Tisserand's Criterion

The Tisserandparameter ( after François Félix Tisserand ) represents an approximation of the Jacobi integral and is approximately a conserved quantity of the circularly simplified three-body problem. It is used in astronomy and space travel.

Definition

The Tisserandparameter a small body ( typically an asteroid or comet ) in relation to a planet P is defined by

Wherein the semi-major axis of the planet, a is the semi-major axis and e is the eccentricity of the small body and i is the inclination of the orbit of the body are small in relation to the planetary path.

The Tisserandparameter is usually given in relation to Jupiter, since the interaction with Jupiter exerts the greatest influence on the orbits of minor bodies of the solar system. For objects beyond the orbit of Jupiter the Tisserand is also calculated with respect to Saturn, Uranus and Neptune.

The requirement that " circularly simplified three-body problem ", means:

While the first assumption in the practical application is justified are the other two however can very strong idealizations

History

Through the interaction with Jupiter, the orbital elements of a comet partly change very much, so sometimes it can be decided only after extensive iterative path calculations, whether it is the same comet or two different comets at two comet observations. The French astronomer François Félix Tisserand published in 1896 a simple criterion to compare the orbits of comets together: by the Tisserandkriterium - the Tisserandparameter for both observations have nearly identical - can decide one very easy, whether it could ever act by the same comet, and can therefore do without in many cases, to the elaborate ( manual ) calculations. Through the use of powerful computers, the Tisserandkriterium, however, has lost much in the second half of the 20th century in importance.

Today's meaning

The present meaning of Tisserandparameters lies in a simple classification of bodies of the solar system. For example, most asteroid ( Tisserandparameter with respect to Jupiter ) of more than 3, while is for the comets of the Jupiter family 2-3 - but there are exceptions to this "rule". However, this is not surprising, since the distinction between comets and asteroids the former is not easy in the outer regions of the solar system due to lack of activity. Other asteroids ( Damocloiden ) move on typical orbits of comets, however, show no activity - So a coma was some originally classified as asteroids objects later found (eg in ( 2060 ) Chiron).

Application in space

When planning a Gravity Assist maneuver, the preservation of Tisserandparameters plays a crucial role. Since the possible orbits are after the flyby severely limited by the Tisserandparameter, it is taken as a basis for the choice of an appropriate target path. If you have found this, this in turn leads directly to the required speed and distance for the flyby maneuver.

• Celestial mechanics