Abstract
A spacecraft that generates an electrostatic charge on its surface in a planetary magnetic field will be subject to a perturbative Lorentz force. Active modulation of the surface charge can take advantage of this electromagnetic perturbation to modify or to do work on the spacecraft’s orbit. Lagrange’s planetary equations are derived using the Lorentz force as the perturbation on a Keplerian orbit, incorporating orbital inclination and true anomaly for the first time for an electrostatically charged vehicle. The planetary equations reveal that orbital inclination is a second-order effect on the perturbation, explaining results found in earlier studies through numerical integration. All of the orbital elements are coupled, but the coupling notably does not depend on the magnitude of the electrostatic charge or on the strength of the magnetic field. Analytical expressions that characterize this coupling are tested with a propellantless escape example at Jupiter. 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. The analytical solutions agree with results from the numerically integrated equations of motion to within a fraction of a percent.
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Gangestad, J.W., Pollock, G.E. & Longuski, J.M. Lagrange’s planetary equations for the motion of electrostatically charged spacecraft. Celest Mech Dyn Astr 108, 125–145 (2010). https://doi.org/10.1007/s10569-010-9297-z
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DOI: https://doi.org/10.1007/s10569-010-9297-z