Harman Patil (Editor)

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

The eccentricity vector e is:

e = v × h μ − r | r | = ( | v | 2 μ − 1 | r | ) r − r ⋅ v μ v

which follows immediately from the vector identity:

v × ( r × v ) = ( v ⋅ v ) r − ( r ⋅ v ) v

where:

  • v is velocity vector
  • h is specific angular momentum vector (equal to r × v )
  • r is position vector
  • μ is standard gravitational parameter

    • References

    Eccentricity vector Wikipedia
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