Eccentricity vector

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In celestial mechanics, the eccentricity vector of a Kepler orbit is the dimensionless vector with direction pointing from apoapsis to periapsis and with magnitude equal to the orbit's scalar eccentricity. For Kepler orbits the eccentricity vector is a constant of motion. Its main use is in the analysis of almost circular orbits, as perturbing (non-Keplerian) forces on an actual orbit will cause the osculating eccentricity vector to change continuously. For the eccentricity and argument of periapsis parameters, eccentricity zero (circular orbit) corresponds to a singularity.

Calculation[edit]

The eccentricity vector is: [1]

which follows immediately from the vector identity:

where:

See also[edit]

References[edit]

  1. ^ Cordani, Bruno (2003). The Kepler Problem. Birkhaeuser. p. 22. ISBN 3-7643-6902-7.