# Position of a satellites satellite depending on orbital periods

I have three celestial bodies, S, E and M. Let's assume, that S is in a fixed position and E rotates around S on a perfectly circular orbit. M rotates around E in the same plane and also on a perfectly circular orbit. (There are also no speed fluctuations involved or anything, just simple circular motions)

Now, E has a orbital period of 1 year, while M has an orbital period of 1/4 years. Now at time zero S, E and M are defined to be at positions (0,0), (10,0) and (11,0) respectively.

After 1/4 years E will of course be positioned at exactly (0,10), however my question is if orbital period is defined in a way, that considers the parents rotation around its parent and so forth, with M positioned at (0,11), or whether it is seen kind of like in a global coordinate system, and its position should be (1,10).

Basically the question is whether the orbit of M rotates depending on Es position in its own orbit. (With respect to the definition of the orbital period)