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toothpaste666
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Homework Statement
Two stars, each of mass M, move in a circular orbit of radius R around their common center of mass C.
a) what is the gravitational force on each star?
b) what is the period of each star's orbit?
c) what is the total mechanical energy (potential + kinetic) of this system?
Homework Equations
[itex]F = \frac{GMm}{r^2} [/itex]
[itex] a_R = \frac{v^2}{r} [/itex]
[itex] v = \frac{2piR}{T} [/itex]
The Attempt at a Solution
a) [itex]F = \frac{GCM}{R^2} [/itex]b) [itex] \frac{GCM}{R^2} = \frac{Mv^2}{R}[/itex]
[itex] \frac{GC}{R} = v^2[/itex]
[itex] \frac{GC}{R} = (\frac{2piR}{T})^2[/itex]
[itex] \frac{GC}{R} = \frac{4pi^2R^2}{T^2}[/itex]
[itex] GC= \frac{4pi^2R^3}{T^2}[/itex]
[itex] \frac{GC}{4pi^2R^3}= \frac{1}{T^2}[/itex]
[itex] \frac{4pi^2R^3}{GC}= T^2[/itex]
[itex] T = (\frac{4pi^2R^3}{GC})^\frac{1}{2}[/itex]
c)
[itex] E = \frac{2GCM}{R^2} + \frac{2v^2}{R} [/itex]
Am i doing these right?
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