit is slightly elliptical. Eeloo has an eccentricity of 0.26, which means its orbit is much more elliptical than Duna’s. If you use the map mode in Kerbal Space Program and zoom WAY out, you will see how the shapes of the orbits of the different planets vary.

In real life, the eccentricity varies from 0.00677 (for Venus) on the low end, to 0.20563 (for Mercury) on the high end (for planets, not going into the realm of dwarf planets, comets, asteroids, etc.).

In the last picture shown in ”Semimajor Axis” above, I show two orbits. The blue one is an (almost) perfect circle, therefore it has an eccentricity of 0. The grey orbit is visibly elliptical (what us common folk call an oval) and has an eccentricity of 0.55.

2.4.6

Inclination

Inclination describes how inclined an orbit is. To have an inclination (an angle in degrees), you need some type of reference point. In the case of orbital inclinations, we use what is called the ecliptic plane.

Draw the Sun on a sheet of paper, then draw the Earth’s orbit around the Sun. That gives you a roughly circular orbit. Now take that page and look at it sideways, that is the ecliptic plane. So if another planet in the system has an inclination of 60 degrees (very unusual, but useful for our understanding), that means that if you were to draw its orbit on another sheet of paper, then you would combine the two sheets at an angle of 60 degrees.

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Most inclinations are given with relation to a specific body. In our solar system, Earth is the reference body, therefore Earth’s orbit has an inclination of zero degrees in relation to the ecliptic plane (since Earth’s orbit DEFINES the ecliptic plane, it couldn’t be any other way).

The planets of Earth’s solar system, do not all orbit on the same plane, they have various different inclinations. The same is true of Kerbin’s solar system. In Kerbin’s system, the planet that has the closest inclination to Kerbin’s orbit is Duna, at 0.06 degrees.

Inclination is important because, when you are planning encounters, if the target is on a different plane, then you have to correct for the inclination of the target, otherwise you will pass the target’s orbit with the target ”above” or ”below” you.

This is a picture, from in game, of two vessels orbiting Kerbin. Both of these vessels are orbiting at an altitude of 100,000 meters:

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The orbit in blue is an equatorial orbit (it has an inclination of 0°). The other vessel (the grey orbit) is NOT in an equatorial orbit; it’s in an orbit with an inclination of 25°. But what does that mean exactly? It helps to visualize the inclination by looking at the equatorial orbit on it’s edge:

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When looking at the equatorial orbit on its edge, it shows as a straight line. As an extra bonus, this shot also shows the ecliptic plane. As you can see, the other vessel’s orbit, when seen edge on, creates an angle between itself and the ecliptic plane. That angle is 25°, and that is why we say the orbit has an inclination of 25°. In our example above, we happen to also have a vessel whose orbit is aligned with the ecliptic plane, but it’s the ecliptic plane reference that defines the inclination angle.

2.4.7

LAN - Longitude of Ascending Node

When an orbit is inclined to the ecliptic plane (has an inclination different than 0°), there will be two points, in that orbit, where the orbit crosses the ecliptic plane. At one of those points it will be below the ecliptic plane and will be crossing the plane to above the ecliptic plane. It will be ”ascending”. So that point will be the ascending node, the other point (where it’s crossing the ecliptic from above to below), is the descending node. So what’s this business with the longitude? The orbit will cross the ecliptic plane at a specific point. Imagine that you were looking out from the ship at this point, and looking straight down at the planet you are orbiting. You would be looking at a specific point on the planet (let’s say, in the case of the Earth, you happened to be looking down at Tokyo). Tokyo’s longitude is approximately 140° E. So the LAN (longitude of ascending node) would be 140°. What this defines is the location of the periapsis and apoapsis of the orbit in relation to the prime meridian (in our case, 140° is relative to the prime meridian of the Earth). The picture below shows an elliptical orbit (the same one from our previous topics), with an LAN of 0°:

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CHAPTER 2. INTRODUCTION

Notice how the periapsis is on the dark side of Kerbin. The same orbit, below, with an LAN of 180°:

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Notice how, now, the periapsis is on the light side of Kerbin. The orbit is ”rotated” 180° in relation to the orbit that had an LAN of 0°. All the other parameters of the orbit remain the same: periapsis, apoapsis, semimajor axis, eccentricity, inclination, etc. With an orbit that is elliptical, we have two main points: the periapsis and the apoapsis. The LAN defines, indirectly, where those two points are in the orbit, in relation to a longitude system defined for the body it is orbiting. Now you might say, ”but Mars (or Duna, for that matter) doesn’t have any ’defined’ longitude system!”. Well, you’re right, kinda. We, humans, self-centered creatures that we are, defined OUR longitude system in relation to the prime meridian. Over the millennia, the prime meridian has varied in location (the place we call longitude 0°), until finally, in 1884, we as a species, decided we needed one standard. We elected the Greenwich Meridian to be THE Prime Meridian and it has been ever since. Even so, that is not the prime meridian that we use when defining the LAN of orbits. The prime meridian for orbital parameters is called the origin of longitude. For Earth-based LANs (and any heliocentric orbits) we use the First Point of Aries. The First Point of Aries has been the origin of longitude for a very long time. It is still used as the origin even though, due to the precession of the equinoxes, the point is no longer in the constellation of Aries. For bodies outside of the Earth solar system, another prime meridian is determined by a method WAY too complicated to explain here, and angles are measured from that meridian. For our purposes, the LAN has a reference meridian, in the Kerbol system, that is used to calculate the LAN. For orbits that have an inclination of 0°, the orbit never actually crosses the reference plane (it is not inclined in reference to that plane, hence the inclination of 0°), it is established that the LAN is also placed at 0° longitude.

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CHAPTER 2. INTRODUCTION

Argument of Periapsis (ω)

The argument of periapsis, typically symbolized by ”ω”, is the angle between the longitude of the ascending node and the periapsis of the orbit. Adding the argument of periapsis to the longitude of the ascending node gives us another parameter: the longitude of periapsis. However, in many circles the terms ”longitude of periapsis” and ”longitude of periastron” are often used as synonyms to ”argument of periapsis”. So it is a parameter, in the strict sense, but probably nothing that we need to worry about in the game.

2.4.9

Mean Anomaly

The mean anomaly of an orbit is a parameter relating position and time for a body in a Kepler orbit. Kepler’s law stipulates that the line connecting the orbiting body to the focus of its orbit sweeps equal areas in equal times during its orbit. The mean anomaly can vary from 0 to 2π radians. But it is not an angle. It is proportional to the area swept, by the line connecting the orbiting body and the focus of the orbit, since the last periapsis. It is kind of an indicator as to how far, past the periapsis, the orbiting body is in its journey around the orbit. Most of the parameters that we have seen up until this point have been parameters that describe the orbit as a whole: how high it is at different points (periapsis and apoapsis), how inclined it is in relation to the ecliptic plane (the inclination), how oval or round it is (the eccentricity), where the orbit crosses the plane when it is inclined (the longitude of ascending node) and where the periapsis is in relation to the LAN (the argument of periapsis). The one thing that we have not described until now is: Where is the orbiting body, on this elliptic orbit that we so painstakingly defined, right now? That’s what the mean anomaly does. This concludes the section about orbital parameters. Below is a graph that illustrates SOME of the concepts explained so far:

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2.4.10

51

Orbital Stability

I’ve mentioned ”stable” orbits a couple of times so far. But what is a stable orbit? A stable orbit is an orbit that will not degrade over long(ish) periods of time. In real life, a stable orbit is very hard to achieve. There are just too many factors that play into the stability of an orbit for it to be considered 100% stable. The International Space Station (ISS), with an orbital periapsis of 330 km, is still subjected to drag from Earth’s upper atmosphere. This drag causes the station to slowly lose altitude, over time, which makes it necessary to

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fire engines on the station to correct it’s altitude. But there are other factors that contribute to the lack of orbital stability for any body orbiting another. All of the bodies in the Solar System exert some influence, however minute, on every other body. This means that even if the ISS was completely free of the atmosphere, the gravitational pull of the Moon, the Sun, Jupiter, and even tiny little Mercury are all influencing it’s orbit. By far, the Earth, being the body that is closest to the ISS AND the body around which the ISS revolves, has the greatest influence on the ISS’s orbit. But it’s orbit will change, very slightly, over long periods of time, due to these other influences. But enough about real-life, it’s depressing. In Kerbal Space Program, things aren’t quite like that. This whole business of calculating all the little, teeny tiny influences of multiple bodies upon each other is what is known, in the astrophysics community, as the n-body problem. There is no exact solution to the n-body problem for n ¿ 2. For any system, that needs to be analyzed, that contains more than 2 bodies, the best we can do is an approximation, and even that takes A LOT of work. Much more than our measly little desktop computers are capable of in any realistic timeframe that would make the game still playable. So, we are limited, by the physics engine used in the game, to 2 bodies. So if a ship is orbiting Kerbin, Kerbin is one body and the ship is the other. The game’s physics engine doesn’t take into consideration any other bodies within the system that might be influencing the ship’s orbit. This makes orbits that we establish, in game, more stable than they would be otherwise. So in game we don’t have to worry about all the other bodies in the system influencing our vessels’ orbits. This however, has some drawbacks. To be able to have transfers from one body (i.e. Kerbin) to another body (i.e. the Mun), at some point the system has to stop considering Kerbin our first body and switch over to the Mun (our ship is the second body in both cases). This is resolved by what is called Spheres of Influence (usually abbreviated as SOI or SoI). Kerbin has a specific SOI that extends from Kerbin’s surface to a specific height. Every

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other body in the system, similarly, have their own SOIs defined. Once your vessel leaves Kerbin’s SOI it is shifted to another SOI. If your ship is not near enough to another body, to be within that body’s SOI, then the SOI of Kerbol (the game’s ”Sun”) is used. Below is a screenshot of a typical Mun transfer:

In this picture, the blue orbit is your orbit, within Kerbin’s SOI, the little circle at the point where the blue transitions to the yellowish line is what is called a ”Mun encounter”. Once we cross that point in the orbit, we are no longer within Kerbin’s SOI, we are then in the Mun’s SOI. The yellow orbit, further along, transitions to the purple orbit, the little circle on the threshold identifies it as ”Mun Escape”. This means that left to

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its own devices, the ship will transition into the Mun’s SOI and continue on until it leaves the Mun’s SOI and transitions back, in this particular case, to Kerbin’s SOI. If I let it go even further along this trajectory, it exits Kerbin’s SOI and transitions to Kerbol’s (the Sun’s) SOI and establishes itself in an orbit very similar to Kerbin’s own orbit around the Sun.

These spheres of influence are what allow the game’s physics engine to resolve the 2 body problem. Any given vessel is only, ever, in one sphere of influence at any given time.

But the 2 body physics limitation also causes a problem with. . .

2.4.11

Lagrange Points

Lagrange points are, in astrophysics, defined points, near two bodies, where a 3rd body (and herein lies the problem) can maintain a consistent position. The calculations of these points requires some intense mathematics that the game’s physics engine is not capable of executing within a timeframe that would make the game playable.

Essentially, a body can position itself at one of these Lagrange points (there are five) and remain in a constant position, in relation to the other two bodies.

This graph indicates the position of the Lagrange points in the Earth-Sun system:

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At L1, the body is stable. The pull from the Sun’s gravity, and the pull from Earth’s gravity, ”drag” the body around the Sun in the same exact amount of time as the Earth takes to orbit the Sun (which is odd, as we’ll see in a bit). L1 is the most ”intuitive” of the Lagrange points: it makes ”sense”; the body is being ”wrestled” by the other two bodies’ gravitational forces, therefore doesn’t quite react as it should.

The other four Lagrange point are less ”intuitive”, but they exist nonetheless. Any object placed at those points, will remain in that exact same, relative spot (not so much a spot, in the case of L4 and L5, as an area).

