Regions of prevalence in the coupled restricted three-body problems approximation

This work concerns the role played by a couple of the planar circular restricted three-body problem in the approximation of the bicircular model. The comparison between the differential equations governing the dynamics leads to the definition of region of prevalence where one restricted model provides the best approximation of the four-body model. According to this prevalence, the patched three-body problem approximation is used to design first guess trajectories for a spacecraft travelling under the Sun–Earth–Moon gravitational influence.

► Approximation of the bicircular model by means of CR3BP.
► Local analysis leads to definition of regions of prevalence.
► Intersecting invariant manifolds for low energy transfer.
► Efficient numerical method based on Box covering technique.