Rocket Mechanics from Kerbal Space Program - part 5/Conclusion

by Michael Lingg

Landing, Rendezvous and Docking

So now we know how to get there and back again for most any definition of “there” we can reach within space. Next it seems like we would like to actually land on our target body to do some surface exploration. Just like trying to reach orbit around our target body through proper maneuvers, rather than lithobraking, let’s talk about how we get from orbit to the surface in a manner our spacecraft can survive.

Atmospheric Reentry

In Part 3 we looked at how to travel to a moon and how to safely return, including trying not to burn up in the atmosphere or be stranded in space. A quick review, the atmosphere gets more dense as we get closer to the surface. In Earth and Kerbin’s atmosphere, if we come into the atmosphere too deep the spacecraft will overheat and burn up, if we come in too shallow the spacecraft will still have enough speed to go right back up into orbit. We prefer to have enough fuel to slow the spacecraft enough to be able to find the happy median point where the spacecraft will be slowed enough to be too slow to return to space, without burning up. WIth atmospheres that are less dense, like Duna or Mars, the atmosphere may be so thin that repeated orbits flying through the atmosphere are required to slow the aircraft down enough to descend to the surface. This is best done with a probe that has no beings that like snacks on board, or with sufficient supplies to handle this potentially long period of atmospheric deceleration.

Powered Descent

Many bodies we want to visit will not have an atmosphere. Places such as Earth’s Moon or the Mun have no atmosphere to slow us down using parachutes, so we need a powered descent to provide a controlled touchdown.

Deorbit

There are three parts of the powered descent, the first is reducing orbital velocity enough that the spacecraft’s periapsis drops below the surface, or in other words to make the spacecraft’s orbital path intercept the surface. The image below shows the effect of the deorbit burn of the rocket, shifting from the blue circular orbit, to the dashed yellow orbit that intersects with Minmus’ surface.

Decelerate

The next step is reducing the horizontal velocity to zero over the desired landing point, at the same time also reducing the vertical velocity. The image below shows our lander reducing the decent velocity in preparation for landing.

Bill Kerman has concerns about this “suicide” burn.

Land

As the deceleration has reduced our velocity significantly, hopefully eliminating our horizontal velocity, the final step is to maintain the controlled descent to touch down on the surface with an appropriate descent velocity. Likely the rocket will be decelerating slowly from our final vertical velocity to a gentle touchdown.

Image 1, eliminate remaining horizontal drift, slow our descent as we approach the surface. Can we avoid skidding sideways and tipping over the rocket?

Image 2, yes we can! The Sparrow has landed, break out the snacks!

Image 3, and enjoy the science!

KSP vs NASA

In KSP the engines are typically more powerful and far more reliable, and there is usually more fuel to play with. So in KSP the orbital velocity can be reduced in one quick burst, and our intrepid Kerbalnauts wait for a while as the spacecraft descends closer to the surface. Next the spacecraft will likely throttle up again to full thrust at the last second, known as a suicide burn as any later will mean the spacecraft does not have the thrust to avoid a crash, to reduce the horizontal and vertical velocities to near zero just above the surface (impossibly reliable computer game rockets are awesome!). Finally the last part of the controlled descent would be more familiar to Apollo astronauts, descending to a gentle touchdown on the surface while using carefully controlled thrust to maintain a good descent velocity.

NASA prefers not to use suicide burns, so their approach is a little different, but effectively uses the same three stages.

Braking Phase

The first step is called the braking phase, the first step in my KSP example. Starting from an orbit around 50,000 feet, NASA used a lower powered, basically spiral descent, where the Lunar Module was continuously slowing its orbital velocity at a constant rate. This constant deceleration of the LM’s lower stage means that at any point in the descent, an abort can occur. Early during the descent there is enough fuel in the lower stage to directly return to orbit, later in the descent the upper stage would separate and return to orbit. Much safer than a “suicide burn”.