But why ”should” they react any differently?

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CHAPTER 2. INTRODUCTION

Altitude vs. Velocity

In any orbit, the semimajor axis (so indirectly, the periapsis and the apoapsis) defines the orbital period. An orbit with a semimajor axis of X has an orbital period smaller than an orbit with a semimajor axis of 2X. I’m not going to go into the mathematics and give you numbers, just accept that it is true. Crunch the numbers if you don’t believe me. If I am orbiting Kerbin at 100 km, I am moving faster than another ship that is orbiting Kerbin at 200 km. If the ship at 200 km takes X amount of time to complete one full orbit, my ship will complete one full orbit in some fraction of X amount of time. So for every orbit that the 200 km ship makes I make more than one orbit at 100 km. Effectively, I’m ”pulling ahead” of the other ship. If I were to raise my orbit to 300 km, then I would be the one moving slower than the one at 200 km and it would pull ahead of me (or catch up, if it were already behind). The further the ships are from the center of mass they are orbiting, the slower they move to maintain that orbit (I’m assuming all circular orbits here, just for sanity’s sake). We discussed the same concept when we were discussing periapsis and eccentricity. As I approach my periapsis (in a non-circular orbit), I gain velocity (because I’m closer to the planet). When I reach my periapsis, I am at the closest point I will ”ever” be to the planet, so I am also as fast as I’m going to get in this orbit. As I pass the periapsis and head toward the apoapsis (gradually getting further from the planet), my velocity decreases until I reach the apoapsis (furthest point, lowest velocity) and start heading back to the periapsis again to begin the next cycle. This is what is ”odd” about bodies at Lagrange points. If a body is at the L1 point, it is, by definition, closer to the Sun than the Earth is, so it should be moving faster than the Earth, pulling ahead of the Earth in its orbit. However, it doesn’t. Because of the interaction between the Sun’s

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gravity and the Earth’s gravity, the body moves as fast as the Earth does around the Sun, effectively maintaining its position with relation to both the Sun and the Earth. I think this information might come in handy later, in something called ”rendezvous”, so keep it in a safe place.

2.4.13

Oberth Effect

As we learned in high school physics, objects in motion have kinetic energy. Kinetic energy is best described as the energy the object gained by being accelerated to its current speed. The Oberth Effect, after Austro-Hungarian-born physicist Hermann Oberth, describes how a vehicle employs it’s kinetic energy to generate more mechanical power, resulting in more usable energy, by the application of an impulse, usually provided by a rocket engine, while in close proximity to a gravitational body. If we skip all the math and get right down to the meat of the matter, what this means to us, in Kerbal Space Program, is that: The same amount of thrust expended (∆v), at a given point in our orbit will result in a final velocity (at distance) to be much larger than expected, depending on where in that orbit the burn occurs. In a previous section, I mentioned that knowing where the periapsis and the apoapsis of your orbit is important, because certain maneuvers work especially well when executed at exactly those points. The Oberth maneuver is one of those maneuvers that works especially well when executed at the periapsis of your orbit. Imagine an elliptical orbit around Kerbin, with a periapsis of 100,000 meters and an apoapsis of 300,000 meters.

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Your vehicle is moving its fastest when it is at the periapsis and its slowest when at the apoapsis. Those speeds, for this orbit are: at your periapsis you are moving at 2,383 m/s. At your apoapsis, you will be moving at 1,853 m/s.

If we now create a maneuver, at our periapsis, where we expend 100 m/s of ∆v, this is what our maneuver would look like:

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Our apoapsis was raised to 498,000 meters (an increase of 200,000 meters), and our periapsis remains the same. The velocities at both points are now: 2,483 m/s at the periapsis (what it was + 100 m/s), but our velocity at the apoapsis has changed to 1,581 m/s.

If we do the maneuver, the same 100 m/s increase, at the apoapsis, the maneuver looks like this:

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In this case, our apoapsis remains the same, and our periapsis increases to 251,000 meters (an increase of 150,000 meters). The velocities at both points are: 1,953 m/s at the apoapsis (what it was + 100 m/s), but our velocity at the periapsis is now 2,066 m/s. In the first case, we increased the semimajor axis of our orbit by 100,000 meters, but in the second case, we only increased it by 75,000 meters. Since the specific orbital energy is dependent on the semimajor axis of your orbit, the specific orbital energy, after the burn, was higher in the first case (burning at periapsis) than in the second, even though the total amount of ∆v, and fuel, expended was the same. The reason for the gain in energy is as follows: When the rocket expels propellant, that propellant is expelled at a specific velocity. When compared with the velocity of the vehicle that is expelling the propellant, part of the energy expelled is lost in the mass that is expelled but part of it is kept by the vehicle. Example: If the velocity of your vehicle is 1,000 m/s, and propellant 1 of the energy of is expelled at 2,000 m/s, then your vehicle might retain 10 the propellant, the remaining 90% of the energy is lost with the propellant

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(not lost, but stays with the propellant expelled). If the velocity of your vehicle is 5,000 m/s and propellant is expelled at the same 2,000 m/s, your vehicle might retain 40% of the energy of the propellant, only leaving the propellant 60% of the original energy. The bottom line is that it is more efficient, energy-wise, for you to do burns of this type around your periapsis than it is anywhere else in your orbit.

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Chapter 3 The Navball

This is your Kerbal Space Program Navball:

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CHAPTER 3. THE NAVBALL Right off the bat, couple of things: • If you want to hide the navball, click on the little black arrow (right above where it says ”Orbit” in the above picture), or press the . (period) key ON THE NUMERIC KEYPAD. • If it’s not showing (like the default in map mode), same thing, either click on the little black arrow at the bottom of the screen, or press the . (period) key on the numeric keypad.

The navball shows you, at different times, certain characteristics of your vehicle that are important: • which direction your vehicle is pointing; • which direction your vehicle is moving; • which direction your target is located; • how much you have to fire your engines to accomplish a maneuver; • which direction you should fire your engines for a maneuver; • how much throttle you are currently using; • what ”mode” the navball is in; • etc. I’m going to explain each indicator on the navball separately. Where they are related to another indicator I will mention that. The first thing we have to understand about the navball, is that it works in different modes. In the picture above, our navball is showing ”Orbit:” and ”335.6m/s”. This indicates that our orbital velocity is currently, 335.6 m/s. We can click on the word ”Orbit:” and it will change to ”Surface:” and, probably, show a different speed. The speed shown when in ”Surface” mode

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is the speed in relation to the surface of the body we are orbiting, launching from or landing on. Additionally, if you have a target selected, and click on ”Surface” on the navball, it will switch to ”Target” and show another speed. The speed shown is the relative velocity between your vehicle and the target (how fast you are moving towards, or away from, your target). So, we basically have three modes that the navball can operate in: we’ll call these ”Orbit mode”, ”Surface mode” and ”Target mode”, hopefully, consistently, throughout the book.

3.1 3.1.1

Navball Indicators Prograde In Orbit mode, the prograde indicator tells you which direction you should point if you want to be facing the exact direction that your vehicle is moving. If you want to increase your orbital velocity, point prograde, in Orbit mode, and thrust in that direction.

In Surface mode, the prograde indicator tells you which direction you should point if you want to be facing the direction that your vehicle is moving relative to the surface of the body you are orbiting/launching/landing. If you want to increase your surface velocity, point toward the prograde marker, in Surface mode, and thrust in that direction. In Target mode, the prograde indicator tells you which direction you should point if you want to be facing the direction that your vehicle is moving relative to your target. If you want to increase the relative velocity between your vehicle and your target, point toward the prograde marker, in Target mode, and thrust in that direction.

3.1.2

Retrograde

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In Orbit mode, the retrograde indicator tells you which direction you should point if you want to be facing the direction exactly opposite of that which your vehicle is moving. If you want to decrease your orbital velocity, point retrograde, in Orbit mode, and thrust in that direction. In Surface mode, the retrograde indicator tells you which direction you should point if you want to be facing the direction exactly opposite of that which your vehicle is moving relative to the surface of the body you are orbiting/launching/landing. If you want to decrease your surface velocity, point toward the retrograde marker, in Surface mode, and thrust in that direction. In Target mode, the retrograde indicator tells you which direction you should point if you want to be facing the direction exactly opposite of that which your vehicle is moving relative to your target. If you want to decrease the relative velocity between your vehicle and your target, point toward the retrograde marker, in Target mode, and thrust in that direction. This maneuver is commonly referred to as canceling or zeroing your speed relative to the target.

3.1.3

Target Prograde

This indicator is, in my opinion, erroneously called the Target Prograde indicator. I don’t like that nomenclature because it alludes to the fact that this indicates the prograde direction that your target is moving. That is NOT the case. What this indicates is what vector you have to follow to get to your target. It indicates where your target is in relation to your ship. If you accelerate directly towards your target by pointing at this indicator and engaging your engines, it will, indeed, become your target ”prograde” indicator, but not quite. Basically, this is the direction that you want to point your ship if you want to go towards your target. It is only HALF of the puzzle you will need to solve to do a rendezvous with a target. Obviously, this indicator will only show up on your navball if you have a target selected.

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3.1.4

67

Target Retrograde

This indicator is also, in my opinion, erroneously called the Target Retrograde indicator. I don’t like that nomenclature because, like it’s brother, it alludes to the fact that this indicates the retrograde direction that your target is moving. That is NOT the case. What this indicates is what vector you would have to follow to move away from your target. Basically, this is opposite the direction that you would point your ship if you wanted to go towards your target. Obviously, this indicator will only show up on your navball if you have a target selected. Note that pro and retro are directions that are 180° from each other. Prograde is opposite (180°) from retrograde. Target prograde is opposite (180°) from target retrograde.

3.1.5

Maneuver Node This indicator tells you which direction to point your vehicle to execute the maneuver that you have created. You create maneuvers in the map screen and once you have adjusted the maneuver to your liking, this is the indicator that you should follow when executing the burn.

Please note that when you create a maneuver node, this indicator shows up immediately on your navball, but you should only execute the maneuver once the correct time arrives. If you do not currently have a maneuver established, then this indicator does not show up on the navball. If you have multiple maneuvers planned, then this indicator is for the ”next” maneuver.

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CHAPTER 3. THE NAVBALL

Level Indicator

This is the last indicator that shows up inside the navball. It indicates where the ”nose” of your vehicle is pointing. Note that this indicator does not move. As you change the attitude of your vehicle, the navball rotates underneath the level indicator to display your current attitude.

3.1.7

Other Navball Indicators

There are a few more items that we need to discuss on the navball and then we will discuss maneuvers. Below the ”artificial horizon” (the blue/brown ”bally” part of your navball), is your heading: ”HDG”. Your heading is indicated in degrees and is counted, clockwise, from whatever is considered ”North” on the navball (indicated by the solid red line going up and down the navball, assuming you are level). On the left side of the navball (between 6:30 and 10 o’clock, if the navball were a clock face) is your throttle indicator. It has a little white arrow indicator that tells you where your throttle is positioned. The very bottom of the scale, your engines are off, the very top of the scale, your engines are at full thrust. The scale also has a red area that currently is not used by the game. I’m assuming that this will be used in the future when it is possible to throttle your engines over their rated thrust. On the right side of the navball, similar to the throttle indicator on the left, is the G-force meter. This meter indicates how many Gs of force your craft is undergoing. This indicator, in the real world, is used to assess the stress being imposed upon the vehicle and the occupants.

