# Newtonian Gravity

# Overview

Gravitation is the principal force that acts over large distances. Gravity cannot
be counteracted, as electromagnetism can, by a rearrangement of gravitational charge;
unlike electric charge, mass always exerts an attractive force. Gravity is
the driving force behind the creation and evolution of stars, galaxies,
and clusters of galaxies. The evolution of the very universe dependent on gravity.

The current theory of gravity is general relativity. Normally when one studies massive
compact stars such as neutron stars or subtle effects such as the perihelion shift of Mercury
or the deflection of light by a star, one must use general relativity. For most problems,
however, the predecessor to general relativity, Newtonian gravity, is sufficient.
Newtonian gravity accurately describes the motion of the planets around the Sun,
the orbit of most binary star systems, the evolution of galaxies, and the local expansion
of the universe.

The general motions of gravitating bodies is very complex. The general three-body problem
has no simple solution. In larger self-gravitating star systems,
the gravitational field changes as the stars execute their orbits. These systems
can only be studied through computer simulation. But in astrophysics we do encounter
many systems with simplifying properties.

## Keplerian Orbits

The Keplerian orbit is the orbit of an object in a binary system. Keplerian orbits describe
the orbits of binary stars, and, to high accuracy, they describe the orbits of the planets
around the Sun. The characteristics of this orbit are easily derived from Newtonian mechanics.
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## Orbits in Isotropic Stellar Systems

The orbits of stars in isotropic stellar systems is a starting point
for exploring the physics of galaxies. When a star orbits
in a self-gravitating stellar system, the orbits are generally open.
Some features of Keplerian orbits, however, are preserved in
the more general gravitational fields of a spherically-symmetric stellar system.
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## Gravitational Stability of Star Systems

The stability of a group of stars depends on the interplay between the velocities of individual stars with the gravitational field of the stellar group. The stability of the group is described by the Jeans length and the Jeans mass. (continue)