Impulsive orbital expansion under isotropic mass loss ($r_p=R,r_a=R/(1-2f),e=f/(1-f)$)

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.