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Notice that the G force scale starts at -5 Gs and goes all the way up to 15 Gs. The ”danger zone” starts at 9 Gs (the red area on the dial) and should be avoided whenever possible. G forces must be kept within tolerable levels both for the airframe and for the crew. Excessive G force on the airframe can cause rapid unplanned disassembly and excessive G forces on the crew can cause everything from lightheadedness and loss of consciousness to death. In Kerbal Space Program, G forces are not taken into consideration (yet) in the stock game. I believe there are mods in the community that implement some excessive G force consequences. On the left side of the navball, right above the throttle indicator, is the RCS indicator. This is simply an on/off indicator to tell you whether RCS is turned on or not. If it is lit up green and says ”RCS”, then your RCS is on. If it is black, RCS is off. To turn RCS on or off, press the r key (default key). On the right side of the navball, right above the G force meter, is the SAS indicator. Like the RCS indicator, it is simply an on/off indicator to tell you whether SAS is turned on or not. If it is lit up white, and says ”SAS”, then your SAS is on. If it is black, SAS is off. To turn SAS on or off, press the t key (default key). These are all of the characteristics of the navball itself. Let’s talk about navigating with the navball.

3.1.8

Using the Navball To Change Your Attitude

or ”What is all this talk about prograde and retrograde?” First let’s clarify what attitude is. I’ve mentioned it a few times before so I want to make sure we understand what I mean. The attitude of an aircraft (or a spacecraft) is the orientation of that craft relative to its direction of travel.

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In space (and even in the air), you can turn completely around from your direction of travel and still continue in that direction of travel, rear-first indefinitely (not indefinitely in the air, obviously). You can turn your vessel up, down, sideways, in any direction that you want and your direction of travel (or speed, for that matter) is not changed at all, until you fire your engines. This is unfamiliar ground for people only exposed to terrestrial modes of transportation and therein lies the problem. In astrodynamics we use the attitude to describe the orientation of the vessel in relation to it’s direction of travel. So if I launch a rocket in a straight line at the Moon (let’s assume that both the Earth and Moon are stationary objects for this example) and I’m going 1,000 m/s. If the nose of my rocket is still pointing at the Moon, we say that the rocket is pointing ”prograde”. So if I were to tell you ”point prograde”, that means point your rocket in the exact direction that it is moving, in our example, straight at the Moon. If I were to tell you ”point retrograde”, that means point your rocket in the direction exactly opposite of the direction that you are moving (i.e. point the tail of your rocket in the exact direction you are moving), in our example, straight back at the Earth. The main reason why these two directions are important is that in space there are no other reference points to which you can really point. I can’t say stuff like ”turn 15° north-northeast once you pass the mountain range” because ”northnortheast” has no meaning in space, nor are there any mountains up there (unless you count the asteroids). We need some reference points to plan maneuvers. Prograde and retrograde are two of them. Radial and anti-radial are another two, normal and anti-normal are another two. You’re thinking ”Oh crap! What is that all about?”. Simple. You’re in another ship, orbiting Earth (or Kerbin, it doesn’t matter), counterclockwise (as seen from the North pole), at a constant altitude, let’s say 1,000 km, traveling at a constant speed. Your orbit is (unnaturally) perfectly circular. Your ship is pointing straight in the direction that it is moving. You are standing in the cockpit, looking out the ”windshield”, straight ahead. Your head is pointed in the same direction as the planet’s North pole, and your feet are pointing in the same direction as the planet’s South pole.

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Where you are looking is prograde.

Right behind your head (180° from prograde) is retrograde.

Straight up, from the top of your head in the direction of the ceiling, is normal.

From the bottom of your feet, straight down (180° from normal), is anti-normal.

Now raise both of your arms straight out from your body (like a ”+”).

Where your left hand is pointing, straight at the center of the planet you are orbiting, is radial (or radial in).

Where your right hand is pointing, away from the center of the planet you are orbiting (180° from radial), is anti-radial or (radial out).

If I now need to give you directions like ”point 30° anti-radial from prograde and 15° normal from prograde”, you know that, assuming you where pointing straight at prograde to start, that you have to rotate your ship 30° to the right and 15° up. My entire direction system is now based on prograde, since knowing that, I can derive all the other 5 ”cardinal” points.

Even if your ship is rotated 180° on it’s long axis and you are, from an external observers point of view (your head is now pointing in the direction of the planet’s South pole), standing on the ceiling, you know that normal is ”above your head” only if your left arm is pointing ”radial in”. If you’re upside down like I said, your left arm will be pointing away from the planet (radial out) and your head will be pointing anti-normal, so you know that the directions I just gave you should now be: 30° to the left and 15° down from your frame of reference.

So let’s take a look at the first picture in this article again:

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Right above the ”HDG” indicator at the bottom, you see a little vertical yellow line. That’s the very tip of the prograde indicator. If your ship’s attitude were the one pictured here, and I told you ”turn prograde”, what would you do on your keyboard/joystick to get there? You would press the w key to push the nose of your vessel (shown by the fixed level indicator in the middle of the navball) ”down” towards the prograde vector which is ”below” your nose in this picture. You can also think of the w key as being ”up”, as in the direction I want the navball to ”rotate”. So the level indicator stays put (it never moves), the navball rotates ”up” (the line that divides the blue from the brown in the navball, moves vertically up your screen), bringing the prograde indicator with it, until it is lined up with the nose of my vessel. It depends on how you see things. The ”pushing up/forward means nose down” paradigm comes from aviation (from where most astronauts were recruited) where to push the nose of a plane down, you push the control yoke forward. I’m not here to say whether one interpretation or the other is ”right”, there is no ”right”, it’s

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anti-radial, remember? It’s all a matter of interpretation and whatever works for you is the best. I only explain this here because throughout this book I will say (and have already said, above) ”up” and ”down”. When I say ”up” I mean press the s key to move your nose up; when I say ”down” I mean press the w key to move your nose down. I want to avoid the confusion of ”you said down, so I pressed s ” even though s is below w on the keyboard, s is up, w is down. That’s what works for me, so that’s how I use them. If you understand them the opposite, that’s great, it works for you, but then you have to translate what I say into your terminology. Now that we understand the basic ”directions” involved in maneuvering in space our next section will cover maneuver nodes.

3.1.9

Maneuver Nodes

To create a maneuver node, you have to switch to map view ( m key). If you now click anywhere on your orbit (the blue line in map mode), a popup will appear with a button ”Add Maneuver”. If you click on that button, a maneuver node is created. When created, the maneuver node doesn’t do anything, it’s just a placeholder. When you start playing with the little handles (6 of them, attached to the maneuver node along the 6 different ”cardinal” directions we just discussed) the maneuver node starts to have meaning. One of the ”golden rules” of orbital maneuvers is this: any change you make to your orbit, affects the opposite side of your orbit. Example: If I ”speed up”, by thrusting prograde, at my apoapsis, I raise my periapsis. If I thrust prograde at my periapsis, I raise my apoapsis. Similarly, if I ”slow down”, by thrusting retrograde, at my apoapsis, I lower my periapsis. If I thrust retrograde at my periapsis, I lower my apoapsis. So a very common orbital maneuver, that we will discuss in more detail later, is circularization. Typically, when you launch a craft, you’re launching it ”upwards” from the planet. I’m not going to say straight up, because that’s a bad idea, but it is in a generally upwards direction. If you look in map mode, as your launching, you will see a parabola forming. The very top of your parabola, your highest point, is your apoapsis, and should

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have a little blue ”Ap” indicator on it. What that parabola is showing you is that, if you leave your ship on it’s current trajectory, it will, eventually fall back to Kerbin. We have an apoapsis in our trajectory, but no periapsis. Actually there IS a periapsis, it’s ZERO, so the game doesn’t show it. But it’s there. If I want to get into orbit, I need to make both my apoapsis and my periapsis higher than 70,000 meters (for a Low Kerbin Orbit). Let’s assume my apoapsis is at 80,000 meters already, my engines are turned off and my current altitude is 50,000 meters. I’m essentially ”coasting” towards my apoapsis. What do I do to get into orbit? What am I trying to accomplish? Low Kerbin Orbit is a trajectory where both apoapsis and periapsis is above 70,000 meters. Ok. . . checklist time:

• Apoapsis above 70,000 meters: check • Periapsis above 70,000 meters: not so much

But wait a minute, didn’t we just talk about ”raising periapsis”? Oh yeah. . . ”If I ’speed up’, by thrusting prograde, at my apoapsis, I raise my periapsis.” Let’s do that. . . I line my ship up, pointing prograde. Wait for the apoapsis, and fire my engines. Nothing seems to happen initially, but my orbit’s getting ”wider”. No, wait! A periapsis just showed up on the other side of the planet. 5,000 meters. . . 10,000 meters. . . 50,000 meters. . . 80,000 meters! Quick, shut down the engine ( x key). My orbit is now ”circularized” (hopefully it’s roughly circular). That’s called ”winging it”. Let’s try that in a less stressful, more planned, way. We’re back at 50,000 meters. Apoapsis is at 80,000 meters. Engines are off. We’re coasting towards our apoapsis.

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In map mode. Create a maneuver node AT your apoapsis:

Click on the little blue ”Ap” indicator (notice the little blue dot on the orbit near the apopasis indicator)

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and select ”Add Maneuver”.

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This creates a maneuver node

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Now what we did before was to thrust prograde, so we’re going to plan this maneuver in the same fashion. So grab the little prograde marker on the maneuver node (it looks the same as the prograde marker on the navball) and pull it slowly away from the center of the maneuver node. An orange-ish line appears on the map. That’s the new orbit you will have, if you execute the maneuver node. There’s also an orange-ish ”Ap” and ”Pe” indicator that tells you what your apoapsis and periapsis will be in this new orbit. If your periapsis isn’t high enough (or hasn’t shown up at all yet), keep ”stretching” that prograde marker handle. The process here is: adjust maneuver by dragging prograde handle; release mouse; mouse over (orange) periapsis to see height; and keep doing that until the periapsis is high enough. Made it too high? Adjust maneuver by dragging retrograde handle; release mouse; mouse over (orange)

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periapsis to see height; and keep doing that until the periapsis is where you want it.

Once you’ve adjusted your maneuver properly, you should have a roughly circular orange-ish orbit around Kerbin with both an apoapsis and periapsis of, roughly, 80,000 meters.

Let’s check out our apoapsis and periapsis for the new orbit:

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Not perfect, but close enough. Both apoapsis and periapsis are out of the atmosphere. So let’s switch back out of map mode. Press m again.

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There’s something new here now. Some kind of meter along the right side of the navball that wasn’t there before. That meter tells you how much thrust is required to complete the maneuver the way you set it up. So it will say something like ”1128.2 m/s”. Below the meter is an estimated burn time, ”Est. Burn”, that indicates, based on the capacity of your engines, how long the computer thinks it will take, at full thrust, to generate that ”1128.2 m/s” worth of thrust, in our case, ”47 s”. Below the estimated burn time is another line of text that says: ”Node in T48s” and is counting down. What this indicates is that you are 48 seconds away from reaching the maneuver node you created. Now we have a maneuver node all set up the way we want it. Let’s execute that maneuver.

3.1.10

Executing Maneuvers

The orbit that you saw in map mode:

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is calculated as if the maneuver were executed in an instant. This means that for your orbit to end up exactly as projected, you would have to change your velocity by 1,128.s m/s instantly, the moment you hit the node. Since that is physically impossible, because your engines don’t work that way, it is an estimate.

Since it is an estimate, we’re going to do our best to estimate how to execute the maneuver as well.

Remember that any change you make in your orbit, affects the opposite side of your orbit (i.e. burning prograde at apoapsis, raises your periapsis and vice-versa). Therefore we are executing our burn at our apoapsis (to raise our periapsis from zero, in this case). But if my burn is going to take 47 seconds and I start it exactly at the node, per the countdown clock, I will be executing the burn, effectively, AFTER having passed my apoapsis.

A good rule of thumb, to execute a burn, is to ”split” the burn evenly around your node. So if the burn is 47 seconds, cut that in half, 23.5 seconds, and start executing the burn 23.5 seconds BEFORE hitting the node; and continue burning an additional 23.5 seconds, after the node. That way the ”error” in your maneuver is distributed evenly at both sides of the node.

