Within the solar system, approximate realizations of the three-body problem occur when a comet approaches a planet while being affected mainly by such a planet and the Sun, and this configuration was investigated by Tisserand within the framework of Newtonian gravity. The exact relativistic treatment of the problem is not an easy task, but this paper develops an approximate calculational scheme which computes for the first time the tiny effective-gravity correction to the equation of the surface for all points of which it is equally advantageous to regard the heliocentric motion as being perturbed by the attraction of Jupiter, or the jovicentric motion as being perturbed by the attraction of the Sun. This analysis completes the previous theoretical investigations of effective gravity corrections to the Newtonian analysis of three-body systems, and represents an intermediate step towards relativistic effects on cometary motions.

An effective-gravity perspective on the Sun–Jupiter–comet three-body system / Battista, Emmanuele; Esposito, Giampiero; Tartaglia, Angelo. - In: INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS. - ISSN 0219-8878. - STAMPA. - 17:11(2020), pp. 1-22. [10.1142/S0219887820501686]

An effective-gravity perspective on the Sun–Jupiter–comet three-body system

Angelo Tartaglia
2020

Abstract

Within the solar system, approximate realizations of the three-body problem occur when a comet approaches a planet while being affected mainly by such a planet and the Sun, and this configuration was investigated by Tisserand within the framework of Newtonian gravity. The exact relativistic treatment of the problem is not an easy task, but this paper develops an approximate calculational scheme which computes for the first time the tiny effective-gravity correction to the equation of the surface for all points of which it is equally advantageous to regard the heliocentric motion as being perturbed by the attraction of Jupiter, or the jovicentric motion as being perturbed by the attraction of the Sun. This analysis completes the previous theoretical investigations of effective gravity corrections to the Newtonian analysis of three-body systems, and represents an intermediate step towards relativistic effects on cometary motions.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2845540