Specific orbital energy

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

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