This technique does not work very efficiently if your burn time is very long (i.e. more than a minute). This is because the longer the burn, the more ”off” the prediction of the resulting orbit is going to be (because the prediction assumes 0 seconds of burn time for the maneuver).

An even better approach is to execute the maneuver in steps. In this particular case, we cannot execute the maneuver in steps. Because this is a circularization maneuver, you don’t have the luxury of executing a smaller maneuver now, and executing another small maneuver on your next orbit. There will be no next orbit unless you circularize your orbit.

An example of a maneuver that can be executed in steps is one where you wish to change your inclination by 90°. Let’s assume that you are in a circular orbit, at 80,000 meters.

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The ∆v for a 90° inclination change is enormous. 3,188 m/s. The estimated burn time is 1 minute and 56 seconds. A burn that long will result in your orbit not being even remotely close to the target you set, because the burn will be executed almost 1 minute before the node and last until about 1 minute after the node. In a case like this, you would be better off executing a smaller inclination change, for example, 20°; on your next orbit, execute another 20° inclination change; and so on until you have achieved the desired orbit. Please note that doing it this way does not make the maneuver ”cheaper” in any way. You will still expend the same 3,188 m/s of ∆v to make the full 90° inclination change, but you will have more control over the resulting final orbit by doing it in steps. In fact, the multiple maneuvers might cost you a little more in terms of ∆v, because of the inevitable errors in piloting. But enough about the economics of maneuvers. . . To execute any maneuver, your want to adjust the attitude of your vehicle, to point to the maneuver node indicator on the navball.

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Once you are pointing directly at the maneuver node indicator, you should wait until the appropriate time to start your maneuver. The discussion above, on when to execute a maneuver, is simply a suggestion that I follow when executing maneuvers. You are free to execute the maneuvers in the fashion that you see best. As you fire your engines, you will notice the ∆v meter on the right side of the navball start to decrease. Once it reaches ”0”, you should stop your engines. Also note that during the maneuver, you should try to keep your vessel pointed in the right direction, towards the maneuver node indicator. If you go ”off” course slightly, you do not have to worry, because both the maneuver node indicator and the ∆v meter are recalculated, in real time, as you execute the maneuver. The system does it’s best to make sure that, when you are done executing the maneuver, you end up with an orbit as close as possible to what was projected when you created the maneuver node. A tip for executing maneuvers: As you approach the end of your burn (when the ∆v meter is almost ”empty”), you might want to throttle down your engines slowly. That way you have more control over the cut off, as close to zero as possible, for your maneuver. If you have a very powerful engine, or set of engines, it will eat through the required ∆v pretty fast, and that will make it harder for your to cut the engines at the appropriate time, most likely ”overshooting” your maneuver. Just remember that the burn time was calculated at full thrust, so if you throttle back the end of the burn, it is going to take longer, so take that into consideration when ”splitting” your burn around the node. Give yourself an extra few seconds of total burn time for a controlled shut down of your engines. Now that we’re ”experts” in maneuvers, let’s start discussing the different types of maneuvers that are typically executed in game.

Chapter 4 Orbital Maneuvers 4.1

Gravity Turn

A gravity turn is a maneuver that is used to optimize the trajectory of the vehicle during launch (or landing). It’s main purpose is the utilization of the body’s gravity to assist in steering the vehicle to its desired trajectory. It has two advantages over using solely thrust in controlling the vehicle:

1. We don’t use the thrust to steer the vehicle, therefore more thrust is available to accelerate. 2. During ascent, the vehicle can maintain a low angle of attack (or zero). This minimizes the stress put on the vehicle from aerodynamic forces, allowing for a less robust, therefore lighter vehicle.

Why use a gravity turn? During launch, the vehicle goes straight up, gaining vertical speed and altitude. Gravity, at this point, is acting directly against the thrust of the vehicle, lowering its vertical acceleration. The losses that occur during this phase of the flight are known as gravity drag.

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The sooner the vehicle pitches over its ascent, the sooner the effects of gravity drag can be minimized. The earlier this pitch over happens, the better. If the vertical velocity of the vehicle is high when the pitch over maneuver is executed, the aerodynamic loads on the vehicle can be very high. This is the general rule, in real life. In Kerbal Space Program, the general rule of thumb is to initiate the pitch over maneuver anywhere between 7,000 meters and 15,000 meters of altitude. In real life, the angle (not the heading, how much we pitch the vehicle over; the heading is entirely up to the desired trajectory, though in most cases in the game we are aiming for an equatorial orbit, therefore the heading is 90°) into which we turn the vehicle, during the pitch over maneuver, varies with the vehicle. An important part of an ideal gravity turn is that the gimbaling of the engines is only used during the initial pitching over maneuver. From that point forward the vehicle’s engines should always be pointing straight down the axis of the rocket. Gravity will slowly turn the rocket further and further towards the horizon as the rocket accelerates. By no longer actively turning the rocket in one direction or another, we minimize the aerodynamic stress that the rocket incurs as a result of such maneuvers. The intent of a gravity turn is to, by the time the rocket levels off (is flying parallel to the ground), have gained sufficient altitude and velocity to be in a stable orbit. With vehicles that are launching from a planet with a dense atmosphere, the smaller the angle of the initial pitch over, the better, since our main goal in this scenario is to get out of the thicker part of the atmosphere more quickly. The faster we get out of the thicker part of the atmosphere, the more we reduce the aerodynamic drag and aerodynamic stress that the vehicle will suffer during launch. Maximum dynamic pressure is another concern during launch. In Kerbal Space Program, as of this writing, it is not yet a concern. Once aerodynamic calculations are included in the KSP universe, it might need to be addressed. Maximum dynamic pressure, sometimes referred to as ”max Q”, is due to the build up of dynamic pressure due to the acceleration against the thicker part of the atmosphere. Again, similar to the turn early or turn late for the gravity turn, it is a tradeoff between gaining more speed while in the lower part of the atmosphere and making the vehicle heavier, since it needs to withstand greater pressure, or a lighter vehicle and gaining less speed while in the lower atmosphere.

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The space shuttle, for example, throttles back its main engines during the initial phase of the ascent as it approaches max Q to reduce stress on the airframe. Once it passes through the thicker part of the atmosphere, it accelerates again to maximum thrust to gain speed as fast as possible.

4.2 4.2.1

Circularizing your Orbit Achieving Orbit

Achieving orbit, for the first time, is one of the most gratifying experiences that you will encounter in game. A lot of beginners in the game tend to launch their rockets straight up. Launching a vehicle straight up will not put your rocket in orbit. A lot of times, even going up at all can be a challenge. For our purposes, we will consider an orbit as a trajectory that your vessel follows in such a way that it will never ”fall” back down to the body it is orbiting. If we take Kerbin as an example, for the vessel to not fall back to the planet, we need to satisfy a single condition: • The trajectory has to be high enough, at all points, that the vessel is no longer being affected by the atmosphere (which causes drag and makes the vessel lose speed)

The parameters of such an orbit are fairly simple: At no point, in our orbit, should our vessel go below ∼70,000 meters. Orbiting is not so much about vertical velocity, as it is about horizontal velocity. For an object to ”orbit” another object, it needs to have a horizontal velocity, in relation to the object it wishes to orbit, high enough that it will constantly ”miss” the object as it continuously ”falls” towards it. What that velocity needs to be varies according to the altitude of the orbit: the closer the orbiting object is to the body it is orbiting, the higher the required velocity to maintain that orbit. The previous statement assumes that the physical characteristics of the two bodies are the same in all cases. Also note that the

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orbital velocities listed in the table below are velocities assumed to be parallel to the surface of the body being orbited. It is entirely possible to achieve the velocities stated below, but if that velocity is not in the right direction, it will not result in an orbit. A few examples: Altitude 70,000 m 100,000 m Orbital Velocity around Kerbin 200,000 m 400,000 m 1,000,000 m

Orbital Velocity 2,296 m/s 2,246 m/s 2,100 m/s 1,879 m/s 1,486 m/s

What this table shows us is that to establish an orbit at, for example, 100,000 meters, we need to be moving, horizontally, at 2,246 m/s. While it is possible to go straight up until we reach 100,000 meters and then turn and accelerate to the necessary 2,246 m/s, it is not, from the standpoint of energy expended, efficient to do that. This is why we typically use a ”gravity turn” during launch. The purpose of the gravity turn is to impart as much horizontal velocity during our launch phase as we possibly can. That leaves us less velocity that we need to add, once we get ”out into space”, to establish the orbit. A typical launch, whose purpose is to establish an orbit, will involve getting our apoapsis above 70,000 meters and imparting some degree of horizontal velocity (by means of a gravity turn), before reaching the apoapsis. An important thing to remember is that when you are launching a rocket, it does not behave like a common terrestrial vehicle, you might be at 50,000 meters of altitude, but if your apoapsis is already at 70,000 meters, or more, you can shut down your engines and coast the rest of the way. Once we reach the apoapsis, we have to execute a maneuver that is called. . .

4.2.2

Circularization

The circularization burn is the maneuver where we take our parabolic trajectory and transform it into an actual (somewhat) circular orbit. In a typical launch, we might reach our apoapsis with an orbital velocity of ∼2,030 m/s. Since orbital velocity (at 100,000 meters) is 2,246 m/s, that means that we need to add another ∼220 m/s of velocity to establish an orbit.

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There are a couple of different schools of thought on how the circularization burn is supposed to be done:

• Point prograde at your apoapsis and burn • Point at the horizon at your apoapsis and burn

Technically speaking, these two methods are essentially the same. The difference lies in interpretation of ”prograde” and ”horizon”. In a perfect system, where I could impart changes in velocity instantaneously, both of these scenarios would be identical. However, that is not the case. I cannot instantly increase my velocity by 220 m/s.

When you are EXACTLY at your apoapsis, prograde IS exactly at the horizon. The problem is that you are only AT your apoapsis for a split second. Your trajectory, before the circularization burn, is a parabola. This means that you reach the peak of that parabola at some point in time and IMMEDIATELY start the downward leg of that parabola. Since prograde means ”the direction that you are moving”, your prograde vector is pointing slightly ”upwards” before reaching the apoapsis, it is perfectly horizontal AT your apoapsis, then immediately shifts to point slightly ”downwards” as you start the ”descending” leg of your trajectory.

The result of this inability to instantaneously accelerate means that whichever of the two methods described above you choose, will result in an approximation to the ”ideal” circularization burn. Feel free to use whichever method suits your play style. For the purposes of this tutorial, I am going to discuss the circularization method using a maneuver node at our apoapsis.

Switch to Map Mode ( m key) and create a maneuver node at your apoapsis, by clicking on your orbit as close to your apoapsis as possible. You might want to zoom way in so that you have better control over where, exactly, the maneuver is created.

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Drag the prograde vector away from the center of the maneuver node. As you do so, you should see the orange-ish colored line that represents what your orbit will be after executing the maneuver.

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Once your periapsis is (about) the same height as your apoapsis, your maneuver plan is complete.

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Look at the ”Est. Burn” time and the time to Node, next to the navball.

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This particular maneuver that I performed came up with a little bug that is important to discuss. The computer calculates your Estimated Burn based on the engines that you have on your craft. However, when I was establishing this orbit, I was throttled way down, because I was trying to adjust my apoapsis as close to 100,000 meters as possible. When the game goes to calculate the burn time, instead of it using the total thrust of the engine, it uses the last thrust that was actually used on the engine(s). So it came up with this great 2 hour and 12 minute estimate. Not very useful, but I assume that it will be fixed at some point by the developers. The actual burn time for this maneuver was ∼10 seconds. Let’s just make believe the computer did it right to illustrate my point. Take the estimated burn time and divide it by two. You are going to start your burn at around T- 5 s. This is because, since the burn will be an approximation (because I can’t change my velocity instantly), I want to split the ”error” that I am introducing to the burn, evenly, on both sides of the point where the computer expects the burn to happen. The net result of doing it this way is that the deviation from optimal that I introduce before the node is reached is cancelled out by the deviation I introduce after the node is reached. This is not optimal, but it’s the best our poor Kerbals can do with the tools at hand, maybe someone will come up with some type of autopilot that can do this better. But. . . moving on. . . Change the attitude of your vessel to point at the blue maneuver node indicator on the navball.

