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

Abstract

Abstract 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 ${a^3 e^4 = a^3_0 e^4_0} = {const}$ .

More by Mukhtar Minglibayev

• DIFFERENTIAL MOTION EQUATIONS OF THE VARIABLE-MASS THREE-BODY PROBLEM WITH REACTIVE FORCES IN A BARYCENTRIC COORDINATE SYSTEMJournal of Mathematics Mechanics and Computer Science · 2026
• Secular Perturbations of Translational–Rotational Motion of an Axisymmetric Body in the Restricted Three-Body Problem with Variable MassesAxioms · 2026
• The equation of motion for the variable mass TRAPPIST-1 exoplanet system in the Jacobi coordinate systemBulletin of the National Engineering Academy of the Republic of Kazakhstan · 2026
• EXACT SOLUTIONS OF EQUATIONS OF THE TWO-PRIMARY-BODY PROBLEM IN THE RESTRICTED THREE-BODY PROBLEM WITH VARIABLE MASSESJournal of Mathematics Mechanics and Computer Science · 2025