V

Fig. 9.5. The Lagrange points.

and two similar equations with the numbers 1, 2, and 3 permuted cyclically. There are two possibilities. Either r1 x r2 = r2 x r3 = r3 x r1 = 0, in which case the masses lie in a straight line, or r12 = r23 = r31, in which case the particles lie at the vertices of an equilateral triangle. In both cases, the equations can be integrated completely, but further work needs to be done to establish

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