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Notice how when I started the burn, the estimate got more realistic. This is one of the characteristics of both the ∆v meter and the maneuver node indicator on your navball. For the duration of the burn, they will constantly update for the same target trajectory. This means that if you deviate from either the path or the burn profile (you’re not burning full throttle, or worse, your stage runs out midburn and you have to switch to another stage) both the meter and the indicator will update for the new total ∆v that still needs to be expended and the vector you should follow. All so that your final trajectory ends up where you projected with the maneuver node (or as close as possible).

Watch the ∆v meter next to the navball, it will slowly countdown the required ∆v for the burn

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When you are close to the end of the burn, throttle down a bit. This gives you more control over engine shutdown, so you can cut the engines at the right time and not ”overshoot” your goal.

Cut engines ( x key) as soon as the ∆v meter reaches 0.0 (or as close as you can get without overshooting).

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Notice that the countdown reads T + 11s. If I started the burn at ∼T - 5s, that means I burned for about 16 seconds total. But wasn’t it 10 seconds? The 10 second estimate is based on full throttle until shut down. Since I throttled down a little at the end of the burn to better control engine shut down, I spent about 3-4 seconds extra burning those last 5-6 m/s off the clock, hence the difference. Also throw in a second or two before I took the screen shot

4.3

Changing your Orbital Inclination

There are a number of different reasons why you might want to change your inclination: • You want to rendezvous with another vessel, that is in an orbit with a different inclination • You have some particular inclination that will work better for your vessel (i.e. a communication satelite, a mapping satelite, etc.) • You want to transfer to another planet that is on an orbit with a different inclination than the planet you are currently orbiting • You just want things to be organized

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Depending on the inclination change that you need, there are a number of different ways that you can proceed. Some of them are expensive (in terms if ∆v), others are cheap (or cheaper, at least). As an example, look at the inclination change that we discussed in ”Executing ˙ Maneuvers”. That was an inclination change of 90°You were in an equatorial orbit, and wanted to change to a polar orbit. That is a hugely ”expensive” maneuver, executed as was described. There are other ways to execute inclination changes that are more ”economical”. Here is our current orbit:

As you can see, we are in an equatorial orbit at approximately 100,000 meters. What we want to do is change this orbit so it is still at 100,000 meters but is at an inclination of 90° (a polar orbit). The maneuver described below will save you ∆v by changing your orbit into a highly elliptical orbit before attempting the inclination change. The main steps of the process are: • Burn prograde at the periapsis of your current orbit to raise your apoapsis until your orbit is highly elliptical. You burn at your periapsis to take advantage of the Oberth effect.

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• When at your apoapsis, burn to adjust your inclination as desired. This should require much less ∆v than the maneuver as originally described. Furthermore, we do the inclination change in steps. With our first burn we will make the orbit ∼30° inclined to the ecliptic plane

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• Notice how we kept the periapsis where it was. Next we’ll do another burn, also at our apoapsis, and change the inclination to ∼45°

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• One last burn, to 90° (we could do smaller increments and save even more ∆v, but this demonstrates what I want to communicate well enough)

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• After your inclination is adjusted, burn retrograde at your periapsis to circularize your orbit once again.

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And now we have a polar (90° inclination) orbit.

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Let’s look at the ”cost” of this maneuver:

• Initial apoapsis change: 504.8 m/s • First inclination change (to ∼30°): 407.6 m/s • Second inclination change (to ∼45°): 307.7 m/s • Final inclination change (to 90°): 701.9 m/s • Recircularization at original altitude (∼100,000 m): 504.9 m/s

Total cost of the maneuver: 2,426.9 m/s of ∆v

If we try to execute this maneuver in one step, without the raised apoapsis, this is what we get:

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A maneuver that costs 3,176.5 m/s. Doing it our way, we saved 750 m/s of ∆v! This works because when you do the inclination change, far away from the orbited body, you can make a much smaller adjustment, and that adjustment is ”amplified” by the increased distance from the orbited body. But why? Imagine you are holding a laser pointer and point at a wall from 1 foot away. For you to move the projected dot on the wall 1 foot to the right, you need to rotate your hand a certain amount. Now back away from the wall 10 feet. Point at the same initial spot on the wall. Move the projected dot 1 foot to the right. Notice how much less you had to rotate your hand to achieve the same amount of ”movement”. This is true of pretty much all maneuvers you make in the game. The earlier you can make an adjustment to your final target trajectory, the easier (and cheaper) it is to do so. An example: You create a maneuver for a Mun intercept and you have a Mun periapsis of 20,000 meters. While you are still in Kerbin’s sphere of influence, you can make a very small change to your course (typically,

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using any engine the change will be TOO LARGE to manage effectively, so you usually use RCS for these kinds of changes), on the order of ¡ 3 m/s, and you can affect your final periapsis around the Mun by tens of thousands of meters. If you wait until you are halfway to the Mun to adjust, you will have to expend more ∆v. The closer you get to the Mun, the more ∆v you have to expend to perform the same adjustment. So always adjust early, as early as you possibly can! But the above explanation was an alternative to a radical 90° inclination change. Typically you are not going to be doing changes of that magnitude in your inclination. A typical inclination change is of a few degrees, just ”tweaking” your orbit really. To perform a maneuver like that is much easier than the maneuver described above. Let’s take a typical equatorial orbit. We have an inclination of 0°.

If we want to transfer to Minmus, an equatorial orbit is not the greatest because of Minmus’ 6° of orbital inclination. Before trying a transfer maneuver, we should ”align planes” with Minmus. That means we are going to make our orbit have the same inclination as Minmus’ orbit. In Map Mode ( m key), zoom out until you can see Minmus, and click on it. This will bring up a dialog, click ”Set as Target”.

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Minmus and it’s orbit will now be yellow in your map view.

Zoom back in to your orbit around Kerbin. Create a maneuver node at the ”ascending node” on your orbit. It is marked by a little yellow marker with ”AN” in it.

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Adjust your camera-view so that you see your orbit and Minmus’ orbit ”edge on”, so that they both appear as lines to you. Also make sure that you are looking from an angle that the ascending node marker and the descending node marker are right on top of each other

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Drag the anti-normal maneuver ”handle” away from the center of the maneuver node until your orbit is lined up with Minmus’ orbit

Execute the node: Point your vessel at the blue maneuver node indicator on the navball; Calculate your burn start time (T - half the burn time); and burn until your ∆v meter reaches 0.0.

Your orbit is now at the same inclination as Minmus, making any transfer you want to do there, that much easier.

4.4. AEROBRAKING

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Aerobraking

If you have ever reentered the atmosphere of Kerbin with a ship, you know that you lose velocity VERY fast as you hit the lowers levels of the atmosphere. It is that loss of velocity that we are trying to exploit when we perform an aerobraking maneuver.

Most approaches to a planet involve a hyberbolic trajectory (one that doesn’t orbit the planet, as much as swing by it). This means that typically you approach a planet at a high velocity in such a fashion that your trajectory is changed by the influence of the planet’s gravity on your vessel, but not changed enough to put you in an orbit around that planet.

Typically, we resolve this issue by firing retrograde at our point of closest approach to the planet and establishing an orbit around it. An alternative to this method, when the target planet has an atmosphere, is to use aerobraking.

So I’m coming into Duna’s sphere of influence FAST!

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WAAAYYYY before I get there, I adjusted my trajectory so that my periapsis around Duna, on arrival, is in the atmosphere. Duna’s atmosphere extends 41,447 meters from the surface. As you can see in the picture below, even though I am 29+ DAYS away from reaching Duna, I’ve already established a periapsis of ∼24,000 meters. I’m going to adjust this further to be around 12,000 meters for maximum aerobraking effect.

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As soon as I reach Duna’s sphere of influence (SoI), I now see that my periapsis is 89,569 meters. This is because the estimate that I was shown, before actually getting there, was slightly off.

One last final adjustment to my periapsis using RCS, because the engine would be WAY too powerful for this minute adjustment.

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Look at my trajectory from another angle. According to the computer’s projection, I will swing by Duna and escape on a hyperbolic trajectory. What the computer is not taking into consideration is the aerobraking that is going to occur.

Now if we wanted to enter orbit around Duna, and get off that hyperbolic trajectory, typically what we would do would be wait until we reach our periapsis, burn retrograde to lose velocity and make our trajectory elliptical and eventually (somewhat circular). Problem with that is that uses fuel. This is where aerobraking comes in, so let’s do this!

I’m coming in FAST, and gaining velocity as I approach my periapsis (I’m currently at 670,000 meters)

4.4. AEROBRAKING

50,000 meters, going 1500+ m/s. Hang on cuz here we go!

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I hit the dense part of the atmosphere HARD, my vessel loses velocity QUICKLY.

4.4. AEROBRAKING

Enough so that my hyberbolic trajectory

is now transformed into a highly elliptical orbit around Duna.

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And still losing speed, lowering my apoapsis even more

I zip through Duna’s atmosphere, losing a lot of my velocity, but not enough to actually land, and come out the other side of the atmosphere still moving at a good clip.

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My apoapsis is now high above Duna

When I hit it my apoapsis, I can thrust prograde, very little, just to lift my periapsis out of the denser part of the atmosphere, but still leave it inside the

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atmosphere. We don’t want to do another hardcore aerobraking session like the last one, but we still want to use the atmosphere to lower our apoapsis some more.

I come around to my periapsis a second time and my apoapsis drops some more due to the aerobraking.

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I can repeat this process, as many times as I want, each pass lowering my apoapsis some more, until I have an apoapsis at the height that I want. After my third pass through the atmosphere

After my fourth pass

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And I can continue orbiting Duna for as long as I want, each pass, in this case, lowering my apoapsis by only 500 meters. That’s pretty precise control. If I wanted to lower it faster, just dip my periapsis further into the atmosphere; if I want to lower it slower, lift my periapsis a little bit more up in the atmosphere. Once I’m at the height that I want, I can thrust prograde at my apoapsis to bring my periapsis completely out of the atmosphere and circularize into a stable orbit.

Or I can even let it go all the way until my apoapsis also falls into the atmosphere, making my trajectory sub-orbital, and I can then (try to) land.

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And there you have it, I successfully established an orbit around Duna (or landed on Duna, depending on which scenario you followed above), while expending very little (or no) ∆v. The amount expended would be typically less than any minor orbital correction that you might make on a typical mission. All thanks to aerobraking. Unfortunately, this maneuver only works on planets that have an atmosphere, but the ”larger” and denser the atmosphere, the better it works! Let’s do the math for the above maneuver: When I first entered Duna’s SoI, I used RCS (about 2.2 m/s worth) to readjust my periapsis; after my first trip through the atmosphere, I burn 9.2 m/s worth of ∆v to lift my periapsis almost out of the atmosphere; after A LOT of orbits, I finally used 56.5 m/s of ∆v to circularize my final orbit. If I went for the landing scenario, don’t count that last 56.5 m/s. To summarize:

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CHAPTER 4. ORBITAL MANEUVERS • Establish 150,000 meter orbit around Duna using aerobraking: 67.9 m/s of ∆v • To land on Duna, using aerobraking: 11.4 m/s of ∆v

With those kinds of budget, you don’t even need an engine! You could do the whole thing with RCS!

