In
classical mechanics, the
Laplace–Runge–Lenz vector (or simply the
LRL vector) is a
vector used chiefly to describe the shape and orientation of the
orbit of one astronomical body around another, such as a planet revolving around a star. For two bodies interacting by
Newtonian gravity, the LRL vector is a
constant of motion, meaning that it is the same no matter where it is calculated on the orbit; equivalently, the LRL vector is said to be
conserved. More generally, the LRL vector is conserved in all problems in which
two bodies interact by a
central force that varies as the
inverse square of the distance between them; such problems are called
Kepler problems.