Apoapsis

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

The greatest radial distance of an Ellipse as measured from a Focus. Taking $v=\pi$ in the equation of an Ellipse

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

gives the apoapsis distance

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

Apoapsis for an orbit

around the Earth

is called apogee,

and apoapsis for an orbit

around the Sun

is called aphelion.