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The use of propellant to maintain the relative orientation of multiple spacecraft in a sparse aperture telescope such as NASA's Terrestrial Planet Finder (TPF) poses several issues. These include fuel depletion, optical contamination, plume impingement, thermal emission, and vibration excitation. An alternative is to eliminate the need for propellant, except for orbit transfer, and replace it with electromagnetic control. Relative separation, relative attitude, and inertial rotation of the array can all be controlled by creating electromagnetic dipoles on each spacecraft, in concert with reaction wheels, and varying their strengths and orientations. Whereas this does not require the existence of any naturally occurring magnetic fields, such as the Earth's, such fields can be exploited. Optimized designs are discussed for a generic system and a feasible design is shown to exist for a five-spacecraft, 75-m baseline TPF interferometer. NomenclatureA c = conductor cross-sectional area a = coil radius c = conductor current density c 0 = constant defined in Eq. (8) i = current J = mission efficiency metric l c = conductor length m coil = electromagnetic coil mass m em = electromagnetic mass m sa = solar array mass m sys = total system mass m tot = total spacecraft mass m 0 = core bus and payload mass n = number of coil turns P = power P w = solar array specific power p c = conductor resistivity R = resistance r = conductor radius s = array baselinë x = spacecraft acceleration γ = mass fraction of total electromagnetic mass η = amp turns µ 0 = permeability of free space ρ = coil density = relative mission efficiency ω = rotation rate

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Effects of the second order perturbative term of the Earth's geopotential on clusters of satellites are analyzed by adding the linearized J2 force onto the right side of Hill's equations as a forcing function. A continuation of previous work, the equations of motion are generalized to orbits of all inclinations, and terms are identified that account for rotation of periapsis within the orbital plane, as well as precession of the longitude of the ascending node. The effect of the periapsis rotation on the cluster is identified as a 'tumbling' mode of the system. Accuracy of the linearization is determined by comparison of the analytic solutions with those obtained using an orbit propagator.