An investigation of the propellant economies of using the gravitational attraction of Jupiter's four large moons to effect the transfer of a spacecraft into orbit around that planet. Use of a simplified model to approximate the maximum possible energy change as a function of the approach energy shows that the maximum energy loss from a flyby of Ganymede, the largest moon, is less than half that required to transfer from a high-thrust approach trajectory to an acceptable elliptical orbit. Thus, chemical retrothrust is necessary to effect the transfer, and a moon swingby may not be justified. With a low-thrust trajectory approach, however, economical gravity assist from a moon is more promising. The lower approach energies of optimal low-thrust trajectories can be further reduced by retrothrusting, and guidance problems are more easily handled. A no-impulse capture could result in a final orbit with a one-year orbital period. Moreover, the relaxation of the required velocity endpoint conditions for low-thrust trajectories may allow significantly increased payloads or shorter flight times. 51 pp. Ref.