4.5

Rendezvous

Here’s the setup. . . I have one ship orbiting Kerbin at an altitude of 1,000,000 meters. It has an orbital inclination of 45°. The second ship is in a 500,000 meter equatorial orbit (inclination of 0°). The blue orbit in the picture below is the ship at 500,000 meters. The yellow orbit is the ship with which I want to rendezvous. This is going to make this section longer, but I did it for two reasons:

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• With this inclination and altitude, I avoid falling behind Kerbin’s shadow, so the screenshots should be better. • This will give me the opportunity to show how you incorporate an inclination change into your rendezvous process.

Make sure you click on your target ship and select ”Set as Target” (this is what makes the orbit yellow, and shows you the ascending and descending nodes).

The first thing we want to do is match planes. At the Ascending Node in my orbit

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I create a maneuver node and adjust by pulling the anti-normal indicator (pink triangle with ”spikes”) down until I have about half the plane change done.

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If I look at my proposed orbit from another angle, you’ll notice that the apoapsis raised significantly

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I can pull the retrograde marker a little to bring that back, if I want, but we’re going to need to do something like that anyway (since it’s almost exactly at the 1,000,000 meter mark) so I’ll just leave it.

Let’s execute this node:

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Our orbit looks like we expected.

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Now we do another inclination change. Same thing: create maneuver at ascending node; adjust anti-normal again

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Inclination looks good, but apoapsis got way out of hand now

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So let’s adjust the retrograde marker of the maneuver node and bring that back

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We execute this second maneuver

Then we time accelerate. Do a couple of orbits, until the intersect markers are somewhat close (couple of hundred kilometers)

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Now create a maneuver node about

1 4

of an orbit BEFORE the intersect

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Drag the prograde marker on your maneuver node, until the 2 purple intersect markers are REALLY close

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And there we have an intersect of 4.8 km (not the closest in the world, but it will do for us). Couple of things we can do here if we can’t get a close enough intersect: • Tweak the other attributes of the maneuver node like radial-in or radial-out to see if we can get a better intercept (least effective) • Click and hold on the middle of the maneuver node (it turns white) and ”drag” it around your orbit to find a better spot to execute the node (most effective) • Or delete the maneuver node altogether and create a new one (more work, but also effective) • Also remember that you can try for the intersect at either the purple intersect (2nd intersect) markers OR the orange intersect (1st intersect) markers. Whichever one you can get to be close first, better for you. Execute the node

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We now have a pretty decent intersect. Now we need to get there and ”establish an orbit” identical to the target ship. To do this, what we want to do is get to the intersect and zero our velocity in relation to the target. If we are (practically) in the same orbit as our target and we are moving at the same speed, we will be stationary in relation to each other. So if we want to have a zero velocity in relation to the target, we need to put our navball in ”Target mode”. Click on the navball where it says ”Orbit” until it says ”Target”. If you were paying attention when you clicked, you’ll have noticed that the prograde/retrograde markers on the navball ”jumped around” when you clicked. If you didn’t, do it again, I’ll wait here. . .

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The reason they jumped is that the prograde and retrograde markers on the navball are now indicating your velocity vector in relation to the target. And the velocity being shown is also in relation to the target. Our objective here is that once we reach the intersect, we want to make our velocity 0 m/s (or as close as we can get it to zero). Like I mentioned above, if we have no velocity in relation to each other, we are stationary in relation to each other. That’s what we want!

Time warp to the intersect. Don’t get too crazy with the time warp or you will overshoot the intersect, and you can’t just come around for the next try, it doesn’t work that way.

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Notice that as we pass the orange intersect markers (1st intersect) on the orbit, the purple ones (2nd intersect) turn orange, since what was our 2nd intersect now became our 1st intersect.

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Once we are near the intersect (notice how I’m ∼1 minute away from the intersect)

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Point retrograde on your navball and turn on SAS ( t key). Time your burn so that you have enough time to bleed off the speed that you have in relation to the target (in my case, 223.4 m/s). Let’s call it 25 seconds. So when I’m 25 seconds from the intersect I will activate my engines.

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I cancelled (almost) all of my velocity in relation to my target and am now sitting at 5.9 km from the target and our relative velocity is almost zero. So we’re pretty much stationary. My original intersect said 4.8 km and I’m at 5.9 km. The discrepancy is because of how I executed the ”zero your velocity” maneuver. I didn’t wait until the very last minute and burn full thrust, I slowly burned off the speed in a controlled fashion, so yeah, it won’t be exact. But 5.9 km is still a respectable intersect, and don’t let any of the 0.1 km and 0.2 km intersect pilots tell you any different. Using RCS (since my velocity is so low now), I point retrograde again and bring our relative velocity to zero.

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Now we need to get closer. . . point at your target prograde indicator in the navball (pink circle) and thrust to about 10 m/s. You’re going to see people saying ”that’s WAY too slow if you’re at 6 km!”. Whatever. . . this whole thing took me 15 minutes of real time to do, I’m not in that much of a hurry! Let them go thrusting about at 60 m/s and we’ll see who ends up with solar panels still attached and who ends up without.

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Notice how the prograde marker popped up in front of us on the navball, because that’s the direction I’m moving. But also notice how it is not EXACTLY on top of the target prograde indicator. That means we are not moving EXACTLY in the direction of the target, but a little off. What we want to do is ”pull” that yellow prograde marker into the middle of the target prograde indicator. To do that, there are two different methods that we can use. The first method is:

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• point to the spot that is almost exactly opposite of the yellow prograde marker on the other side of the target prograde marker

See how I’m pointed to almost the exact opposite position, compared to the yellow prograde, except on the other side of the target prograde marker? Use RCS

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forward ( h key) to thrust in that direction A LITTLE BIT to pull the yellow prograde marker where you want it. Wherever you are pointing when you thrust is where the prograde marker is going to move towards.

I screwed that one up, on purpose. See how my prograde is now to the right of my target? Point to the left of the target and thrust there

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Now we’re all lined up, heading toward the target. But all this thrusting to adjust the markers has brought our speed up to 53.9 m/s. . . let’s slow that down, we don’t want to plow into the other ship. Point yellow retrograde, and fire your

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engines (since it’s a pretty decent amount of velocity, RCS will take too long), but use a slow burn, you don’t want to overshoot. . . bring it down to the 10 m/s we wanted.

Notice how retrograde and target retrograde are also lined up. The second way to adjust you’re prograde when closing on the target is:

4.5. RENDEZVOUS • use the RCS keys ( i

147 , j

, k

So. . . if you were in this situation:

and l

to adjust your trajectory

148 you would press the i the target indicator

CHAPTER 4. ORBITAL MANEUVERS key to ”push” the prograde indicator ”down” toward

if you were in this situation:

4.5. RENDEZVOUS you would use the j target indicator.

149 key to ”push” the prograde indicator ”left” toward the

One of the big advantages of the second method is that you will not end up with your closing speed as high as the first method (53.9 m/s), which can be very important if you are closing from a smaller distance. At smaller distances, you don’t want to end up accelerating too much toward your target, or bad things will happen.

So. . . whatever method you use, eveything should be lined up and you should be approaching your target at a reasonable speed. . .

If it’s taking too long to get to the target, DO NOT ACCELERATE MORE! Use time warp. I’m not saying you have to only do rendezvous at 10 m/s, what I’m saying is: find a velocity you are comfortable with and stay there. Don’t adjust your velocity to speed things up. Use time warp, because once you are REALLY close, you can instantly leave time warp. If you accelerated to make things go faster, when you are REALLY close, you CAN’T instantly slow down (gotta point in the right direction, fire engines or RCS, be careful not to overshoot, etc.). It’s a lot harder to do that ”on-the-fly” when you are 20 meters from your target and going too fast!

Depending on how well aligned you managed to get those two markers, they will tend to drift as you get close to your target (I did pretty good actually, they only drifted a tiny bit and I’m already at 196 m). If they drift, use the same process you used to align them initially, to realign them.

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I’m moving WAY too fast (see? I told you!). . . gotta slow down. . . Bill jams on the brakes

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Now align your prograde vector again, using either of the two methods described above

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A little bit of time warping and here we are, up close and personal, with our target ship. 12 meters is not bad to start a docking procedure, but we’ll do that in the next section.

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Before wrapping up, some other tips to discuss: • When trying to adjust your velocity, if the change is small (less than 5-10 m/s), use RCS. • Using RCS forward ( h key) is the same as using your engines to thrust very slowly in the direction you are pointing. This is sometimes exactly what you want/need: very fine adjustments. Likewise, RCS backwards ( n key) is very useful for reducing your velocity without having to do ”space-flips” (see below). • If you are pointing prograde and want to reduce your velocity, it is more efficient to STAY pointing prograde, and thrust RCS backwards ( n key) than to flip 180° and thrust forward and then have to flip 180° again. It will save RCS monopropellant and even if you are only using torque to turn around, it’s still a lot faster to thrust backwards than to flip around.

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CHAPTER 4. ORBITAL MANEUVERS Obviously, this doesn’t apply if you have to make a significant change in your velocity (requiring engines), since engines don’t thrust backwards (unless you mount a set facing forward on your craft, there’s nothing to say you can’t!). • Ditto if you are pointing retrograde, but need to increase your velocity. Just thrust backwards, same concept. • Another adjustment you can make, similar to the two above. If we want to ”pull” the yellow prograde we thrust forward after pointing in the appropriate direction. But if we overshoot our target prograde indicator (we ”pulled” it too much), you don’t have to turn and adjust again. Just thrust backwards (assuming you are using RCS), if thrusting forwards ”pulls” the prograde, thrusting backwards ”pushes” it away from wherever you are pointing! • Always try to be as precise as possible when positioning the yellow prograde vector over your target prograde vector. The more precise you are, the less adjustments you will have to make to your trajectory as you get closer. • In my example above, I was only pointing a little off the target indicator, to illustrate the point, but you can point further away and use less thrust to achieve the same correction. I only did not do that because if I pointed 90° away from the target prograde indicator, it wouldn’t have been visible on my navball and my explanation would be vague. Just make sure that the vector you are pointing is correct (if yellow prograde is to the left, you point to the right; if yellow prograde is above, you point below; etc) for the adjustment you want to make. • And finally, keep your velocity in check. Those darn solar panels are attached with bubble gum and will fall off at the slightest nudge! Use time warping liberally during rendezvous. Use it a lot, but not high time warps otherwise debris will happen!

Just so you have an idea of how hard this was: Even with making sure to take all the screenshots at the right times, actual play time from the very first screenshot to the very last screenshot in this section, was about 15 minutes real time. Game time was a lot more than that due to the time warping (especially when I was waiting for that ∼200 km intersect). All maneuver nodes were created manually, no MechJebbing any of them. I did Hyperedit both of those ships into their initial positions, but that was it. Infinite fuel was on (but probably didn’t need to be).

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I did dock both of those ships together after completing this section so I can use the same two ships in the next section ”Docking”. I’ll undock them and move them about 50 meters apart before starting that one. This was a very fun section to write and I hope you enjoyed it!

4.6

Docking

Our Starting Point We’re going to continue where we left off in the rendezvous section. At the end of that section, we were 12 meters from our target. Since I know that it is sometimes difficult to achieve an approach that close, I’m going to back away from our target vessel and start the docking procedure from around 50 meters. So our starting point will be our two vessels, with 0 m/s relative velocity between them, and about 50 meters apart.

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Pre-Docking Checklist Make sure your navball is still set to Target mode. If it’s not, click on where it says ”Orbit” or ”Surface”, and the speed right underneath, until it says ”Target” Typically, at this point in the maneuver, you will not be using engines. We are way too close to our target and we don’t want to ram into it, so if you haven’t already, start using RCS. Turn on RCS by pressing the r key. Another thing that we have to do to prepare for the docking procedure is to select the port, on our ship, that we are going to use to dock. Right click on the port, and select ”Control From Here”.

