The quasi-conservation of Tisserand's parameter is a consequence of Tisserand's relation.
- TJ, Tisserand’s parameter with respect to Jupiter as perturbing body, is frequently used to distinguish asteroids (typically ) from Jupiter-family comets (typically ).
- The roughly constant value of the parameter before and after the interaction (encounter) is used to determine whether or not an observed orbiting body is the same as a previously observed in Tisserand's Criterion.
- The quasi-conservation of Tisserand's parameter constrains the orbits attainable using gravity assist for outer Solar system exploration.
- TN, Tisserand's parameter with respect to Neptune, has been suggested to distinguish Near Scattered Objects (believed to be affected by Neptune) from Extended Scattered trans-Neptunian objects (e.g. 90377 Sedna).
- Tisserand's parameter could be used to infer the presence of an intermediate-mass black hole at the center of the Milky Way galaxy using the motions of orbiting stars.
The parameter is derived from one of the so-called Delaunay standard variables, used to study the perturbed Hamiltonian in a 3-body system. Ignoring higher-order perturbation terms, the following value is conserved:
Consequently, perturbations may lead to the resonance between the orbital inclination and eccentricity, known as Kozai resonance. Near-circular, highly inclined orbits can thus become very eccentric in exchange for lower inclination. For example, such a mechanism can produce sungrazing comets, because a large eccentricity with a constant semimajor axis results in a small perihelion.
- Tisserand's relation for the derivation and the detailed assumptions