The Numerical Determination of Nominal Libration Point Trajectories and Development of a Station-Keeping Strategy


In the circular restricted three-body problem, three-dimensional bounded motion associated with the collinear libration points is known to exist from previous studies. One such type of trajectory is a "Lissajous" orbit, named after a French physicist of the 1800s. Future mission plans include trajectories near the interior libration point (L_1) in the Sun-Earth system and may consider Lissajous orbits as part of the trajectory design. Except for the special case of the halo orbit, the numerical computation of Lissajous paths has been limited. The present work considers the determination of such trajectories numerically for an arbitrary, predetermined number of revolutions. A method developed previously for the numerical determination of such orbits in the circular restricted three-body problem is extended for use in the elliptic restricted three-body problem, as well as with a model that uses polynomial representations of ephemeris data to locate an arbitrary number of attracting bodies. A spacecraft moving on a Lissajous path near the L_1 libration point of the Sun-Earth system will occasionally cross the solar disk (as seen from Earth), and the intense solar activity will result in the loss of the communications link to Earth. Previous studies provide linear estimates for maneuvers directed perpendicularly to the ecliptic plane that "shape" the orbit such that the spacecraft remains a "safe" distance from the excluded region. Another result for this study, then, was the extension of this method to a higher (third) order analysis. Finally, the third order maneuver estimates were used to numerically compute Lissajous trajectories that incorporate this strategy. Since Lissajous trajectories are, in general, unstable, spacecraft moving on these paths must use some form of trajectory control to remain close to their nominal orbit. While many station-keeping studies for Earth-orbiting spacecraft have been completed, similar effects have not yet been directed toward investigations involving spacecraft in libration point orbits. A final goal for this effort was the development of a station-keeping strategy applicable to libration point trajectories. A method was developed that uses maneuvers executed (impulsively) at discrete time intervals. The analysis included investigation of a number of the problem parameters that affect the overall maneuver (propellant) costs. A number of sample orbits that use trajectory design parameters associated with three missions currently under development and scheduled for launch later this decade are presented to demonstrate the successful use of the techniques. The results from numerous station-keeping simulations are also summarized to facilitate evaluation of the adopted strategy.


Mechanical and Aerospace Engineering



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