Barker equation
= Barker equation
{c}
For a <parabolic trajectory> with <periapsis> radius $r_p$, put $D=\tan(f/2)$, where $f$ is <true anomaly>. The Barker equation is $t-t_p=\sqrt{2r_p^3/(GM)}(D+D^3/3)$. Since $r=r_p(1+D^2)$, it is equivalent to the <radius-time relation for a parabolic Kepler orbit>. The sign of $D$ distinguishes approach from recession; $t_p$ is the <periapsis> time.