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 LawF = 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 = 

