Abstract
Ultra-cold atom experiment in space with microgravity allows for realization of dilute atomic-gas Bose-Einstein condensate (BEC) with macroscopically large occupation number and significantly long condensate lifetime, which allows for a precise measurement on the shape oscillation frequency by calibrating itself over numerous oscillation periods. In this paper, we propose to measure the Newtonian gravitational constant via ultra-cold atom BEC with shape oscillation, although it is experimentally challenging. We also make a preliminary perspective on constraining the modified Newtonian potential such as the power-law potential, Yukawa interaction, and fat graviton. A resolution of frequency measurement of (1-100),mathrm {nHz} at most for the occupation number 10^9, just one order above experimentally achievable number Nsim 10^6{-}10^8, is feasible to constrain the modified Newtonian potential with Yukawa interaction greatly beyond the current exclusion limits.
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