Orbital compactness ($GM/(R{c}^2)$)

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 $P=(2/5)(c^5/G)[GM/(R{c}^2){]}^5$. Compact objects permit smaller noncontact orbits than extended stars and hence larger orbital compactness; near merger the Newtonian approximation must be replaced.