Hall, Glen R.Atanasova, Diana2020-03-032020-03-032020https://hdl.handle.net/2144/39615In this thesis, we consider the planar parabolic, hyperbolic, and highly-elliptic restricted three-body problems (R3BP). In particular, we formulate sufficient conditions for no transit (escape of the infinitesimal body) to occur in the near-parabolic R3BP using the disturbing function derived in Mamedov (1987) as our starting point. We take a middle approach between purely numerical and strictly analytic in the form of infinite series expansions to derive approximation mappings modeling the dynamics. Motivated by the long-term dynamics of the highly-elliptic R3BP, we study an annulus map with properties which are unexpectedly different from those of the "standard" annulus map.en-USMathematicsAnnulus mapParabolic restricted three-body problemTransit orbitsThesis/Dissertation2020-02-28