A Derivation of the Newtonian Gravitational Constant

Abstract

This paper derives the Newtonian gravitational constant G using a model in which gravitational waves of fundamental wavelength 61.458 fm are generated in the Sun by a spinning magnetic monopole. By considering the propagation of these waves both within and above the ecliptic plane, the model predicts a total outgoing gravitational‑wave energy of 6.70333 x 10-11, close to the normalized Newtonian gravitational constant G = 6.67430 x 10_11 J. To reconcile the small difference between these energies, the paper incorporates results from earlier studies of gravitational waves emitted by a magnetic monopole ejected during the SN 1054 supernova. Those studies showed that gravitational waves originating outside the solar ecliptic plane reach the Solar System with an energy of approximately 90 keV. Subtracting this external gravitational‑wave contribution from the outgoing solar monopole energy yields a corrected expression that matches the empirical value of G. The result suggests that the Newtonian gravitational constant may represent the net gravitational‑wave energy produced by the Sun’s monopole after accounting for external gravitational‑wave contributions originating outside the ecliptic plane.