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ABSTRACT We investigate the secular evolution of a four-body planetary system, where two planets move around a binary star configuration on quasi-elliptic orbits. It is assumed that the masses of all bodies can change isotropically at different rates and the bodies attract each other according to Newton’s law of universal gravitation. The purpose of this work is to investigate an influence of variability of the masses of the binary stars and their planets on the dynamical evolution of the planetary system. We consider the case of small eccentricities and inclinations of the bodies orbits and assume that their orbits do not intersect during evolution. Differential equations of the perturbed motion in the osculating analogues of canonical Poincaré elements were obtained in a general case of the many-body problem with variable masses in our previous work. Here we solve these equations numerically and investigate the secular evolution of some fictitious circumbinary 2-planet system under assumption that the two stars of the binary system lose their masses independently at different rates. In order to demonstrate the dynamical features of the equations we use the known parameters of the TOI-1338 system. Comparing the results of calculations in the cases of constant and variable masses, we show that the isotropic variability of the masses of bodies can influence substantially the secular perturbation of the orbital elements.
Minglibayev et al. (Sat,) studied this question.