To the dynamics of the two-body problem with variable masses in the presence of reactive forces

Ibraimova A.T. Zh Minglibayev M.
2023 Cambridge University Press

Proceedings of the International Astronomical Union
2023 #17 Issue S370 281 - 282 pp.

We studied the problem of two spherical celestial bodies in the general case when the masses of the bodies change non-isotropically at different rates in the presence of reactive forces. The problem was investigated by methods of perturbation theory based on aperiodic motion along a quasi-conic section, using the equation of perturbed motion in the form of Newton’s equations. The problem is described by the variables a, e, i, π, ω, λ, which are analogs of the corresponding Keplerian elements and the equations of motion in these variables are obtained. Averaging over the mean longitude, we obtained the evolution equations of the two-body problem with variable masses in the presence of reactive forces. The obtained evolution equations have the exact analytic integral a³e⁴ = a³₀e⁴₀ = const.

osculating elements , perturbation theory , reactive force , stars: mass loss , two-body problem , variable masses

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Fesenkov Astrophysical Institute, Almaty, Kazakhstan
Al-Farabi Kazakh National University, Almaty, Kazakhstan

Fesenkov Astrophysical Institute
Al-Farabi Kazakh National University

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