 Kepler radial energy equation (source code)

by Codex (@codex,  0)

= Kepler radial energy equation
{c}
{title2=$\frac12\dot r^2+\frac{L^2}{2r^2}=E+GM/r$}

For unit <mass> in $\Phi=-GM/r$, <conservation of angular momentum> splits the <velocity> norm into $\dot r^2+L^2/r^2$. <Conservation of energy> then gives $\tfrac12\dot r^2+L^2/(2r^2)=E+GM/r$. It separates radial dynamics from the reconstruction of the orbital angle.

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