# Specific orbital energy

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.[1] According to the orbital energy conservation equation (also referred to as vis-viva equation), it does not vary with time:

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where

- is the relative orbital speed;
- is the orbital distance between the bodies;
- is the sum of the standard gravitational parameters of the bodies;
- is the specific relative angular momentum in the sense of relative angular momentum divided by the reduced mass;
- is the orbital eccentricity;
- is the semi-major axis.

It is expressed in MJ/kg or . For an elliptic 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.