《A Regularized Two-Body Gravity Formula with No Free Parameters》

Newton's law of universal gravitation F = GM1M2/r^2 diverges as r → 0. This paper proposes a minimal regularization scheme: replacing the singular denominator r^2 with r^2 + r_s^2, where r_s = 2G(M1+M2)/c^2 is a characteristic length scale uniquely determined by the total mass of the system. The modified force law exactly reduces to Newtonian gravity in the far field and converges to the finite value GM1M2/r_s^2 in the near field, eliminating the singularity entirely without introducing any additional free parameters. Solar system tests---perihelion precessions of Mercury, Venus, Earth, and Mars---show that the extra precession induced by this model is below current observational precision, with correction magnitudes ranging from 10^-14 to 10^-16. The framework is indistinguishable from Newtonian gravity on solar system scales, while offering a testable prediction in the strong-field regime (r ~ r_s): the effective orbital velocity at the inner edge of an accretion disk is approximately 0.430c, about 5.4% higher than the general relativistic value of 0.408c.