= Inspiral time under Poynting–Robertson drag
{title2=$t_{\rm PR}$}
For the <Poynting–Robertson drag invariant> $C$ and $A=\beta GM_\star/c$, the orbit-averaged time to the point-star limit is
$$
t_{\rm PR}=\frac{2C^2}{5A}\int_0^{e_0}\frac{u^{3/5}}{(1-u^2)^{3/2}}\,du.
$$
This 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.
Back to article page
