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Driven by the desire to find positions that satisfy keepout constraints for aspace-based telescope mission, this work develops a process for tracing a pointin space in the regime of the restricted three-body problem to a halo orbit,characterized by its out-of-plane amplitude, and its position on that haloorbit, denoted by the halo orbit time. This process utilizes third-ordersolutions from the Lindstedt-Poincare method, which have been partiallyinverted to expect a point in space as an input. Three different methodologiesthat use these partially inverted expressions are presented. Results areproduced for 1,000 randomly selected points using all three methods and arecompared to truth. Ultimately, the method that employed two distinct accuracymetrics yielded the most accurate results for the dataset.

Tracing Position in the Regime of the Restricted Three-Body Problem to a Halo Orbit