 Inspiral time under Poynting–Robertson drag

For the Poynting–Robertson drag invariant $C$ and $A=\beta G{M}_{\star }/c$, the orbit-averaged time to the point-star limit isThis tends to $a_0^2/(4A)$ for a circular orbit and to $4Q_0^{1/2}{q}_0^{3/2}/(5A)$ for a highly eccentric orbit. Stellar radius, sublimation, collisions, and failure of orbital averaging can terminate the evolution earlier.