The Laplace–Runge–Lenz (LRL) vector is a fundamental concept in celestial mechanics and classical mechanics, particularly in the study of central force problems, such as the motion of planets and satellites around a central body (like the Sun). ### Definition The LRL vector \( \mathbf{A} \) is defined in the context of the motion of a particle under a central force, such as gravity.
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For the signed inverse-square force on a particle of mass , with Hamiltonian , the Laplace-Runge-Lenz vector is conserved. Attraction has and repulsion has . It obeys and . For unit mass in a Kepler orbit, .