Testing weakest force with coldest spot

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 $N\sim10^6-10^8$, is feasible to constrain the modified Newtonian potential with Yukawa interaction greatly beyond the current exclusion limits.