# Gravitation: Potential

### Terms

#### Terms

Gravitational potential energy  -  Is defined by the integral:

 U(r) = -

Where is the force due to gravity and we define U(∞) = 0 . Doing the integral gives:

 U(r) = -

which reduces to U = mgh near the earth.
Gravitational potential  -  Is defined as the gravitational potential energy that a 1 kilogram mass would have at some point in space. It is given by:

 Φ g = -

which reduces to Φ g = gh near the earth.
Principle of Equivalence  -  Asserts that all types of matter fall at the same rate. That is, g for a brick is the same as g for water. This means that the inertial mass appearing in Newton's Second Law is equivalent to the gravitational mass appearing in the Universal Law of Gravitation.
Inertial mass  -  The mass m i that appears in Newton's Second Law F = m i a .
Gravitational mass  -  The mass that appears in the Universal Law of Gravitation.
Shell Theorem  -  States that any spherical mass can be treated as though all its mass were concentrated at its center for the purposes of calculating gravitational force. Also, that a spherical shell of matter exerts no gravitational force on a mass inside it.

#### Formulae

Energy for a circular orbit around the sun

 E =

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