Astrophysics: Binary Star System (29 of 40) Relative Motion of a Binary System with Arbitrary Mass

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We will learn about the relative motion of a binary system with arbitrary masses. When M is much, much larger than m, we can assume M to be stationary with m revolving around M. But if M is NOT much, much larger than m, then both revolve around the barycenter, which is the center of mass of the system.

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[danielbarroso]

Dear Teacher, in the video Kepler's First Law-part 3 of 3, we assumed that the large mass didn't move and we arrived to the conclusion that the trajectory of the small mass around the large one is an ellipse. What would happen if we used the reduced mass to calculate the trajectory of the masses, instead of assuming the large mass doesn't move? Could we directly change the small mass (m) by the reduced mass (mr) in the final equation obtained in that video? Or should we do the whole derivation from scratch working with the reduced mass to obtain the azimuthal equation in terms of mr instead of m?

Thank you!!

[imademedikasurya]

please prove this system orbit period formula