by Mike Lingg
Most LinkedIn posts are related to doing better at a job, or similar. I thought it might be interesting to post a more fun educational topic, so these posts are not meant to help someone get a new job, though if these do lead to a new job, let me know! I figure a lot of us in the professional world have at least a passing interest in space and rockets, so I am covering some basic topics on how flying a rocket in space works.
So a caveat to my post here, I have no background in physics (beyond the basic engineering prerequisites) or astrophysics. All of my knowledge comes from Kerbal Space Program (https://www. kerbalspaceprogram. com), along with internet videos and some other internet research. My plan here is to provide some simple examples of concepts of the physics of space that (hopefully) anyone here can understand. I may fail at making everyone, or anyone, understand, but it can’t hurt to try. Also some people may know some of these concepts, but I’m trying to provide a reasonably complete background for all of the topics as well.
Given these posts will be based on Kerbal Space Program, do not assume this is a full description of real physics. Many things have been simplified, but I believe are all an accurate simplification of real physics. Any place I know how things are being simplified, I will add to the discussion, and feel free to correct me anywhere the representation is inaccurate.
ORBITING
The first step in flying a rocket is getting to space. Robert A. Heinlein is quoted as saying "Once you're in orbit, you're halfway to anywhere". This is not completely accurate, but not completely wrong. Here is a delta-v map for getting anywhere in the solar system: https://imgur. com/delta-v-map-of-solar-system-SqdzxzF (I will talk in more detail on this concept in later posts). In short, getting to earth orbit costs more energy than going from orbit to the moon or Mars, and getting to orbit is nearly half the energy cost of sending a rocket to Saturn (but not orbiting Saturn, we will discuss why in more detail in a later post).
So to start with, what is an orbit? In simple terms an orbit is a circular path around a body in space, preferably at an altitude that is high enough to both avoid colliding with terrain and avoid atmospheric drag, the second of which can lead to a decaying orbit, or dropping the orbit over time until the orbiting object hits the ground. More formally, an orbit is a regular, repeating path (an ellipse) that one object in space takes around another object in space (https://www. nasa. gov/learning-resources/for-kids-and-students/what-is-an-orbit-grades-5-8/). This means the two objects will not collide and the object travelling along the repeating path will periodically return to (or close to) the same point in space.

We have a definition of an orbit, but what prevents gravity from just causing our orbital object to fall back down and crash the object we are orbiting? This would be our horizontal velocity.

The image above shows the effects of increasing horizontal, or orbital, velocity on a rocket (the red curve is the lowest velocity, green is higher velocity, yellow is the highest velocity), relative to the object we are orbiting, in this case a moon. If our rocket’s velocity is 0, the rocket is going to just follow gravity straight down to the moon our rocket is sitting above. As velocity increases the point of impact moves further and further toward the edge of the moon, so it takes longer before the rocket impacts the moon, as shown by the red line. This continues until the velocity is so high that the rocket’s momentum is approximately equal to the pull of gravity and our rocket circles the moon. This is a circular orbit, orbital velocities above and below this can produce stable elliptical orbits, so long as the rocket trajectory will not impact the ground or escape the body it is orbiting. If we keep accelerating the rocket will eventually reach escape velocity where our orbit changes from a closed ellipse, to an open hyperbola (the yellow curve), and our rocket will never return to the moon it is orbiting.
This makes it sound like we just need to go fast enough to orbit, but it is not quite that simple. One of the earliest methods described for reaching space was the space gun, or Verne Gun (https://en. wikipedia. org/wiki/Space_gun) described by Jules Verne. In short, a projectile (possibly containing humans) is fired into space. If the humans on board could survive the acceleration, would they achieve orbit? Not quite (though it is viable to reach the moon, which I will discuss in future posts).

