Orbital compactness
= Orbital compactness
{title2=$GM/(Rc^2)$}
The dimensionless ratio of gravitational radius to orbital scale measures how relativistic a bound orbit is. In an equal-mass circular binary with individual orbital radius $R$, the leading <quadrupole formula> gives $P=(2/5)(c^5/G)[GM/(Rc^2)]^5$. Compact objects permit smaller noncontact orbits than extended stars and hence larger orbital compactness; near merger the Newtonian approximation must be replaced.