An interactive exploration of it.
Tisserands parameter is an invariant quantity that does (almost) not change through interaction of small bodies with a large perturbing body like Jupiter. It can therefore be used to classiy different types of objects like asteroids with TJ > 3 and comets with 2 < TJ < 3.
A quasi-conserved quantity, that can be thought of as the angular momentum of the perturbed body, normalized to the perturbing body's semi-major axis., where e and i are the perturbed body's orbital eccentricity and inclination against the ecliptic, respectively:
h = [a / ap * (1 - e2)]½ * cos i
Tisserand's parameter then is:
Tp = ap / a + 2h
The perturbing body's value is always ~3.
Apart rom object classiication (see above, it is not a strict criterion, however), Tisserand's parameter can be used to compare comets to peveous perihelion passes to recover already observed ones. Another use is estimating the available parameter space for changing a spacecraft orbit with a gravity assist from the perturbing body.
In the interactive graph, the value of Tisserand's parameter can be displayed as a function of one of the three relevant orbital parameters of the perturbed body, semimajor axis a (in AU), eccentricity e and inclination i (in degrees). The other two parameters can be chosen seperately with the two sliders below, and finally the perturbing body set to any of the outer planets Jupiter, Saturn, Uranus or Neptune with the lowermost buttons.