Approach Phase

This continues until about 10,000 feet and the rocket’s vertical and horizontal velocities are significantly reduced. The next phase is the approach phase, where the LM shifts toward an upright orientation where the crew can see the surface they are approaching and further descend to 700 feet. The only numbers I find state that at the end of the approach phase the forward velocity is down to 60 fps and the vertical velocity is down to 16 fps. This suggests the rocket is mostly fighting gravity during the approach phase, meaning most of the rocket’s thrust is preventing gravity from accelerating the descent, continuing to descend to the surface and reducing horizontal velocity when over the desired landing area.

Landing Phase

Finally in the landing phase, the LM has found its landing area, is sitting around 700 feet to start with, and is seeking out a smooth, boulder free location (which Apollo 11 had difficulty with). Once a smooth location has been identified, the LM uses thrusters and small horizontal thrust to position itself over the landing location, and perform a controlled descent to a gentle touchdown. While the touchdown was gentle, the idea with the LM was to cut thrust just at touchdown, and the weight of the LM would compress its landing legs. Apollo 11 touched down so gently the landing legs failed to compress, and Neil had a really big step to get down or back into the LM. One book I read on the landing suggested that Aldrin may have delayed his descent to the Moon until Armstrong was confident that they could make the jump back up. I believe I read that Pete Conrad in Apollo 12 cut the throttle as soon as the little over 5 foot long contact probes detected touchdown, and the LM dropped heavily to the ground.

Rendezvous and Docking

Standard Rendezvous

I had intended to have a full part on rendezvous and docking, but we covered the rendezvous method pretty well in the chapter for transferring to a moon. So we will briefly refresh on rendezvousing here, and cover the rest of the topic to docking. These equations tell you for your orbit, your target body orbit, and the gravity of the body you are orbiting, what the appropriate angle difference is for when you should perform the transfer burn:

So based on these equations and a transfer from a spacecraft around LKO (77Km) to a spacecraft at higher orbit (500Km), lets do the math real quick. First we compute the transfer orbit between the original and destination orbit, this is simply the average of the two orbits.

We take the specified altitudes, and add the diameter of Kerbin, as we typically consider orbits as the elevation from the surface, but this computation is the distance from the center of the orbit.

The value of mu or the standard gravity is required to compute the time of this transfer orbit. The standard gravity is not simply the gravity acceleration on the surface, 9.8 m/s we are used to. It is a value that allows us to convert from a cubic distance, the cube of our orbital radius, to the orbital period. Above shows the definition of mu for Kerbin, where 6.674 is a gravitational constant and 5.29 is Kerbin’s mass in kilograms.

So now we can compute the time of the transfer orbit. Note the full orbit would be double this value, but the 2x is not being included as the Hohmann transfer orbit will always intersect with our destination in half an orbit.

Plugging in our numbers we get a 1400 second transfer orbit.

To compute the phase angle the only additional component we need is how long our target orbit period is, so we can determine how far our target will travel in its orbit while our transfer travels to an intersection. This uses the same equation we just used, but our target altitude is 500Km + 600Km and we need to double the result to get the period for the full orbit.

Now we can compute the phase angle

Plugging our numbers in we see that the target needs to be about 49 degrees ahead of us in its orbit (note I seem to have missed the 2x in the previous version of this equation). This appears to match the image below for where KSP’s maneuver planner shows we need to perform our transfer (from the blue orbit) to the higher orbit to intersect with our target (at the yellow orbit).

Now we will look at the next parts of rendezvous and docking.

Unintuitive Near Rendezvous

You might think once the spacecraft is in sight of the other spacecraft or station it is planning on docking with, you just point at your target and fire the rockets. Unfortunately for Gemini 4, whose astronauts were not trained on the techniques of orbital rendezvous, this does not work.

When in orbit, if you are behind your target and you accelerate towards the target, you accelerate your orbital velocity which will raise your orbit relative to your target. As the spacecraft increases in orbital altitude, it loses velocity, and eventually starts falling back from the target. This is shown by the images below with the blueish rocket chasing the yellowish rocket and the blue rocket accelerates toward the yellow rocket to intercept. The orbit of the blue rocket starts to rise and fall back a bit by the second image, and fall back more by the third image. Note this is an extreme maneuver for better visibility, so the blue rocket actually catches up to the yellow rocket and then starts falling behind. Gemini 4 was using more gentle closing maneuvers, so they would only close in briefly before orbital mechanics started moving them away from their target.

