Osculating-element evolution under isotropic mass loss ($\dot{\mathbf{e}}=-(\dot{\mu }/\mu )(\mathbf{e}+\hat{\mathbf{r}})$)

For isotropic stellar mass loss the eccentricity vector obeys $\dot{\mathbf{e}}=-(\dot{\mu }/\mu )(\mathbf{e}+\hat{\mathbf{r}})$. With true anomaly $f$ and $e>0$, this gives $\dot{e}=-(\dot{\mu }/\mu )(e+\cos f)$ and $\dot{\varpi }=-(\dot{\mu }/\mu )\sin f/e$. The osculating pericentre satisfies $\dot{q}/q=-(\dot{\mu }/\mu )(1-\cos f)/(1+e)$, hence cannot decrease during mass loss and is instantaneously stationary at pericentre. The vector form is nonsingular at a circular orbit.