Eccentricity vector
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 is: [1]
which follows immediately from the vector identity:
where:
- is velocity vector
- is specific angular momentum vector (equal to )
- is position vector
- is standard gravitational parameter
See also
References
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