Consider a rocket sitting on a large asteroid or moon without any atmosphere to complicate things. If the rocket is fired, or launched, straight up with full orbital velocity (an angle of 90 degrees, the white curve is slightly less than 90 degrees so upward and downward arcs are separately visible), gravity will act perfectly opposite of the rocket’s velocity. At orbital velocity the rocket does not have enough speed to escape the asteroid, so gravity will slow the rocket until it reverses velocity and is accelerated back into the asteroid. If the rocket exceeds escape velocity, it will never return to the asteroid, which is still not orbiting.
So let’s fire our space gun, or launch our rocket, at an angle, yet still at orbital velocity. As we increase the angle of launch (example is the poorly drawn yellow curve), we move the impact point of the rocket further and further from our launch point, until at a launch angle horizontal to the surface of our asteroid (0 degrees), the path of our rocket (the green curve) will be an ellipse that returns back to where we started. So are we in orbit?
The answer is a qualified yes. If there is terrain higher than our launch point, we will collide with the terrain. If we have launched from the highest elevation on the asteroid, we will return to our previous point. In a perfect world, this means we should just avoid scraping the terrain we launched from, or we could use a retractable launch tower.

If we are using a tower to launch from a slightly higher elevation, why not just use the rocket to reach this higher elevation. Then we can move to a high enough altitude to avoid terrain, before rotating the rocket to a horizontal orientation (as we previously described) and achieving orbital velocity. This concept is shown in the image above.
Interestingly the higher the orbit, the lower the orbital velocity (for mathematical details, see https://wiki.kerbalspaceprogram.com/wiki/Tutorial:_Basic_Orbiting_(Math)). This would seem counterintuitive as everything we know about flying in the atmosphere tells us that higher altitude means higher potential energy. If we look at the previous image of travelling to a higher altitude before circularizing our orbit, we can see that the higher (larger diameter) the orbit, the more energy the rocket has to reach the altitude at which to circularize. So even if the orbital velocity is lower, the energy to reach the orbital altitude is higher. So a higher altitude is still a higher potential energy. We will discuss this more in the next chapter about orbital maneuvers.
Some of the complications thrown in by the real world. The appropriate orbital velocity is found by a computation based on the mass of the planet and the radius of the orbit. I am not going into this level of detail, but you can read more on this at other sites: https://www. nagwa. com/en/explainers/142168516704/. I’ve mentioned a few times about the orbit returning to the same point, this does not quite happen. In fact, orbits precess, or the orbital ellipse rotates around the main body due to many factors including relativity. Other sites can be looked at for more information: https://en. wikipedia. org/wiki/Apsidal_precession. Finally an orbit remaining perfect assumes the body being orbited has an even gravity, in fact Kerbal Space Program determines orbits based on all mast being concentrated as the center of the body being orbited. Mass concentrations were considered during moon landings because the moon is somewhat lumpy and has a non uniform density. More details on this phenomenon can be found elsewhere: https://en. wikipedia. org/wiki/Mass_concentration_(astronomy).
So now we know, if we want to reach orbit we need to get up to an altitude high enough to avoid terrain of the object we will be orbiting, or higher yet depending on the mission, and then reach the horizontal orbital velocity. Well this is for a body with no atmosphere, what happens if we do this in an atmosphere, such as earth or Kerbin?

Well, things start getting really hot, really fast. To reach low orbit in Kerbal Space Program requires a velocity near 2400 meters per second, or around mach 7. This can result in heating of 1,800 degrees celsius, which has negative effects on the rocket.

Unless what you want is to turn your rocket into many itty bitty little pieces. The Nike Sprint missile (https://www.youtube.com/watch?v=kvZGaMt7UgQ) is an example of a real rocket that reaches extremely high velocities in the atmosphere to try to intercept ballistic missiles. These velocities are so high the first stage booster disintegrates from the heat while the more heat tolerant upper stage continues to accelerate.
Beyond the heating issues, simple atmospheric drag acts against our rocket’s speed. Even if heating was not an issue, firing a space gun horizontally within the atmosphere would result in the projectile decelerating from drag until it is slower than orbital velocity, and finally impacting the ground. This drag reduces as we head upward and the atmosphere density reduces to near vacuum.
You would think we would want to just go straight up and get out of the atmosphere as fast as we can. Unfortunately gravity is still causing us problems. If the rocket goes straight up, before long the force of gravity will be greater than the drag of the atmosphere. At the same time, accelerating upward does not add to our horizontal orbital velocity, so part of that acceleration is lost to gravity as the rocket gains altitude. On a body with no vacuum, you want to transition from gaining altitude (vertical thrust) to gaining orbital velocity (horizontal thrust) as soon as you possibly can without colliding with the ground so as much thrust as possible can go into your orbital velocity, then gaining altitude can be done more efficiently by increasing orbital velocity (we will go into this in detail in the next chapter on orbital maneuvers). Reaching orbit when dealing with an atmosphere is about balancing gravity vs atmospheric drag. At first the rocket should accelerate nearly vertically to get out of the densest atmosphere, then the angle of the rocket should transition over time from vertical to horizontal, moving from getting up out of the atmospheric drag to increasing orbital velocity as the rocket moves into thinner atmosphere. This is often performed with a gravity turn, where the rocket nose is turned slightly off of vertical, and then gravity pulls the nose down through the rest of the flight to make the proper gradual transition from vertical to horizontal. At least where the rocket scientists are smart enough to design the rocket and flight plan to perform a proper gravity turn.

