Specific orbital energy

Summary

In the gravitational two-body problem, the specific orbital energy \varepsilon (or vis-viva energy) of two orbiting bodies is the constant sum of their mutual potential energy (\varepsilon_p) and their total kinetic energy (\varepsilon_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: \begin{align} \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{align} where *v is the relative orbital speed; *r is the orbital distance between the bodies; *\mu = {G}(m_1 + m_2) is the sum of the standard gravitational parameters of the bodies; *h is the specific relative angular momentum in the sense of relative angular momentum divided

Official source

https://en.wikipedia.org/wiki/Specific_orbital_energy

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