Test of the gravitational interaction between milligram masses using a miniature torsion pendulum

Abstract Precision tabletop measurements of gravitational force are important for probing the fundamental nature of gravitation. Although gravitational experiments have spanned test masses from macroscopic objects to individual quantum systems, the mutual gravitational interaction between small—particularly microscopic—masses remains largely unexplored. Recent advances have extended such studies into the sub-100 mg regime, however, probing gravitation at still smaller masses continues to pose significant challenges. Here, we report a measurement of gravitational interaction between two 7.6 mg silicon wafers using a miniature Cavendish-type torsion balance combined with a rotating mass-modulation technique. Over separation distances from 0.654 to 1.554 mm, the measured forces agree with Newtonian predictions, achieving a maximum uncertainty of 50 aN (2 σ ) and enabling constraints on Yukawa-type deviations from Newtonian gravitation. From these data, we determine the gravitational constant G = 6.67(35) × 10 −11 m 3 kg −1 s −2 (1 σ ). This work measured the gravitational interaction between milligram-scale objects, representing a significant step toward bridging the classical and quantum regimes of gravitation.