= Impulsive orbital expansion under isotropic mass loss
{title2=$r_p=R,\quad r_a=R/(1-2f),\quad e=f/(1-f)$}
Suppose an initially <circular Kepler orbit> of radius $R$ surrounds central <mass> $M$, and a fraction $0<f<1/2$ is removed quickly compared with the <orbital period>. Assume no recoil or wind <drag>, so the satellite's <position> and <velocity> are continuous through the change. Its <specific angular momentum> stays $\sqrt{GMR}$, while its new <specific orbital energy> is $-GM(1-2f)/(2R)$. The resulting <elliptic Kepler orbit> has <semi-major axis> $a=(1-f)R/(1-2f)$, <pericentre> $r_p=R$, <apocentre> $r_a=R/(1-2f)$ and <orbital eccentricity> $e=f/(1-f)$. The limiting loss fraction $f=1/2$ gives a <parabolic Kepler orbit>; larger losses unbind the initially circular satellite. Slow removal instead produces <adiabatic orbital expansion under isotropic mass loss>, which preserves circularity to leading adiabatic order.
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