Calculating launch windows and rendezvous maths

[kerbinorbiter]

how would you be able to calculate a certain launch window?

i'm also stuck on the rendezvous equations (i really need a detailed explanation because i want to do this in KOS for my Soyuz scripts)

thanks in advance!

by launch window i mean an inclined orbit not interplanetary window I.e a ISS window

Edited April 26, 2017 by kerbinorbiter
clarification of context

[Freshmeat]

I am not entirely certain what you want to do. If you want to into the same plane as an orbiting station, you wait until the plane of the station is directly above KSC before launching at the correct inclination. If you do it with KOS, you might be able to get a slight time offset to compensate for the fact that you do not start at full speed, but in my experience I get larger errors from controlling the rocket than being off by a few minutes. A fully automated launch require knowledge of the orbital parameters of the station as well as Kerbin itself, and is far beyond what I can describe in a single post. It is at that time you need to study celestial mechanics somewhat seriously, as in college level textbooks. @OhioBob 's homepage gives the equations, but it is somewhat condensed, as it is not a textbook.

[ElWanderer]

I'll second the reference to OhioBob's page. 

I wrote up my solution to launching into an inclined plane here (specifically the etaToOrbitPlane function):

https://github.com/ElWanderer/kOS_scripts/blob/master/documentation/lib_launch_geo_readme.md

The hard part was finding out where the orbit plane would be, as opposed to the ground track of whatever's in the orbit plane. The latter seems a lot more common in the results of Google searches. The kOS code I've written and am still writing is available if you want to go exploring from that link.

My rendezvous code isn't too bad, though it's not very realistic. The approach I take is to make sure the orbits intersect then set-up a phasing orbit of the right period so that the two craft meet at the intersection some number of orbits later. The maths of that was a headache to figure out, particularly trying to account for all the combinations of being ahead of/behind the target and in a shorter/longer orbit.

In real life, I'm pretty sure they go through a series of phasing orbits that are entirely below the altitude of the station so that in the event of loss of control, there is no collision risk. Effectively, intersection occurs very late on in the process.

Edited April 28, 2017 by ElWanderer

[OhioBob]

Maybe this article will help you... http://www.klabs.org/history/papers/lunney_gemini_rendezvous.pdf