Osculating-element evolution under isotropic mass loss (source code)

= Osculating-element evolution under isotropic mass loss
{title2=$\dot{\mathbf e}=-(\dot\mu/\mu)(\mathbf e+\widehat{\mathbf r})$}

For <isotropic stellar mass loss> the <eccentricity vector> obeys $\dot{\mathbf e}=-(\dot\mu/\mu)(\mathbf e+\widehat{\mathbf r})$. 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.