  In this talk, we report our recent study of constraining the non-Newtonian
gravity at femtometer scale. We incorporate the Yukawa-type non-Newtonian
gravitational potential consistently to the Skyrme functional form using the
exact treatment for the direct contribution and density-matrix expansion method
for the exchange contribution. The effects from the non-Newtonian potential on
finite nuclei properties are then studied together with a well-tested Skyrme
force. Assuming that the framework without non-Newtonian gravity can explain
the binding energies and charge radii of medium to heavy nuclei within 2%
error, we set an upper limit for the strength of the non-Newtonian
gravitational potential at femtometer scale.
