how do you know if two planets orbiting around their center of masses have the same angular speed?

Question

anonymous · Answer

I assume by this you mean " ... orbiting around their center of mass ... " rather than "center of masses".  It seems minor but it could be confusing - a system composed of several objects has a single center of mass, though each object has a center of mass individually.

I am also going to assume that the angular speed is measured relative to the center of mass (it wouldn't make much sense to be measured from anywhere else) in which case the two objects would have to have the same angular speed because they would always have to be on exactly opposite sides of the center of mass, by definition.

anonymous · Answer

hi i dont understand how being on the opposite side affects the angular speed. isn't angular speed=mvr? can u explain further?

anonymous · Answer

The fact that they ALWAYS are on the opposite side implies that their angular speeds are equal.  If one were faster than the other, then they would not stay on opposite sides, right?

anonymous · Answer

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