An Etymological Dictionary of Astronomy and Astrophysics

The condition for the stability of a → three-body system. Three-body systems exist widely in the → solar system and → extrasolar systems, including Sun-planet-moon systems, planets-star systems, and → triple star systems. This concept of stability was introduced by Hill (1878). He used the → Jacobi integral to construct bounds of motion for → conservative systems with time-independent → potentials, which was introduced to study the stability of the Moon in the Sun-Earth → restricted three-body problem. The stability is defined by the → zero-velocity surface based on the Jacobi integral. The concept of the Hill stability has been used by many researchers to study the stability of three-body systems. The studies include the Hill stability in the full → three-body problems, the hierarchical three body problems, and the restricted three body problems (See, e.g., S. Gong & J. Li, 2015, Astrophys Space Sci. 358,37).

See also: Hill, G.W.: Researches in the lunar theory. Am. J. Math. 1(2), 129-147 (1878); → stability.