# Specific orbital energy

In the gravitational two-body problem, the specific orbital energy ${\displaystyle \varepsilon }$ (or vis-viva energy) of two orbiting bodies is the constant sum of their mutual potential energy (${\displaystyle \varepsilon _{p}}$) and their total kinetic energy (${\displaystyle \varepsilon _{k}}$), 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:

{\displaystyle {\begin{aligned}\varepsilon &=\varepsilon _{k}+\varepsilon _{p}\\&={\frac {v^{2}}{2}}-{\frac {\mu }{r}}=-{\frac {1}{2}}{\frac {\mu ^{2}}{h^{2}}}\left(1-e^{2}\right)=-{\frac {\mu }{2a}}\end{aligned}}}

where

It is expressed in MJ/kg or ${\displaystyle {\frac {{\text{km}}^{2}}{{\text{s}}^{2}}}}$. 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.

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