Abstract
A special case of the 3-body problem is the limiting case in which one of the masses tends to zero. In the traditional derivation of the restricted 3-body problem, one is asked to consider the motion of a particle of infinitesimal mass moving in the plane under the influence of the gravitational attraction of two finite particles that move around each other on a circular orbit of the Kepler problem. Although this description is picturesque, it hardly clarifies the relationship between the restricted 3-body problem and the full problem. Here we shall find the equations of first approximation when one mass tends to zero which then defines the restricted problem.
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