This is VERY important if you have ports that are not lined up with your pod/probe (like on my ship). When you are using docking controls (like the IJKL/HN keys, or WASD/Shift-Ctrl keys in docking mode), the direction that your ship is going to move when you press a key is in relation to whatever port on which you said ”Control From Here”. So in the case of my ship, which has it’s docking port mounted on the side of the main body of the craft, if I don’t ”Control From Here” on the correct port, my controls will be crazy to understand.

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If done properly, on my ship, for example, when I press h to move forward, the RCS is going to thrust in such a fashion that the docking port I am controlling from moves forward (which means the ship, as a whole, will be moving sideways). Another thing that you should do is decide which port, on the target ship, you wish to dock TO. Right click on that port and select ”Set As Target”.

If you still can’t pick out the target docking port on the target ship to be able to right click on it, you’re not close enough. Setting the target to the specific port makes the game now show you the distance between YOUR docking port and the target docking port. When you set a ship as a target (like you did in Map mode for the rendezvous), the system is actually targeting the ship’s center of mass. Since, typically, the docking ports are not located at the center of mass, the distance indicator to that center of mass doesn’t really help us for the docking procedure. So once you are close enough, target the specific port with which you want to dock. Before trying to do any close-up-and-personal maneuvering near your target, switch your camera to CHASE mode (press v a few times, until it says ”Camera: CHASE”).

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Once your camera is in Chase Mode, rotate your camera (by holding the right button and moving the mouse) until you are looking straight at the backside of your docking port. In the case of the ship being used for this tutorial, since I have two docking ports on opposite sides of the ship, I want to be looking straight down at the docking port opposite the one from where I am controlling.

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Another tip is that if you are using RCS, you can point at your where you want to go (prograde/target) and press h to thrust forward. When you want to brake, instead of flipping your ship around and pressing h , just point prograde and press n (RCS thrust backwards). That way you don’t waste time turning your ship around dozens of times, which also uses RCS. Now that you have positioned your camera properly, in Chase Mode, the IJKL keys make sense: i = down, k = up, j = left and l = right, just like your WASD keys. While WASD will rotate your vessel in the corresponding direction, IJKL will ”translate” your vessel in that direction. What is translation? Imagine you are standing up straight: to rotate left, you turn your entire body left to face left; to translate left, you would continue facing the same direction and

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you would ”side-step” left. It is also called ”sliding” or ”strafing” in some games. It’s NOT changing your orientation but still moving. The next thing we want to do is position our target ship so that our docking process is easier. If you are in a ship in orbit, pointing prograde, as you circle the planet you are orbiting, your ship’s orientation doesn’t change (the prograde slowly moves away from the nose of your vehicle and loops around a complete 360° for every orbit you complete). The net result of this is that if you are in a separate vehicle, stationary in relation to that first ship, it looks as if that ship is ”tumbling” in front of you. In real life, there are usually pilots in both ships and they can maintain a certain attitude to avoid the ship tumbling out from under you as you are trying to dock with it, but in Kerbal Space Program, where we can only control one ship at a time, these attitude changes of the target ship, along the course of it’s orbit are unavoidable. There is, however, a ”trick” to minimize this problem. If you orient the docking port of the target ship to point EXACTLY in the normal, or anti-normal direction, the ship will still ”tumble”, but in such a fashion that the docking port, for your purposes, is stationary (because the ship is tumbling ”around” the docking port). To accomplish this, switch to your target ship (pressing the [ or ] keys), and select the port you were going to dock with and ”Control From Here” on the docking port you want to use. Now on your navball, point in the ”normal” direction. In an equatorial orbit, if you were pointing prograde to start, turn 90° ”towards” the planet (radial-in), then 90° ”up” (in the direction of the north pole of the planet). In an equatorial orbit, my navball should look like this:

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Because my ships are not in an equatorial orbit, my navball, for this maneuver, will look like this:

Once you have positioned your target ship’s docking port pointing ”normal”, turn on SAS ( t key). Good!

Switch back to your original ship (pressing the [ or ] keys). Since we switched vessels, we lost our target designation, so right click on the target docking port on the target ship again and select ”Set As Target”. Just to make sure, select the port you want to use for docking on your ship, right click and select ”Control From Here”.

If we want these docking ports to connect, they have to meet as ”flat” as possible. Since we oriented the target ship’s docking port in the normal direction, we have to orient the docking port, on the ship we are docking from, in the antinormal direction.

For an equatorial orbit, anti-normal on the navball, will look like this:

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In my case, my antinormal direction looks like this on my navball:

We do the same thing we did on the target ship and lock in SAS ( t key) on our docking ship. If we’ve done this properly, we can now use the translation controls on our docking ship and the orientation of our docking port will not change (if it does, SAS will bring it back to where we want it). Now it’s just a matter of getting the two docking ports in front of each other and then closing the distance between them.

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Before we move on to docking these two ships I want to discuss the orienting of the ports to normal and anti-normal. If you are not in an equatorial orbit, it might be difficult to figure out where those two points are on the navball. An easy way to figure that out is to create a ”dummy” maneuver node, and adjust as if you were performing a burn in the desired direction. Doesn’t matter how ”long” of a burn since you won’t be actually executing it. Once you’ve created the node, there will be a maneuver node indicator on your navball in the exact position that you need it. Orient your ship in that direction, engage SAS ( t key), and then you can delete the maneuver node. This is where we currently stand, docking ports are aligned (orientation-wise) properly. and we’re still about 50 meters from our target. (I know this screenshot is horrible, but it was the best I could do. Trust me, they’re aligned in this picture).

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Docking Before we actually start the docking process, let’s look at some tips on using RCS: • Use RCS sparingly. . . if you are holding any given RCS thrust key for more than 1 second, you’re doing it wrong! The closer you get, the shorter the bursts should be (really just quick taps on the keys). • Learn the translation controls IJKL/HN as opposed to WASD/QE. That way you can leave the WASD keys to adjust orientation with your left hand (or just let SAS take care of rotation, if you set it as described above), while still translating using IJKL with your right hand. • For the beginners (people who don’t have experience docking), only adjust one axis at a time. Example: use the I/K keys to adjust your ”up” and ”down” position until your docking port is at the same height as the target docking port. Once you are done that part of the maneuver, your velocity in relation to the target should be 0 m/s (or as close as possible). THEN start using the J/L keys to adjust your ”left” and ”right” position until your docking port is aligned properly with the target docking port. When you are done with that part of the maneuver, again, your velocity in relation to the target should be 0 m/s. While this process consumes more RCS monopropellant (instead of making a bee-line straight for the docking port), it is much easier to accomplish this way. • Use time warping to accelerate the process. Don’t increase your speed to much over 0.1-0.3 m/s during the final approach. Example: you’re too ”high” in relation to the target port: quick burst of RCS using the i key; your ship will start to slowly move down; If you’ve got 10-20 meters that you need to go down, time warp; once you are near perfect position, exit time warp; quick burst of RCS using the k key (to cancel out the initial burst when you pressed the i key); you should now be stationary again; The objective of our docking procedure is to make the two ports come into contact as ”flat” as possible. We already know that the ports are currently ”flat” in relation to each other because of the pre-docking steps we took above. Since we did the ”Control From Here” on the docking port we are using, the navball is now oriented as if we were ”inside” the docking port, looking straight out. This is where our problem currently is:

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The target indicator is nowhere near, where it needs to be. For us to be able to dock, the target indicator needs to be ”dead-center” on our navball. Let’s deal with the ”up”/”down” position first. I can see in the navball picture right above that my target is ”below” me. So I thrust with RCS down ( i key). The target indicator slowly moves up. When the target indicator is almost centered, vertically, in the navball (about halfway up)

166 I thrust RCS up ( k 0.0 m/s again.

CHAPTER 4. ORBITAL MANEUVERS key) to cancel my downward movement, until I’m at

Now let’s deal with ”left”/”right”. As you can see in the last navball picture, target is far to the left, so I thrust RCS left ( j key). The target indicator slowly moves right towards the center of the navball

As the target indicator gets close to the center, we see that our vertical alignment is not great. I stop the sideways movement by thrusting RCS right ( l key) back to 0.0 m/s. Let’s readjust that vertical. I thrust RCS down again ( i key).

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After a few more small adjustments, I stop my movement and it looks like I’m perfectly aligned. Now we move in for the docking. Thrust RCS forward ( h key).

As we start to move forward, we notice how the target indicator drifts away from center pretty quickly. This means we weren’t as perfectly aligned as it looked. The closer you get the bigger the tiny discrepancies will show. So we stop, thrusting RCS backwards ( n key).

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And readjust the centering of the target indicator in the navball. Nice and centered again.

Up until this point, I only showed you screenshots of the navball. I did this for a reason. When you are maneuvering in to dock, that’s where you should be looking. The directions on the navball (up, down, left and right) don’t change. If you look at the ships, depending on the position that your camera is in, they could

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be completely backwards. However, once you get really close (like the 5 meters I’m at now), you are pretty much docked and it’s just a matter of nudging them together, so at this point watch the ships. Let’s try moving in again. . . h

key. . .

As we move in, we very lightly control position using IJKL. TINY, TINY bursts. We’re at 3 meters. This might work! But I’m in the dark again, let me rotate that camera so we can actually see this docking.

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2.7m. . .

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2.5m. . . This is where the magnets on the docking ports kick in and start to pull your two ships together. . .

2.4m. . .

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And we’re docked!

Docking is a very delicate and complex maneuver. Your biggest enemy when docking is velocity. Make sure you keep the velocity as low as you possibly can. Use time warping to get through the long boring parts. The more gentle you are on the RCS controls, especially during those last few meters, the more successful you will be. The ships used in this tutorial have docking ports mounted radially. I do not suggest you do that. It is much simpler when the docking port is oriented forward from the normal position your ship flies. However, design constraints sometimes force you to do things like mounting them radially. Once you have a lot of experience with docking, you can probably mount them anywhere you want and not notice the difference. For starters, stick with mounting them forward (unless you can’t for design reasons). There are some very important things to know about docking and docking ports:

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1. Docking ports must be the same size to dock to each other. You cannot dock a Clampotron Jr, to a regular sized Clampotron, or a regular sized Clampotron to a Clampotron Sr. 2. A very common mistake is putting the docking ports on backwards. This is especially true of the Clampotron Srs. Whichever side is ”up” (in the VAB), or ”front” (in the SPH), when first picking the docking port from the parts list, is the side that actually docks. If you are not sure which side is up, grab the part and press space in the VAB/SPH and that will reset the part’s orientation to as if you had just picked it from the parts list. 3. When docking ports are close enough together to dock, there is a magnetic force that they exert on each other to complete the docking, sometimes having SAS on when trying to dock, causes it to not dock. You can still use SAS during the docking maneuver, just make sure to turn it off for that last half meter or so of approach. 4. When you undock two docking ports, the magnetic force mentioned above ”turns off” to allow you to separate the two vessels without pulling them back together. The magnets only ”reset” if you move the docking ports a certain distance from each other (something like 5-10 meters). So if you just undocked (usually to adjust a docking position) and can’t redock, try backing away about 5-10 meters and THEN redocking. Some people have said that quick saving and quick loading also resets the magnets, I have not confirmed this. 5. The ”Rockomax HubMax Multi-Point Connector” DOES NOT HAVE DOCKING PORTS ON IT!. If you want to dock to it, you HAVE to add the docking port to it. Ditto for the ”BZ-52 Radial Attachment Point”. 6. The ”Inline Clamp-O-Tron” and the ”Clamp-O-Tron Shielded Docking Port”, on the other hand DO HAVE docking ports built into them. You have to right click the part to ”open” and expose the docking port once you have launched (can’t do the right clicking part during assembly). I sincerely hope that this section helped you learn the fine art of docking!

