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We have developed a sensitive gravimeter concept that uses an extremely low-friction bearing based on a permanent magnet (PM) levitated over a high-temperature superconductor (HTS). A mass is attached to the PM by a cantilevered beam, and the combination of PM and HTS forms a bearing platform that has low resistance to rotational motion but high resistance to horizontal, vertical, or tilting motion. The combination acts as a low-loss torsional pendulum that can be operated in any orientation. Gravity acts on the cantilevered beam and attached mass, accelerating them. Variations in gravity can be detected by time-of flight accelerator, or by a control coil or electrode that would keep the mass stationary. Calculations suggest that the HTS gravimeter would be as sensitive as present-day superconducting gravimeters that must be cooled to liquid helium temperatures, but the HTS gravimeter needs cooling only to liquid nitrogen temperatures.