We describe the status of a project aimed at building an improved superconducting microwave cavity system suitable for use on the International Space Station, ISS. Cavity frequency variations are mainly caused by acceleration effects due to gravity and vibrations, temperature variations, and fluctuations in the energy stored in the cavity. At present, acceleration effects appear to be the predominant limit, and a new support system has been designed to reduce the effect. Significant applications include the measurement of general relativistic effects, the time-dependence of the fine structure constant and the measurement of the anisotropy of the velocity of light, either with two cavities or in conjunction with other types of clocks. Another important application is as a low noise flywheel oscillator for the atomic clocks co-located on ISS.
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