How to rendezvous like a boss.

[KiT]

Disclaimer:

Ha-ha, all of the following is a theoretical speculation. I havent actually tried any of this yet!

What you will need:

MS excel or at least a calculator;

KSP orbit calculator, or the ability to manually calculate orbital velocities and apo-/periapses for all kinds of orbits.

Part 1:

Target is in a circular orbit (oh hey, you can use it for Mun landings).

Get in some circular orbit on the same plane around the same body, preferably with altitude difference under 10 times (so if your target is at 100km, you should be between 1000km and 10 km). And of course your altitude shouldnt match the target\'s.

Now Grab your calculator.

Write down the orbital periods of your target\'s orbit, and the duration of a Hohmann transfer between the orbits. A Hohmann transfer takes exactly half of an orbital period, so your objective is to time it in such way that you finish it right when your target happens to be at the same place as yourself.

Let\'s say you are orbiting Kerbin at 200km, and the target is at 100km.

Your orbital period: 39,88 min. Your target\'s orbital period: 32,64 min, transfer time: 18,1 min.

18,1/32,64 = 0,554. This means that when you start your first burn, the target should have 55,4% of its full orbital period remaining until it reaches the rendezvous point. You, on the other hand, will be at 50% (as hohmann transfer takes half a period, and the point where the transfer is over IS the rendezvous point). The difference is 5,4% of a full orbital period, or 19,63°.

Now go use some program to draw a circle with a 19,63° angle in it for visual aid. Wait for when the target is 19,63° behind you, start the hohmann transfer. By the time you finish the transfer, the target should be somewhere nearby.

If the target is on a higher orbit, you make the same calculations, but the target should be ahead of you, not behind.

Protip: If your orbit is 5,35 times higher than your target\'s orbit (or lower if you wanna go from lower to higher), the required orbit difference will be at 90°. Use it if you are bad at measuring angular difference by eye and have loads of spare fuel.

Part 2:

The target is on elliptic orbit.

Now this is a little more fun. Also dont forget that a circular orbit is a special case of an elliptic orbit, so all of the following is applicable for circular orbits as well.

First, you need to get in an elliptic orbit around the same body on the same plane as your target, in such way, that the location of your periapsis matches the target\'s periapsis. Now all you really need to do is to make sure that you reach that periapsis at the same time as your target.

First you need to calculate when the target is going to be there. To find that out, you need to catch the moment it reaches the periapsis or apoapsis, you then check its orbital cycle with KSP calculator, and with these you can easily tell the times the target will be going through periapsis.

Then, once you reach the periapsis, adjust your orbit in such way, that by the time you make a full orbital cycle (or a bunch of them), the target also passes the periapsis. As result, you and your target will pass the periapsis at the same time, and all you will need to do is to quickly adjust your orbit to match the target\'s.

[KiT]

Oh, and here are some EXTREMELY UGLY (and not entirely accurate) pictures for those who just cant stomach the walls of text.

[Klopchuck]

Great post - putting it to work right now rescuing some stranded kerbonauts. When you get close to another ship, does it get designated on the screen or the navball? If so, how close do you need to be?

[Majiir]

You\'ll see a purple marker appear in space when you\'re within 100km. I usually do orbital maneuvers until I\'m less than 1km away, at which point I do direct burns with my main engine, and then when I\'m within 50m I use RCS thrusters to position myself.

This mathematical approach is good for fast rendezvous, but might there be a more reliable way to align the phases of the orbits? (Maybe put both ships into non-circular orbits so you can get timestamps for each one hitting an apoapsis, and do the maths from there?)

[Cepheus]

I\'ll have to test this out when I get a chance. It\'s always nice to have more than one guide out.

[Narwhalasaur]

Thanks for this. I was wondering yesterday if part one was a viable way of doing things. The validation is nice! ;D

[Somerled]

First, you need to get in an elliptic orbit around the same body on the same plane as your target, in such way, that the location of your periapsis matches the target\'s periapsis. Then, once you reach the periapsis, adjust your orbit in such way, that by the time you make a full orbital cycle (or a bunch of them), the target also passes the periapsis.

Since the math never works for me, I do something more or less the same.

I do it instead by aligning the orbits as close as possible, then adjusting phase. The phase part is fun (for me at least). If you\'re lagging behind, then decrease your apoapsis; too far ahead, increase apoapsis (all adjustments done at periapsis, obv.). Correct as you get closer. No math, and just a few more burns than necessary. I like it because you have to burn away from your target to get closer. Squeeeee orbital mechanics!