American physicist Peter Fong's 1996 The Unification of Science and Humanity, outlines the semblance of Newtonian sociology, i.e. sociology based on physics. [1]

“In astronomy, it was once thought that the advance of the perihelion and the change of eccentric of the planetary orbits were expressions of God’s will that was beyond the control of Newton’s laws. These phenomena were eventually explained by the very laws which Newton applied to the interactions among the planets. This established the planetary system as a purely mechanical system in which there was no role for non-mechanical entities.

Chemistry presented challenges. Things may disappear and reappear. Concepts such as those of phlogiston and caloric theory competed with the Newtonian concepts. But eventually it was learned that chemistry was entirely reducible to physics as a mechanical system.

Biology presented even greater challenges. There are phenomena in biology apparently not shared by inanimate material agencies: birth, growth, reproduction, and death. There is no sex in physics and chemistry. But through molecular biology most manifestations, including sex, can now be explained on a mechanical basis. All previously supposed non-mechanical elements have been eliminated.

Since humans are part of the biological system, it is logical that there be a Newtonian derivation of the social sciences. However, we cannot ignore the existence of apparently non-mechanical elements manifested in such notions as virtue, evil, liberty, and equality. These will have to be accounted for in a Newtonian framework. Then the social sciences can be developed as hard sciences—like physics and chemistry—that are well-established, complete, exhaustive and exclusive. Such development would be one of the most important intellectual developments of this century. Right now, the existing social sciences are like the natural sciences before Newton, with conflicting concepts and principles that are competing with each other, without a body of firmly established knowledge the solution of practical problems.”

“It may be reasonable to suppose that the corpuscular-kinetic format of the immediate world of human experience is duplicate in the nature of human organization—thereby giving rise to a Newtonian sociology reducing ‘society to a cluster of human atoms, complete and self-contained each in itself’ and only mutually attracting and repelling each other.”

— Michael Foley (1990), per citation of Alexandre Koyre [2]