Periapsis

$\begin{figure}\begin{center}\BoxedEPSF{ApoapsisPeriapsis.epsf}\end{center}\end{figure}$

The smallest radial distance of an Ellipse as measured from a Focus. Taking in the equation of an Ellipse

$\begin{displaymath} r = {a(1-e^2 )\over 1+e\cos v} \end{displaymath}$

gives the periapsis distance

$\begin{displaymath} r_-=a(1-e). \end{displaymath}$

Periapsis for an orbit

around the Earth

is called perigee,

and periapsis for an orbit

around the Sun

is called perihelion.