Editing Orbital mechanics (section)

====Energy====
Under standard assumptions, [[specific orbital energy]] (<math>\epsilon\,</math>) of elliptic orbit is negative and the orbital energy conservation equation (the [[Vis-viva equation]]) for this orbit can take the form:
:<math>{v^2\over{2}}-{\mu\over{r}}=-{\mu\over{2a}}=\epsilon<0</math>
where:
*<math>v\,</math> is the speed of the orbiting body,
*<math>r\,</math> is the distance of the orbiting body from the center of mass of the [[central body]],
*<math>a\,</math> is the [[semi-major axis]],
*<math>\mu\,</math> is the [[standard gravitational parameter]].
Conclusions:
*For a given semi-major axis the specific orbital energy is independent of the eccentricity.

Using the [[virial theorem]] we find:
*the time-average of the specific potential energy is equal to <math>2\epsilon</math>
*the time-average of <math>r^{-1}</math> is <math>a^{-1}</math>
*the time-average of the specific kinetic energy is equal to <math>-\epsilon</math>