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

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SUMMARY

Kepler's Third Law establishes that the orbital period (τ) of two gravitationally bound stars with equal masses is proportional to the distance (d) between them raised to the power of 1.5 (d^1.5). This relationship can be expressed mathematically as τ ∝ d^(3/2). The radius of each star's orbit is directly proportional to the distance separating the two stars, which is crucial for deriving the period of their orbits.

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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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