 Eccentricity vector

For an attractive Kepler orbit with gravitational parameter $GM$, velocity $\mathbf{v}$ and specific angular momentum $\mathbf{h}=\mathbf{r}\times \mathbf{v}$, the eccentricity vector isIts magnitude is the orbital eccentricity, and it points toward periapsis for a noncircular orbit. It is a normalized attractive Laplace-Runge-Lenz vector; it remains constant under the pure inverse-square force.

The eccentricity vector, often denoted as **e**, is a vector that describes the shape and orientation of an orbit in celestial mechanics. It is particularly relevant in the context of conic sections, which are used to describe orbits of celestial bodies (like planets, comets, and satellites) around other massive bodies.