Effective potential

The effective potential is a term of the mechanics, which is useful in the treatment of central forces, such as the gravitational force in the planetary motion. The azimuthal energy movement is combined with the potential energy in the effective potential.

A body that moves in a central force field at a distance from the center of power, has a total energy which is composed of the potential energy and kinetic energy. In polar coordinates, we have:

The azimuthal fraction of the kinetic energy can be obtained by the angular momentum

Express and summarize the potential energy:

Wherein said effective potential is defined as follows:

The second term on the right side of this equation is also referred to as centrifugal potential barrier or angular momentum.

Since the angular momentum in a central force is constant, one now has to deal only with an ordinary differential equation in the radial coordinate, which is to be solved. The solution of the differential equation is done by applying the method of separation of variables with the constants of motion and as parameters.

For initially results in two intersections and with the effective potential curve between which the body moves in its orbit. Both distances coincide for the minimum of the effective potential and obtained a circular orbit.

See also: Central force and centrifugal potential in the article centrifugal

• Classical Mechanics