What you’re really asking about is a field of physics called “orbital mechanics.”
I was forced to study this for one semester. Why they made a EE study orbital mechanics... I have no idea. Never used it since. Every other course where I asked at the time “Why are we studying this nonsense?” I have used.
Orbital mechanics... going on 30 years and still haven’t used it.
But rather than my trying to coach you through it, here’s a link to a guy’s page where he lays most of the issues you have out in pretty compact form. You’ll need a little background in Newtonian physics, but not much of the heavier math usually involved (integral calc, DiffEQ’s and Lagrangians) to nut your way through this stuff:
http://www.braeunig.us/space/orbmech.htm
ugh... orbital mechanics. that and modern physics I’ve never really used. At least relativistic physics was entertaining... OM on the other hand, should have been interesting given the lectures were from original notes from the Mercury program, but the retired McDonnell engineer instructing had all the charisma of a sheet of drywall.
Yikes.