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

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 J/kg = m2s−2 or MJ/kg = km2s−2. 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.