THERE are five equilibrium points to be found in the vicinity of two orbiting masses. They are called Lagrange Points in honour of the French-Italian mathematician Joseph Lagrange, who discovered them while studying the three-body problem in which two of the masses are very much heavier than the third. These Lagrange Points occur as stationary solutions to the equations of motion when the relative positions of the three bodies are fixed. That is, the three bodies maintain a constant separation between any two of the bodies.
The stability of Lagrange Points L1 and L2 is an important consideration for some of the space missions. Currently, the solar observatory SOHO is parked at L1. MAP will be positioned at L2. NASA's Next Generation Telescope is also proposed to be stationed at L2. Both L1 and L2 are sort of semi-stable points. That is, small departures from equilibrium will tend to grow exponentially with time. A satellite parked at L1 or L2 will wander off within a few months unless periodic course corrections are applied.
