Orbits in After Effects I'm new to After Effects and I might be asking about obvious stuff, but I searched this site and elsewhere and can't find an answer. 

Basically I want to orbit some points in a setup similar to the Sun - Earth - Moon (Sun is static, Earth goes around the Sun, and the Moon goes around the Earth), and I need each moving point to have its position change over time so that I can parent other stuff to them.  

I'm trying to animate this graphic:



I've got the epicycle (the small circle) to rotate around point T (Terre), while V (Venus) is rotating on the epicycle. I have a beam between T and the center of the epicycle (C), but I would also need to add a beam between C and Venus. 

I can get Venus to rotate on the epicycle either by making it an ellipse on it's own layer and then parenting it to the epicycle; or I can add it as another ellipse on the same shape layer as the epicycle, making V rotate with the epicycle. But in both cases the position of Venus remains invariable, so the beam can't follow.

How do I make point V rotate on the epicycle such that its own position changes over time allowing me to add a beam between it and the center of the epicycle?

I'm confused by all the different Position parameters, if I create V as an ellipse on its own shape layer there'll be 3 different position parameters and none if them will change over time if V is parented to the epicycle. I've also tried alt-pick-whipping these 3 to the position of the epicycle with no luck.
I would probably start from the smallest orbit and work my way out.  If you adjust the anchor point for each object that is rotating, a simple rotation keyframe should make it rotate around the center.

Once you have the smallest thing rotating, you include that composition in another composition and adjust the anchor point similarly to make it rotate around the center of the new composition.

If you need oblong orbits, you can also use a path instead and animate it along the path.

You can keep nesting them indefinitely for as many nestings as you need. It isn't a 100% accurate simulation since the actual orbital mechanics are a bit more complicated, but it gives a simple simulation of them and can easily support various periods for each part.