﻿ Gravitational potential

# Gravitational potential

The gravitational field is in physics, a force field that is caused by the existence of masses and is manifested by an attractive force on other masses. It is in the classical mechanics, thus, the cause of the gravitation. In the physics literature the term gravitational field is occasionally synonymous with the gravitational field, in the stricter sense, especially in geodesy but also astronomy, however, this is a composite of the gravitational field and the centrifugal force field to describe the effective acceleration on rotating celestial bodies, such as the earth and is therefore treated separately there.

## Potential and field

The field -causing potential is called gravitational potential. The gravitational field can be written as gradient of the gravitational potential:

Where the location is. The gravitational field, ie, the force generated by the field on a body of mass, then

The term represents the potential energy Represents the potential can be determined by solving the Poisson equation for a known mass density

The gravitational constant.

## Field strength

The amount of the gravitational field is called gravitational field strength or gravitational acceleration. What is special is that the acceleration is independent of the sample mass ( the mass of a body in the field). Work no other forces as is the exact acceleration of a test mass in the field.

A point mass has the potential

And the corresponding radially symmetric field

At intervals, which are orders of magnitude greater than the extent of the mass, any mass can be annhähernd considered as point-like. A proof mass is in this gravitational field, we obtain directly the Newtonian law of gravitation, which is the amount of attractive force acting between the centers of mass located at a distance, :

Since each any substantial ground in ( almost ) point-like mass parts can be disassembled, you can turn any gravitational field as a sum of many point masses represent:

The locations of the point masses.

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