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.

Related formulas

Variables

ϵspecific orbital energy (J/kg)
μsum of the standard gravitational parameters of the bodies (m3/s2)
asemi-major axis (m)