Then if you are ahead of your target in orbit, the exact opposite happens. You end up reducing your orbital velocity, lowering your orbit relative to your target. As your altitude drops, you accelerate away from your target. This can be seen in the image below, where the blueish rocket is ahead of the yellowish rocket, and the blue rocket burns toward the yellow rocket, slowing its orbital velocity. In this case the blue rocket loses altitude relative to the yellow rocket, and starts to accelerate ahead as it loses altitude.

On the other hand if you are not ahead or behind your target, but your target is on an intersecting orbit with a different inclination, you will intersect eventually, or you can just burn normal or anti-normal to intercept your target at a preferred time.

The proper method of closing in with a target when the target is ahead or behind in the orbit is to actually burn away from your target, then orbital mechanics will take you back toward the target while dropping or gaining in altitude relative to your target, finally you can burn toward your target as you accelerate past it to intercept, and then zero out relative velocities with your target.

The image below tries to illustrate this maneuver. The bluish rocket is trying to intercept the yellowish rocket. To perform the intercept the blue rocket first slows down to lower its orbit. This results in the blue rocket accelerating as it loses altitude and starting to catch up in orbit to the yellow rocket. Then, at the purple “sprocket” maneuver node, the rocket will accelerate toward the yellow rocket to intercept the orbit where the two orange triangles show their interception toward the top of the image. This is similar to trading fuel for more time efficient orbital transfers discussed in the last chapter.

Docking

If you are very close to your target, say less than a kilometer, now you can just thrust toward your target or adjust your relative velocity as appropriate. This makes docking much more intuitive than rendezvous.

In KSP it is relatively easy as you are given a relative velocity indicator to your target. My preferred approach is to just have each rocket point directly at each other and one rocket move slowly toward the other rocket until they dock. This does not work so well with stations that cannot precisely orient themselves, so a more careful approach is needed.

On the initial approach I just put the relative velocity directly toward my target (make sure it is towards, not away). Below we see how the rocket starts with almost no relative velocity relative to our target station, and we then accelerate to a bit under 10 m/s to close in on our destination. The positive velocity direction is shown by the prograde indicator in yellow, almost directly overlaid over the pinkish circle showing the direction to the target.

Even this close to our target, orbital mechanics still do cause me to drift. In the left image you can see how the yellow prograde marker has drifted up and left. So I counter this drift with my RCS thrusters.

After I get close enough I will zero out the relative velocity so I can then move to line up with the target docking port. I prefer using RCS thrusters to zero out the velocity so I can keep the rocket pointed mostly at the station. The images below show the deceleration and eventual stop relative to the space station.

In the next image we see the rocket translating sideways to get better lined up with our target docking port.

Once lined up with the docking port, zero out relative velocity again and then thrust slowly toward the docking port. The image below shows our approach to the docking port, where the velocity is less than a meter per second and slowing as we approach the dock.

Continue at an appropriate closing rate, probably half a meter per second or slower, until connection is made with the docking port.

NASA docking is very similar. Apollo docking would have mostly been “by the seat of the pants” to close in and dock, while more modern spacecraft use various Radar, LIDAR and other methods to determine relative distance and closing rates. NASA would also be a bit more conservative than I am so would stop at more points and use slower closing rates.

Conclusion

So now we have covered most everything you need to know about travelling in space, you are ready to fly a rocket!  …or maybe not. We have covered the fundamentals of traveling in space, from basic orbital mechanics and efficient transfers to precision landings and complex rendezvous maneuvers. While this provides the foundation to fly rockets in KSP and start to understand real space missions, we have really just scratched the surface. Real rocket scientists must also master propulsion systems, guidance and navigation, thermal management, life support systems, mission planning, and countless other disciplines.

The beauty of the Kerbal Space Program is that it lets you experience the core challenges that NASA engineers face, orbital physics, the need for precision, and the satisfaction of a successful mission. Whether you're landing on the Mun or simulating Apollo astronauts' journey, you have now seen the orbital mechanics knowledge that makes it all possible. Go explore the Kerbol system, or follow along with humanity’s continued journey!

If there is anything else you would like to learn about, just let Michael Lingg know.