Newtonian and relativistic theory of orbits and emission of gravitational waves

TL;DR

This review explores the classical and relativistic theories of orbital motion, including gravitational wave emission, focusing on the Newtonian framework, post-Newtonian corrections, and various orbit classifications.

Contribution

It provides a comprehensive comparison of Newtonian and relativistic orbital theories and calculates gravitational wave luminosity for different stellar encounters.

Findings

Derived gravitational wave luminosity for various orbit types

Analyzed relativistic corrections to orbital motion

Classified orbits based on motion conditions

Abstract

This review paper is devoted to the theory of orbits. We start with the discussion of the Newtonian problem of motion then we consider the relativistic problem of motion, in particular the PN approximation and the further gravitomagnetic corrections. Finally by a classification of orbits in accordance with the conditions of motion, we calculate the gravitational waves luminosity for different types of stellar encounters and orbits.