Details

Autor(en) / Beteiligte

• Haranas, Ioannis
• Shehata, Youssef M.
• Cobbett, Kristin
• Gkigkitzis, Ioannis
• Kalafatis, Dimitrios Theodore
• Gauthier, Ryan

Titel

The Invariance of the Tisserand Parameter in Various Gravitational Theories

Ist Teil von

• Earth, moon, and planets, 2023-10, Vol.127 (2), p.3, Article 3

Ort / Verlag

Dordrecht: Springer Netherlands

Erscheinungsjahr

2023

Quelle

Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals

Beschreibungen/Notizen

• In today’s gravity research there exists a number of gravitational theories which predict the existence of various corrections to the classical gravitational potential. In this paper using the different potentials that exist in the literature and with the help of Gauss’ planetary equations we examine the time rate of change of the Tisserand parameter as a function of the time rate of change of the three orbital elements involved. We find that the Tisserand parameter remains constant over a full orbital revolution in all the different potential resulting from the various theories. This fortifies and generalises the use of Tisserand parameter not only in case of Newtonian dynamics but also in more extended theories of gravity, thus ensuring its validity in determining the identity of a returning comet. Furthermore, we find that the parameter remains unchanged even in the case where a gravitational potential derived from a D- dimensional gravitational force, in the case where D  = 4. Next quantization of orbits calculation is performed and the constancy of the Tisserand parameter is also recovered. Finally, assuming fractal orbits we obtain an expression for the fractal dimension of three well known Jupiter family comets in terms of their orbital elements and the constancy of the Tisserand parameter is also recovered.