Tisserand's parameter

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. It is named after French astronomer Félix Tisserand, and applies to restricted three-body problems, in which the three objects all differ greatly in size.

For a small body with semimajor axis ${\displaystyle a\,\!}$, eccentricity ${\displaystyle e\,\!}$, and inclination ${\displaystyle i\,\!}$, relative to the orbit of a perturbing larger body with semimajor axis ${\displaystyle a_{P}}$, the parameter is defined as follows:

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