Tisserand parameter

A dimensionless quantity used to compare small-body orbits relative to a perturbing planet. It is approximately conserved during gravitational encounters in the circular restricted three-body problem.

Jacobi integral: A conserved energy-like quantity in the circular restricted three-body problem, defined in a frame rotating with the primaries. The Tisserand parameter approximates a transformed Jacobi integral when the small body's orbit is far from the planet.
Jupiter-family comet: A short-period comet whose orbit is strongly influenced by Jupiter and typically has a period under 20 years. Its Tisserand parameter relative to Jupiter is commonly used to distinguish it from other comet populations.
Orbital resonance: A dynamical configuration in which orbiting bodies exert repeated gravitational influence because their orbital periods form a simple ratio. Resonance organizes long-term orbital evolution, whereas the Tisserand parameter constrains encounter-related changes.
Félix Tisserand: A French astronomer and mathematician whose work included celestial mechanics and the study of cometary orbits. The parameter bears his name because he developed the relation in studies of planetary perturbations.
Circular restricted three-body problem: A model of two massive bodies on circular orbits and a third body whose mass is negligible. The parameter's approximate conservation is derived within this model.
Centaur (small Solar System body): A small Solar System body orbiting among the giant planets, often on an unstable path between them. Tisserand parameters relative to giant planets help trace possible transitions into and out of Centaur orbits.
Öpik theory: A statistical framework for estimating close-encounter velocities and collision probabilities between small bodies and planets. It uses encounter geometry and velocity relations that can be compared with Tisserand-based constraints.
Three-body problem: The problem of predicting the motion of three bodies interacting through gravity. The restricted version of this classical problem provides the dynamical setting behind the parameter.
Orbital elements: Parameters such as semimajor axis, eccentricity, and inclination that describe an orbit's size, shape, and orientation. Its usual expression combines these orbital elements with the planet's orbital distance.
Damocloid: An asteroid-like object with a highly eccentric orbit resembling that of a long-period or Halley-type comet. A low Tisserand parameter relative to Jupiter can flag comet-like dynamics in objects lacking visible activity.

Linked from 2 pages