Low Thrust Trajectories From Low Earth Orbits to the Moon

Open Access
Al Jaberi, Saeed
Area of Honors:
Aerospace Engineering
Bachelor of Science
Document Type:
Thesis Supervisors:
  • Robert Graham Melton, Thesis Supervisor
  • David Bradley Spencer, Faculty Reader
  • George A Lesieutre, Faculty Reader
  • Robert Graham Melton, Honors Advisor
  • Astrodynamics
  • the Three Body Problem
  • CR3BP
  • Low Thrust
  • Jacobi Integral
The bases and principles of the circular restricted three body problem (CRTBP) were analyzed and used to find spacecraft trajectories between a low-Earth orbit to the Moon. Since CRTBP does not have a general solution, numerical techniques were adapted to find approximated solutions. The most important parameter in the study was the Jacobi constant C. The Jacobi integral (constant) is the only conserved quantity in the three body system. Different values of C correspond to different geometries and permissible regions for a spacecraft in the Earth-Moon system. These permissible regions are delimited by the zero-velocity curves. Transverse, constant-level thrust trajectories were simulated to examine the range of C values that could be reached. The goal was to reach a Jacobi constant of -1.59411; at this value, the permissible region of the spacecraft expands enough to allow a transfer from Earth’s orbit to an orbit around the Moon. Only a reachability criterion was considered; the optimal control problem of how to steer the thrust to achieve a lunar arrival is beyond the scope of this research.