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.
The eccentricity vector is: 
which follows immediately from the vector identity:
- is velocity vector
- is specific angular momentum vector (equal to )
- is position vector
- is standard gravitational parameter