The path to which the ISEE-3 satellite is controlled is a periodic solution to the three-dimensional equations for motion about the interior libration point of the sun-Earth-satellite three-body system. These particular periodic halo orbits are constructed using analytical and numerical methods. The third-order analytical solution is obtained by application of successive approximations in conjunction with a form of the LindstedtPoincart method. The ISEE-3 mission orbit is one member of a family of orbits which are locally approximated by the analytical development. This orbit is produced from standard differential corrections procedures using the third-order solution as the initial approximation.
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D. L. Richardson (1980) studied this question.
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