esanmouli / phy637

PHY637

Effective Potential of the Reduced Three Body Problem and Lagrange Points

• Solving the three body problem requires finding the trajectory of three masses with some initial velocities which move under their mutual gravitational interactions.

• A highly non-linear and chaotic system, no analytical solutions yet

• One way to find an analytical solution- by considering one mass to be negligible (i.e. a first order approximation) - this is the reduced three body problem.

• Under this approximation, forces acting on the smallest mass are:

1. Gravitational force due to the two large masses

2. Centrifugal force

3. Coriolis force

• This allows us to solve for the velocities of the small mass with a first order approximation

• This gives rise to five special points- Lagrange points that remain stationary with respect to the frame of reference, i.e. all forces cancel out at these points, giving rise to zero relative motion.

• The effective potential and Lagrange points of the Sun-Earth system is given by: Link text Here