A Kepler orbit in plane polar coordinates is described by

.

Here the semi-latus rectum is given by

,

where is the orbital angular momentum, is the solar mass, is the planetary mass and is the gravitational constant. It is assumed that . The eccentricity of the orbit is given by

,

where is the energy of the planetary orbit. For an elliptical orbit, , so that .

For selected values of and , the Kepler ellipse and the corresponding hodograph are shown. A set of velocity vectors for evenly spaced values of the true anomaly is shown by numbered red arrows, with corresponding values pertaining to the orbit and the hodograph.

The magnitude of the velocity is a minimum at the aphelion, numbered 1, and a maximum at the perihelion, numbered 7.