The center of mass of a satellite, which consists of two masses connected by a rigid, massless tether, moves in a circular non-equatorial orbit about an oblate planet. The satellite is made to tumble forward essentially in the orbital plane such that its average pitch rate relative to the local vertical equals the orbital rate. This tumbling motion is phased such that the tether axis is aligned with the local vertical 1/8th of an orbit prior to each crossing of the equatorial bulge and with the local horizontal 1/8th of an orbit alter each crossing. The angular momentum of the orbit is increased by this phasing of the force from the equatorial bulge with the variations in satellite orientation. Periodic modulation or "pumping" of the tether length in resonance with the equatorial crossings is required to maintain this phasing, and the resulting transfer of energy from the pumping mechanism to the orbit increases the altitude of the mass center.;The dynamics of this orbit-boosting effect are examined in detail through a second-order perturbation analysis. Elastic deflections of the tether and the effects of atmospheric drag are neglected. Equations of motion governing the orbital and attitude behavior of the satellite are presented, and a formula for the rate of orbit-boosting is obtained and shown to be maximized for a polar orbit. The correct schedule for varying the tether length is derived through consideration of the rate of work required by the tether-pumping mechanism. The analytical results for the polar orbit case are checked through a numerical simulation which includes a feedback control scheme for maintaining the optimum orbit/attitude phasing. Out-plane deviations from the nominally in-plane tumbling motion are analyzed for the non-polar orbit case and are shown to remain small. The effects of higher-order perturbations and some practical application issues are also discussed.
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