Image from https://www. facebook. com/photo. php?fbid=719418188077408&id=240760572609841&set=a. 240767269275838. Apoapsis is the highest altitude of the orbit and periapsis is the lowest altitude of the orbit, when they are equal the orbit is perfectly circular.
The flight path looks something like this image above. Note that in addition to nicely balancing accelerating the orbital velocity against gravity and atmospheric drag, the curve of the gravity turn can conceptually be thought of as travelling less distance when compared to boosting straight up to the orbital altitude and then straight to the right to reach orbital velocity.
I’m not that good at designing or flying simulated rockets, so in my rocket games, I fly a simplified version of a gravity turn with the following steps.
Launch from the pad at an angle of 80 degree angle to the east
At 100 meters per second, reduce that angle to 70 degrees
At 3000 meters altitude, reduce that angle to 60 degrees
At 7000 meters altitude, reduce that angle to 50 degrees
At 12000 meters altitude, reduce that angle to 40 degrees
At 30000 meters altitude, reduce that angle to 30 degrees
At 40000 meters altitude, reduce that angle to 20 degrees
At 50000 meters altitude, reduce that angle to 10 degrees
At 60000 meters altitude, reduce that angle to 0 degrees
This profile gets the rocket out of the densest atmosphere quickly, then transitions to horizontal acceleration, having just enough vertical velocity left after transitioning fully to horizontal so the rocket can pop up above 70,000 meters, where Kerbin transitions to a pure vacuum (zero drag) in Kerbal Space Program.

My approach results in a flight profile that looks something like this graph. It is a little flatter than the optimal gravity turn, but I find it works quite well, I think in part because my rockets are a touch unstable and using fins in the atmosphere keeps it going the right direction. The point is that rocket scientists can fine tune a launch to reduce weight as far as possible, but in a game world where resources are not as tight, a reasonable flight profile can be produced without all of the math.
One complication in the real world, that does not exist in Kerbal Space Program, is the transition to true vacuum is much less concrete. The Karman line is considered to be 100 kilometers, yet there is enough atmospheric drag for an orbit to reenter in hours. Low Earth Orbit, from 160 to 2,000 kilometers, can hold a stable orbit for days. At 350 kilometers and above (still starting within LEO), atmospheric drag starts to become negligible, and can mostly be ignored above 700 kilometers. Though solar storms can expand the atmosphere and change these numbers, mostly at lower orbits.
One final concept for reaching orbit is the direction of your orbit. If the object you are launching from, planet, moon, asteroid, etc, is not moving then your rocket could orbit in any direction equally. However all objects in space are rotating in some direction. This direction of rotation is east on earth or Kerbin. This means launching from these bodies, your rocket already has some velocity in the direction of east, so as the nose of the rocket lowers toward the horizon during the gravity turn, it should point toward the east if you want to add as much of this rotation to your orbital velocity, reducing the amount of energy to reach orbital (horizontal) velocity. Other orbits are still possible, but will require a greater change of velocity to reach a stable orbit, likely fighting the rotation, or at least not using it.
This covers KSP mechanics for orbit. In future posts I will discuss more advanced orbital mechanics such as changing orbits, transiting to or from a moon or other planets, landing and rendezvous and docking.
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