4.7

Gravity Assist

A gravity assist, also known as: gravitational slingshot or swing-by, is a maneuver where a spacecraft approaches a planet, moon or other celestial body, and uses it’s

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gravity to alter it’s course and/or change it’s velocity. The strange part of a gravity assist is that it looks like it shouldn’t work. Take a look at the diagram below:

In the diagram above, the length of the arrows represent the magnitude of the velocity. The longer the arrow, the higher the velocity. Looking at the above diagram we see that the vehicle approaches Jupiter at a specific velocity, gains velocity, due to Jupiter’s gravitational influence, reaching it’s highest velocity at the closest approach to Jupiter, and then slowly loses velocity as it leaves the influence of Jupiter’s gravitational field. It’s velocity is the same as it leaves as when it entered. If you were standing on Jupiter watching this maneuver, you saw a craft approaching Jupiter at, let’s say, 1,000 m/s. As it fell into Jupiter’s gravity well, it picked up speed, until at it’s closest approach it was moving at, let’s say, 1,500 m/s. Then it started to lose velocity, at the same rate that it gained it, until once it leaves Jupiter’s gravity well, it is moving at the same 1,000 m/s that you observed when you first saw it approaching. So, what’s the point? The point is that all the velocities discussed in the previous two paragraphs, and shown in the diagram are in relation to Jupiter (or to you standing on Jupiter). Jupiter is not a stationary object. It is moving around the Sun at a pretty good clip. When you perform a gravity assist, you ”steal” some of that velocity from Jupiter and add it to your vehicle’s velocity. Look at this diagram that includes a vector for Jupiter’s movement around the Sun:

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When you add in Jupiter’s movement vector (the red vectors above), you can see that both the Vin and Vout (blue) vectors are larger than the simple vehicle’s velocity vectors (black). Let’s put this in context: If you were standing on the Sun (bring sun block!) and were watching this maneuver, you would see that the vehicle is traveling at a velocity of, let’s say, 2,000 m/s, in relation to you, around the Sun. It is approaching Jupiter at 1,000 m/s, just like before. From your standpoint, Jupiter is also traveling at a velocity of, let’s say, 1,000 m/s, in relation to you, around the Sun. You see the spacecraft gain velocity as it approaches Jupiter, and you see it lose velocity as it moves away from Jupiter, but from THIS standpoint, outside of Jupiter’s frame of reference, the gain and loss are not equal. As it approaches Jupiter you see it gain way more than the 500 m/s that the observer on Jupiter saw, because you also see it gain the angular momentum of Jupiter’s orbit, so you see, for example, a gain of 1,300 m/s. The vehicle is now moving at 3,300 m/s in relation to the Sun. As it departs Jupiter’s gravity well, it loses those same 500 m/s that the observer on Jupiter saw it lose, but it keeps that 800 m/s, that it gained from Jupiter’s orbital velocity, ending up, to you, looking like it is now moving at 2,800 m/s and on a different trajectory than what it was on before. The important part of this whole thing, is that it was accomplished without expending any fuel. All using gravity. You can adjust your approach to the body that you want to use for a gravity assist so that the angle, and the amount of speed you gain, when you leave their gravity well, is the one you want.

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This entire process also works to reduce your velocity. The only thing that changes is the direction in which you approach the body you want to use for the gravity assist. If you perform the maneuver as below, you will lose orbital velocity, proportional to Jupiter’s orbital velocity. If we use the same numbers we used above, your resultant orbital velocity, in relation to the Sun would be, after the maneuver, 1,200 m/s; instead of gaining 800 m/s, your vehicle would lose 800 m/s.

Disclaimer: All the numbers used in the two examples above are completely random and used for example purposes only. Jupiter’s true orbital velocity is more like 13,000 m/s. The proportion of velocity gained/lost in the two maneuvers is also completely random. The numbers were chosen to illustrate the point that you gain/lose some fraction of the body’s orbital velocity, but not all of it. The actual result of a gravity assist maneuver, be it to gain velocity or lose velocity, will vary in accordance to the angle at which you approach the body and the distance of your closest approach to the body. A gravity assist is not really a maneuver that I can simulate ”on demand”, especially if you consider that I would have to show you multiple maneuvers, very similar in nature, with small variations so that you could evaluate the different end result of each maneuver based on the variations. I will leave you here with this information and hope that it helps you executing this type of maneuver.

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4.8

CHAPTER 4. ORBITAL MANEUVERS

Landing

Landing sounds like a fairly simple maneuver, however it is one of the more complex maneuvers that you will execute in the game.

The reason it is difficult is that for you to land successfully (without exploding or otherwise destroying your vehicle), you must do so at a very low velocity, typically less than about 5 m/s. The problem is that for you to maintain proper attitude when you are moving this slowly and being pulled by gravity, all at the same time, is very difficult because your ship is very unstable. Using SAS to control your attitude at this phase of the maneuver is HIGHLY recommended.

Another point that sometimes people overlook, is that for you to land successfully, your velocity, in relation to the surface that your are trying to land on, should be as close to 0.0 m/s as possible. However in game, there is no indicator of your horizontal velocity. You have to gauge, based on the vertical speed indicator (next to the altimeter), and the speed indicator (above the navball) and kind of deduce what your horizontal velocity might be. Usually it’s easier just to view the terrain and see if you are moving in relation to it.

Disclaimer: I don’t claim that this is the best or most efficient way to perform a landing. I’m sure there are people that can do this WAY better than I can, but this WORKS (not that any other method doesn’t). If you like my method, enjoy, if you don’t like my method, write a thorough description on how to perform this better and I will be happy to include it in the next edition of this book.

But let’s try to do this. Our starting point is a circular, equatorial orbit at 30,000 meters, around the Mun. Our intention is to land somewhere north of the big crater that sits right below the equator of the Mun.

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Our first step in landing is to do a deorbit burn. What that means is we want to transform our now, ”perfectly”, circular orbit, into a suborbital trajectory. To do this, we wait until we are about 14 of the way around the Mun, BEFORE our desired landing site, and burn retrograde.

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We want to burn retrograde enough so that our blue trajectory line ends up slightly AFTER where we want to land. The reason for this is that the blue trajectory line is a perfect parabola and we don’t want to perform a parabolic landing maneuver (they are possible, but extremely difficult). What we want to do is make our trajectory ”overshoot” our target landing site by a little bit, this means we will still be ”in the air” as we pass over our desired landing site.

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It is at this point that we want to burn retrograde again to lower our velocity to virtually 0.0 m/s. This will allow us to descend straight to our desired landing site.

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If you do this correctly, and follow your retrograde vector as you burn, you will end up with your retrograde vector pointing straight up to the middle of the blue part of the navball (which means your prograde vector is straight down, which is what we want!).

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When we turn off our engines at this point, we will start to gain velocity again. This is the Mun’s gravity pulling us down. This is where things get complicated. We don’t know how high up we are because the altimeter on the main flight screen is showing altitude to sea level. The actual surface of the Mun is going to show up WAY before that reaches anything close to 0. The only way, without mods, to know your true altitude in relation to the surface is to check the radar altimeter in the cockpit. Press c .

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As you can see, the radar altimeter is showing that we are about 800 meters above the surface. Quick switch back to regular flight screen ( c again)

Our dumb altimeter is telling us we are ∼3,600 meters off the surface. We do the math and figure that we should reach the surface when the flight altimeter reads somewhere around 2,800 meters. Don’t cut it too close or ground will show up faster than you think. But we’ll double check that anyway. We continue to fall. We’re expecting surface around 2,800 m. So what I like to do is wait for a nice round number (3,000 m, in this case) and double check our math. So I wait until ∼3,000 rolls around on the altimeter.

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Once I’m there, I press c to switch back to the cockpit. If our math is right, our radar altimeter in the cockpit should be showing about 200 meters

Bingo! It looks like it’s a little below 200 meters, so let’s readjust our estimate of surface from 2,800 meters to 2,850 meters just to be on the safe side.

Time to slow down big time

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This is where things get hairy. The slower you are going, the harder it is to keep that retrograde vector at the top of the navball (pointing straight up). But you have to chase it! Make sure it stays at the top! Throttle up and down to keep a reasonable velocity (something between 3-10 m/s).

We’re still descending

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We’re at 2,919 meters. Our radar altimeter should be marking around 75-100 meters if our math is right. Let’s see.

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Looks like almost 100 meters exactly (it’ll be nice when we have a digital radar altimeter). So let’s assume we’re gonna be reaching the surface at about ∼2,820 meters. Nice and slow

We can see our shadow! Altimeter is reading 2,823 meters (don’t know why I cut that out of the screenshot). Still controlling throttle up and down to maintain a low vertical velocity.

4.8. LANDING

And we’re down! Cut thrust ( x And your landing is complete!

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key) so it doesn’t hop back up in the ”air”.

And it looks like we ended up where we wanted!

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A brief recap: • Burn retrograde about

1 4

of an orbit before your desired landing site

• Burn until your trajectory ends slightly beyond your desired landing site • Once you are over your landing site, burn retrograde to 0.0 m/s. You are now falling straight down • Control descent (throttle up/down) to maintain both a reasonable velocity and a good attitude for the vehicle • Check true distance to surface via radar altimeter in cockpit. Estimate regular altimeter surface altitude. • Recheck true altitude/altimeter reading often during descent. Adjust estimate accordingly. • Below 100 meters true altitude, keep speed low (less than 5 m/s). • Watch for shadow (day landing) or use lights on your vehicle (night landing) to gauge visual distance to surface

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• Try to land with less than 5 m/s of velocity (less than 3 m/s is even better) • Cut engines immediately upon touchdown • Call Mission Control and say ”The Eagle has landed!” or some other memorable phrase.

Suicide Burn or How I learned to live dangerously! A suicide burn is a very aptly named maneuver because in many instances it will result in pieces of ships and/or kerbals strewn across the landscape. My above landing procedure, while ”easy”, is not even close to an efficient landing. I used more than half of the fuel in the two stage lander to accomplish that landing. The most efficient way to land is to wait until the last possible moment, and burn retrograde at full thrust in such a fashion that as you reach the ground, you velocity is exactly 0.0 m/s (or low enough that things don’t fall apart upon touchdown). I have two problems with suicide burns:

1. I don’t know, with any degree of certainty, my exact altitude above the surface. This information is crucial to know exactly when to start a suicide burn (remember, you start it at the last possible moment) 2. I don’t know, with any degree of certainty, how fast my vehicle can decelerate. This can be mitigated if I’ve flown the same vehicle various times and know how it ”responds”. But remember that the vehicle will perform differently depending on it’s mass. If I have full tanks, it will be sluggish, if I’ve already burned off have my fuel, it will be more responsive.

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So, a suicide burn to me sounds like, well. . . just plain suicide (I guess the burn part comes in when the explosion happens). But we can work with this. . . instead of being super cautious (like I was above) and decelerating to ∼10 m/s at 200 meters of altitude, you can ”semi-suicide” and let it ride until about 100 or even 50 meters, then burn full thrust to cancel all that vertical velocity, and just be cautious those last 25-50 meters. It’s really up to you. A suicide burn is nothing more than a launch in reverse and is truly the most efficient (fuel-wise) method of performing a landing. I think an unassisted (i.e. manual) suicide burn is just crazy. No one in real life would even attempt to perform such a maneuver without the assistance of a computer (MechJeb, anyone?), but to each his own. It would be like giving the astronauts on the shuttle manual control of engine gimbals to maintain the attitude of the craft during launch (yeah, that would end well!). I hope this information will help you on your way to planting flags on various celestial bodies in the Kerbol system!

Thank You! Thank you for reading this book! It was a joy to write and I anticipate the other volumes will be the same. Stay tuned for news on the next volume!

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