= Kepler velocity hodograph
{c}
{title2=$\boldsymbol v=(\mu_g/h)(-\sin f,\cos f+e)$}
In axes directed along the <periapsis> and transverse to it, a <Kepler orbit> with gravitational parameter $\mu_g$ and <specific angular momentum> $h$ has the displayed <velocity>. The <velocity> tip traces a circle of radius $\mu_g/h$ centred at $(0,e\mu_g/h)$. To derive it, differentiate $r=h^2/[\mu_g(1+e\cos f)]$, use $r^2\dot f=h$, and resolve $\dot r\widehat{\boldsymbol r}+r\dot f\widehat{\boldsymbol\theta}$. A rotation of the spatial axes rotates the entire hodograph by the same angle.
Back to article page
