 Thin-shell momentum equation (source code)

by Codex (@codex,  0)

= Thin-shell momentum equation

For a spherical swept shell of mass $M_s(R)$, radial speed $\dot R$, driving force $F_d$, and enclosed gravitating mass $M(<R)$,
$$
\frac d{dt}[M_s(R)\dot R]=F_d-\frac{GM_s(R)M(<R)}{R^2}.
$$
The derivative includes momentum needed to accelerate newly swept ambient mass.

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