spinning and rotation of planets

[wilsonlye]

consider two planets, planet X and planet Y with masses, Mx and My separated with distance, D and they orbits about the centre of mass of the system which remains stationary.

we know that period of orbit for X and Y are the same because they are always collinear with the centre of mass

suppose Mx much more bigger than My, then the centre of mass of the system is almost at the centre of planet X, thus planet X will spin in its own axis.

then how to explain in system consists of multiple stars and planets. It seems to be too complicated, and the ratio of masses between planets is not infinite.

[Creator]

suppose Mx much more bigger than My, then the centre of mass of the system is almost at the centre of planet X, thus planet X will spin in its own axis.



This is an incorrect assumption.
In general, the spin is independent of orbital center of mass, usually referred to as the barycenter.
For a planet of uniform density , the position of barycenter doesn't affect spin.

....

[jambaugh]

I don't really see a question here. What do you want explained? Don't make the mistake of equating "effectively zero" with "exactly zero" in those ratios.

When you change "the system" by adding more bodies you change where the center of mass will be. Yes the motions will be complex. But still the total center of mass remains unchanged (or moves with constant velocity depending on your frame of reference).