The period must depend on both masses. After an extensive Internet search I found this:mancity said:Homework Statement: Two stars orbit their common center of mass as shown in the diagram below. The masses of the two stars are 3M and M. The distance between the stars is d.
Determine the period of orbit for the star of mass 3M.
Relevant Equations: T^2=4pi^2R^3/GM
Why do we add the two masses (3M+M=4M) and use that for M in the equation of kepler's 3rd law?
Namely why is it T^2=4pi^2R^3/G(3M+M)
Two stars orbit their common center of mass by exerting gravitational forces on each other. As they orbit, the stars move in elliptical paths around the center of mass, with the more massive star typically having a smaller orbit.
The orbital period of two stars orbiting their common center of mass is determined by their masses and the distance between them. The larger the masses of the stars and the closer they are to each other, the shorter the orbital period will be.
Yes, two stars orbiting their common center of mass can have different masses. The more massive star will have a smaller orbit, while the less massive star will have a larger orbit. The center of mass will be located closer to the more massive star.
Some observable effects of two stars orbiting their common center of mass include variations in brightness as they eclipse each other, Doppler shifts in their spectra as they move towards or away from Earth, and changes in their positions in the sky over time.
Astronomers study two stars orbiting their common center of mass using techniques such as radial velocity measurements, light curve analysis, and astrometry. These methods allow astronomers to determine the masses, orbital periods, and distances of the stars involved in the binary system.