The term is named after French astronomer Félix Tisserand who derived it[1] and applies to restricted three-body problems in which the three objects all differ greatly in mass.
In the three-body problem, the quasi-conservation of Tisserand's invariant is derived as the limit of the Jacobi integral away from the main two bodies (usually the star and planet).
[2] Numerical simulations show that the Tisserand invariant of orbit-crossing bodies is conserved in the three-body problem on Gigayear timescales.
The value of the Tisserand parameter with respect to the planet that most perturbs a small body in the solar system can be used to delineate groups of objects that may have similar origins.
For example, such a mechanism can produce sungrazing comets, because a large eccentricity with a constant semimajor axis results in a small perihelion.