Analytical theory for orbits of electrostatically charged spacecraft and direct calculation of planet-to-planet transfers

Joseph W Gangestad, Purdue University


The first three-quarters of this thesis reports on the results of the development of analytical theory to describe the motion of electrostatically charged spacecraft in a planetary magnetic field. The motion of an electrostatic charge in a magnetic field yields a Lorentz force, which, when applied to a spacecraft, produces a source of propellantless thrust that may be harnessed to alter the vehicle’s orbit. The equations of motion for electrostatically charged spacecraft are developed in two- and three-body regimes, and equilibria and the stability of orbits are investigated. An equilibrium solution identified in the three-body system produces a control law that permits propellantless, marginally stable stationkeeping orbits near Enceladus, a moon of Saturn. Notably, the feasibility of such a mission is primarily affected by the navigational accuracy, rather than the charge level. Next, Lagrange’s Planetary Equations are derived with the Lorentz force as the orbital perturbation. The orbital elements are coupled, but the coupling in equatorial orbits is independent of charge level and magnetic field strength. Analytical expressions that characterize this coupling demonstrate constraints on the Lorentz force’s ability to raise a Lorentz spacecraft’s orbital energy to escape, and a numerically integrated example of escape at Jupiter confirms the analytical results. A closed-form solution exists that constrains the set of equatorial orbits for which planetary escape is possible, and a sufficient condition is identified for escape from inclined orbits. Lastly, the analytical theory is extended to accommodate propellantless planetary capture with the Lorentz force. Analytical solutions are applied to a capture at Jupiter and compared to similar arrival scenarios with the Galileo and Juno spacecraft. The last quarter of the thesis, on a separate topic, identifies a new parameterization of the tour-design problem, dubbed “FastTour,” that permits direct calculation of planet-to-planet transfers without the need for solving Lambert’s problem or performing so-called “ v8-matching.” Solution for the roots of a single function on a finite domain yields the transfer orbit and all of its associated quantities (e.g. orbital elements and time of flight). This parameterization also enables calculation of launch windows, whereby entire ranges of the parameter space, such as departure date, can be disqualified from containing candidate trajectories, eschewing the need (as in traditional methods) to perform computationally costly function evaluations where no transfers exist. Compared against the traditional tour-design algorithm, FastTour calculates pork-chop plots 7–10 times faster.




Longuski, Purdue University.

Subject Area

Aerospace engineering

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