circular movement of 3 bodies

Question

Im trying to find the $(x,y)$ coordinate of 3 bodies which move in circle -
for example (sun > earth > moon).
Assume sun is always at (0,0).
Earth orbit around the sun.
Moon orbit around earth. (no masses etc.)
Assume we have: initial angle, speed, radius.
earth has distance from sun, moon has distance from earth.
How can I calculate the current position of the moon using these variables?

Answer 1

\begin{align*} \mathbf{r}_{earth} &= (R\cos \Omega t,R\sin \Omega t) \\ \mathbf{r}_{moon} &= (R\cos \Omega t+r\cos (\omega t+\phi),R\sin \Omega+r\sin (\omega t+\phi)) \\ \end{align*}