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I investigate whether, in the context of Newtonian physics, a satellite can change its orbit by cyclic shape changes without any external forces other than gravity. This question has been discussed in the context of general relativity, and Wisdom has estimated that a swimmer near the surface of the Earth using meter-sized deformations can achieve a displacement of ~10^–23 m. I show that much larger displacements, ~10^–7 m, can occur for a Newtonian swimmer. Such a swimmer can change its orbit by rotating about its center of mass and trading chemical, solar, or other energy for orbital energy, without the need for any propellant. ©2004 American Association of Physics Teachers.