# Specific Orbital Energy

## Description

In the gravitational two-body problem, the specific orbital energy (or vis-viva energy) of two orbiting bodies is the constant sum of their mutual potential energy and their total kinetic energy , divided by the reduced mass. According to the orbital energy conservation equation (also referred to as vis-viva equation), it does not vary with time.

For an elliptical orbit the specific orbital energy is the negative of the additional energy required to accelerate a mass of one kilogram to escape velocity (parabolic orbit). For a hyperbolic orbit, it is equal to the excess energy compared to that of a parabolic orbit. In this case the specific orbital energy is also referred to as characteristic energy.

## Variables

ϵ | specific orbital energy (J/kg) |

μ | sum of the standard gravitational parameters of the bodies (m^{3}/s^{2}) |

a | semi-major axis (m) |