What is eccentricity vector?

The eccentricity vector describes the direction and magnitude of the eccentricity of an object in orbit around another object. It is a vector that points from the center of the orbit to the point where the object is closest to its host. The magnitude of the eccentricity vector is equal to the eccentricity of the orbit, which is a measure of how elliptical the orbit is. If the eccentricity is zero, the orbit is circular, and the eccentricity vector is also zero. If the eccentricity is greater than zero, the orbit is elliptical, and the eccentricity vector points in the direction of the closest point of the orbit. The eccentricity vector is an important tool in the study of celestial mechanics, as it can be used to calculate various parameters of the orbit, such as the period and orbital energy.