Kepler's Third Law: Proportional Orbit Period to Distance^1.5

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Kepler's Third Law states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. In the case of two gravitationally bound stars of equal mass, their orbital period (tau) can be shown to be proportional to the distance (d) raised to the power of 1.5, or d^(3/2). The radius of each star's orbit is directly related to the distance between them, which is crucial for deriving the relationship. Understanding these principles allows for the calculation of orbital periods based on their separation. This discussion emphasizes the mathematical relationship between orbital period and distance in a binary star system.
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Two gravitionally bound stars with equal masses m, separated by a distance d, revolve about their center of mass in circular orbits. Show that the period tau is proportional to d^1.5

Could someone get me started on this? I have no idea where to begin!

Thanks!
 
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First of all, state Keppler's Third Law.

Also, realize that d^1.5 is the same as d^(3/2)

And then notice how the radius of the orbits is directly proportional to the distance between them.
 

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