# Eccentricity vector

From Infogalactic: the planetary knowledge core

In celestial mechanics, the **eccentricity vector** of a Kepler orbit is the vector that points towards the periapsis and has a magnitude equal to the orbit's scalar eccentricity. The magnitude is unitless. 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

- ↑ Cordani, Bruno (2003).
*The Kepler Problem*. Birkhaeuser. p. 22. ISBN 3-7643-6902-7.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>