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I'am trying to figure out how to describe a trajectory of an object as a function of time. The object is a spacecraft and it sets of from Earth, travels around the moon, and then heads back to Earth.

http://courses.ncssm.edu/math/NCSSM Student Materials/InvestigationsTrimester 3/Moon.pdf

I found a solution to this in this pdf (p. 5-6), but I have some questions.

I want to find r(t)= ( x(t) y(t) ). This pdf points me in the right direction (i think), but I how can I find the acceleration in the x and y directions? I´ve tried different things, but I always end up a very frustrating loop, where everything is dependent of each other.

I´ve also look at Keple's laws, but i can't find a solution where i get r(t)= ( x(t) y(t) ). Instead I get r("angle") = ( x("angle") y("angle") ).

Thank you :-D

Henrik