Rendezvousing with Objects in Elliptical Orbits

[Candre]

In pursuit of god-like spacecraft control andabilities, I have found that rendezvous is kinda un-intuitive and hard to eyeball. And that is with circular orbits. What about elliptical orbits? I\'ll detail my method below:

Lets say we want to rendezvous with a damaged space station that was struck by stray orbital debris and is now in a 100km by 300km orbit around Kerbin. We must send a rescue craft up and then return the Kerbals safely to the surface. How are we to get there in the first place?

Step 1: Get the rescue craft into a circular orbit with a 100km altitude, the same as the periapsis of the station.

Step 2: Adjust the inclination such that one of the apsides coincides with the station\'s periapsis.

Step 3: We\'re going to want to wait until our rescue craft reaches the periapsis of the station. The station won\'t necessarily be there with the rescue vehicle.

Step 4: This is the part where mathematics comes in - we\'ll need to calculate how long it will take the station, wherever it may be in its orbit, to return to its periapsis. We will then need to calculate the height of the opposite apside of our rescue vehicle such that the orbital period of the rescue vehicle equals the return-to-periapsis time of the stranded station. Then adjust the orbit accordingly. I know how to calculate orbit periods, but I need to know how to calculate time-to-periapsis.

Step 5: When the rescue vehicle gets within visibility range of the station, we will then thrust until we match the speed of the station.

Step 6: Approach the station as you normally would.

Of course, this doesn\'t really deserve it\'s own topic. It\'s an inefficient method that is probably not the best way, if not the worst way. So I call on our orbit geniuses to contribute their methods and tips so we aren\'t totally in the dark when cool things like comets appear in-game. If you\'ve got any questions, comments, or concerns, please voice them!

Right now my internet is getting a bit funky. I\'m just going to go post this while I can and work on the rest offline. I\'ll try to finish the example I put in and detail the calculations, provided that I can figure out how to calculate time-to-periapsis.

[Kosmo-not]

This is not an inefficient method. It just can take more time than some other methods.

Time to periapsis can be calculated by calculating the area of the ellipse between the angles of its periapsis and its current position. This cannot be solved for analytically, but there is a method of calculating it that involves and affine transformation. Here is a link to a website I used equations from to put in a rendezvous spreadsheet of mine: http://bado-shanai.net/Platonic%20Dream/pdAreaofEllipticSector.htm

You also calculate the area the rendezvous target sweeps out per second (easy to calculate). Divide the area of the ellipse segment by this area per second to get how many seconds to periapsis.

I\'m sure you know how to do the rest.

[Cykyrios]

While I don\'t really know how to calculate the 'time to Pe' (thanks Kosmo-not, was easy enough >.<), I have a little spreadsheet which allows me to calculate the difference in MET between the 2 ships at Ap/Pe, then the next time you get to this point, you simply have to burn such that the resulting orbit will take that time difference longer or shorter to complete, and after a full orbit, you will be within reach of your target. This may be a bit too fuel consuming though.

I attached the spreadsheet with some values that may help you.

[vexx32]

Also, if the object you are rendezvousing with is in focus (i.e., you are 'flying' it), the game will show you the time to periapsis/apoapsis just by hovering over the point with your mouse in addition to the altitude. 0.15 only, of course.