Deriving Equations for Moon's Orbital Acceleration

[neo32]

Hello, I need help on deriving a equations for the moon's acceleration around the earth. I've already found the total acceleration (a=Gm/r^2) but what i need to do is split this acceleration up into its x and y components, and derive equations in terms of a, r, x, and/or y for any given position in the moon's orbital path

So far I have ax = a*cos(T) and ay = a*sin(T) where T is the angle from the x-axis. What I'm having trouble with is deriving T. If those are wrong to begin with, can someone put me on the right track? Thanks!

 

[Doc Al]

Please don't double post. You already have a thread on this topic open here https://www.physicsforums.com/showthread.php?t=94978, which is where this belongs.