= Equal-mass circular binary
{title2=$\omega^2=Gm/(4a^3)$}
Two equal point <masses> can move around the same fixed circle of radius $a$ in diametrically opposite positions. Their stationary <centre of mass> is the circle's center. A separation $2a$ gives gravitational <force> $Gm^2/(4a^2)$ on each <mass>, and <Newton's second law> equates it to $ma\omega^2$. The common <angular speed> is therefore fixed by the displayed relation. Opposite tangential <velocities> produce the same sense of angular rotation.
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