Abstract
Although the classical N-body problem plays a fundamental role in modeling space systems, its assumption of constant mass is often insufficient for accurately describing many phenomena in the real world. A dynamic description of the variable mass N-body problem is a pressing issue for investigating phenomena such as stellar mass loss in space systems or the motion of space vehicles. In this work, the equation of motion for the seven-planet TRAPPIST-1 exoplanetary system, which has variable, non-isotropic masses and reactive forces, is derived in the absolute, relative, and, specifically, the Jacobi coordinate systems. Jacobi coordinates simplify the system’s kinetic energy compared to the traditional common center-of-mass coordinates and allow the problem to be separated into independent two-body problems. The bodies attract each other according to Newton’s law of universal gravitation, while the variability of mass leads to the appearance of reactive forces, which significantly complicate the problem. To simplify the internal dynamics of the system and increase computational stability, the problem was investigated using Jacobi coordinates, and the differential equations of motion were obtained. This research offers a new, more precise method for the analysis and computation of the dynamics of variable mass systems. Based on these differential equations, one can adopt the barycentric coordinate system and apply perturbation theory.