A Cryogenic Resonant Sphere in Deep Space Listening for the High-Frequency Tail of a Bounce Spectrum

This paper presents a space mission design, computed from stated assumptions and not measured, built to measure one quantity: the characteristic strain of the bounce spectrum tail at 3 kilohertz, for which the design case adopts 1.10e-21 in characteristic strain. The instrument is a 60-centimetre solid niobium sphere cooled to 50 millikelvin, suspended in a drag-free spacecraft at a Lagrange point, with six resonant transducers on its surface that together reconstruct the amplitude and direction of any excitation of its quadrupole modes. It operates from a halo orbit about the Sun-Earth L1 point, chosen for an unobstructed view of the Sun-facing hemisphere and steady thermal input for 3 years. The one-day measurement uncertainty is 4.00e-21 in characteristic strain; averaged over the full mission of 1096 days it falls to 1.21e-22 in characteristic strain, giving a signal-to-noise ratio of 9.1 for the design case and a five-sigma detection limit of 6.04e-22 in characteristic strain. The spacecraft has a dry mass of 1610 kilograms, a wet mass of 1800 kilograms including propellant, and a total electrical load of 3082 watts supplied by a solar array of 8.71 square metres at the operating distance. Every performance figure in this paper comes from the deposited computation; the design is simulated, not measured, and no hardware described here has been built or flown.