Tisserand's parameter

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Tisserand's parameter (or Tisserand's invariant) is a value calculated from several orbital elements (semi-major axis, orbital eccentricity and inclination) of a relatively small object and a larger "perturbing body". It is used to distinguish different kinds of orbits. The term is named after French astronomer Félix Tisserand, and applies to restricted three-body problems in which the three objects all differ greatly in mass.



For a small body with semi-major axis , orbital eccentricity , and orbital inclination , relative to the orbit of a perturbing larger body with semimajor axis , the parameter is defined as follows: [1] [2]

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


The parameter is derived from one of the so-called Delaunay standard variables, used to study the perturbed Hamiltonian in a three-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.

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  2. Bonsor, A.; Wyatt, M. C. (2012-03-11). "The scattering of small bodies in planetary systems: constraints on the possible orbits of cometary material: Scattering in planetary systems". Monthly Notices of the Royal Astronomical Society. 420 (4): 2990–3002. arXiv: 1111.1858 . doi: 10.1111/j.1365-2966.2011.20156.x .
  3. "Dave Jewitt: Tisserand Parameter". www2.ess.ucla.edu. Retrieved 2018-03-27.
  4. Jewitt, David C. (August 2013). "The Damocloids". UCLA – Department of Earth and Space Sciences. Retrieved 15 February 2017.
  5. Merritt, David (2013). Dynamics and Evolution of Galactic Nuclei. Princeton, NJ: Princeton University Press. ISBN   9781400846122.