The discussion focuses on determining the required angular velocity ($\omega$) for two equal masses maintaining a constant separation distance ($r_0$) while rotating around each other, akin to a binary star system. Key equations include the gravitational force $|F_{g}|=\frac{m^{2}G}{r_{0}^{2}}$ and centripetal acceleration $a_{c}=\frac{v_{\tan}^{2}}{r_{0}}$. The tangential velocity is expressed as $v_{\tan}=\omega \,r_{0}$. The center of gravity serves as the reference point for calculating angular velocity, with the bodies orbiting in a uniform circle of radius $\frac{1}{2}r_0$.
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Ackbach said:To me it seems as if you have to balance the potential energy due to gravity against the rotational kinetic energy. That is, it seems as if you're in outer space with two equal masses, and they are rotating around each other like a binary star system. If the distance between them is constant, how fast are they rotating around each other?
dwsmith said:Fast enough to not be pulled in by the others gravity and a slow enough that they don't fly off.
dwsmith said:Is this question talking about the position vector for the center of gravity of the two bodies?
If we set the origin to be the center of gravity, the bodies orbit it in a uniform circle with radius 1/2r_0.
I can just find the angular velocity on this circle?