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An introduction to the dynamics of an electrostatically charged spacecraft in two-and three-body regimes is presented, with particular attention to a promising application at Enceladus. Equilibrium solutions to the equations of motion are found, and the stability of the orbits assessed. The perturbative Lorentz force, produced by interaction of the spacecraft with a planetary magnetic field, creates trajectories that are not possible with Newtonian gravity alone. A heuristic, analytical control law with single-variable scalar feedback allows a charged spacecraft to remain near the collinear Lagrange points on either side of Enceladus. The mission feasibility depends on the charge requirement, which is primarily affected by the navigational accuracy. For example, an insertion error into the cis-Enceladus Lagrange point of 10 km in position and 1 m=s in velocity requires a specific charge of approximately 0:05 C=kg. Other significant gravitating bodies in the Saturnian system do not have a substantive effect on the charge requirements or on the stability. Given a sufficiently accurate insertion, a charged spacecraft could maintain station near Enceladus without propellant. Nomenclature A= magnetic vector potential, T km A = tether cross-sectional area, mm 2 a = acceleration vector at Enceladus, m=s 2 a = acceleration at Enceladus, m=s 2 B = magnetic field vector, T B 0 = magnetic moment, T km 3 E = planetary electric field vector, km=s 2 C F g = specific gravitational force vector, km=s 2 F L = specific Lorentz force vector, km=s 2 I = tether current vector, C=s I = tether current, C=s L = Lagrangian, km 2 =s 2 l = length of tether, km M = generalized specific angular momentum, km 2 =s m tot = total mass of tether spacecraft, kg P = tether power, W q = specific charge, C=kg R = radius of reference circular orbit, km r = position vector, km r = radial unit vector r = radial coordinate, km r E = orbital radius of Enceladus, km U eff = effective potential, km 2 =s 2 u k = roots of the effective potential (k 1, 2, 3), km 1 V = tether voltage, V v = inertial velocity, km=s v rel = velocity relative to magnetic field, km=s Z = resistance of tether ribbon, = tuning parameter of control law v i = perturbation of velocity in the i-coordinate direction, km=ŝ = polar unit vector = polar coordinate, rad = gravitational parameter, km 3 =s 2 E = gravitational parameter of Enceladus, km 3 =s 2 S = gravitational parameter of Saturn, km 3 =s 2 = azimuthal unit vector = azimuthal coordinate, rad = resistivity of tether material, m = orbital angular velocity of Enceladus, rad=s ! = planetary rotational angular velocity, rad=s ! S = rotational angular velocity of Saturn, rad=s

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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