Elliptic Orbit - Energy

Energy

Under standard assumptions, specific orbital energy of elliptic orbit is negative and the orbital energy conservation equation (the Vis-viva equation) for this orbit can take the form:

where:

  • is orbital speed of orbiting body,
  • is distance of orbiting body from central body,
  • is length of semi-major axis,
  • is 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 2ε
    • the time-average of r−1 is a−1
  • the time-average of the specific kinetic energy is equal to –ε

Read more about this topic:  Elliptic Orbit

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