# Two bodies gravitational system with variable mass and damping-antidamping effect due to star wind

## TL;DR

This paper investigates a two-body gravitational system with variable mass and damping effects caused by star wind, deriving key physical quantities and applying the model to comet Halley.

## Contribution

It introduces a novel model incorporating variable mass and damping-antidamping effects in a gravitational two-body problem, with explicit derivations of constants of motion, Lagrangian, and Hamiltonian.

## Key findings

- Derived constant of motion, Lagrangian, and Hamiltonian for the system.
- Analyzed the period of motion using the constant of motion.
- Applied the model to simulate comet Halley's motion.

## Abstract

We study two-bodies gravitational problem where the mass of one of the bodies varies and suffers a damping-antidamping effect due to star wind during its motion. A constant of motion, a Lagrangian and a Hamiltonian are given for the radial motion of the system, and the period of the body is studied using the constant of motion of the system. An application to the comet motion is given, using the comet Halley as an example.