  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.
