= Orbit-averaged drag work
A weak perturbing relative acceleration $\mathbf f$ changes <specific orbital energy> at rate $\dot\varepsilon=\mathbf v\cdot\mathbf f$. Since $\varepsilon=-\mu/(2a)$ for a <Kepler orbit>,
$$
\dot a=\frac{2a^2}{\mu}\mathbf v\cdot\mathbf f.
$$
For a circular <Kepler orbit> under $\mathbf f=-\kappa\mathbf v+\mathbf g$ with constant $\mathbf g$, the constant-force term averages to zero over an unperturbed orbit. Thus $\langle\dot a\rangle=-2\kappa a$. This is a leading-order orbital average; a strong constant force can distort the orbit instead.
Back to article page
