Symmetries in the Popovici-Manev photogravitational field

The Popovici-Manev photogravitational field is generated by a Manev-type attraction force and the repelling radiative force considered by Constantin Popovici. The equations of the two-body problem in this field are written as a system of first-order ODE, and  the symmetries of the system are displayed. It is proved that the group of symmetries of the problem in either Cartesian or polar coordinates is (a) a subgroup (with four elements) of the group of symmetries (with eight elements) of the two-body problem associated to a quasihomogeneous potential; (b) isomorphic to Klein’s group. These properties hold also for collision-blow-up and infinity-blow-up McGehee-type coordinates. If we apply Levi-Civita regularizing transformations, the vector field admits a group of symmetries with eight elements, but its subgroup which is physically meaningful is again isomorphic to Klein’s group.

Mira-Cristiana Anisiu
Tiberiu Popoviciu Institute of Numerical Analysis

Vasile Mioc
Astronomical Institute of the RomanianAcademy

celestial mechanics – photogravitational models – symmetries.

M.-C. Anisiu, V. Mioc, Symmetries in the Popovici-Manev photogravitational field, Rom. Astron. J. 14 (1) (2004), 71-80

https://www.astro.ro/~roaj/volume/abs14_1.html#7

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