Bondi k-calculus

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Tisserand's parameter (or Tisserand's invariant) is a combination of orbital elementsTemplate:Vague used in a restricted three-body problem, named after French astronomer Félix Tisserand.

Definition

For a small body with semimajor axis , eccentricity , and inclination , relative to the orbit of a perturbing larger body with semimajor axis , the parameter is defined as follows:[1]

The quasi-conservation of Tisserand's parameter is a consequence of Tisserand's relation.

Applications

Related notions

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.

See also

External links

References

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