Gravitational Potential Energy!

The gravitational potential energy of the earth (for example) is given by

UG(r) = - mgRe2/r,
where Re is the earth's radius and g is the gravitational acceleration on the surface. Notice that the potential energy is always negative, and that it goes to zero only at an infinite distance from the earth. On the surface of the earth it has the (negative) value UG(Re ) = - mgRe.

The “escape speed” at any point, near any body in space, is the speed that will result in a total energy E = 0 for another body which is instantaneously at that point!

Remember that we have two conserved quantities in orbital motion: the total energy E and the angular momentum vector L.

Center of Mass and Orbits!

Elliptical Orbits!