Newton's theory of gravitation is expressed as a mathematical relationship between distances and masses. It can be deduced from Kepler's equations (which are also mathematical).
Are there even older physical theories formulated by equations?
History of Science and Mathematics Stack Exchange is a question and answer site for people interested in the history and origins of science and mathematics. It only takes a minute to sign up.
Sign up to join this communityNewton's theory of gravitation is expressed as a mathematical relationship between distances and masses. It can be deduced from Kepler's equations (which are also mathematical).
Are there even older physical theories formulated by equations?
The first physical theory which was mathematically expressed is the Pythagorean theory of music. According to the legend, Pythagoras himself discovered the relation between musical intervals and the ratios of lengths of strings. (Based on this discovery, Pythagoras jumped to the conclusion that "Numbers rule the world", so mathematical physics was born). This seems to be the earliest quantitative discovery of physics. Based on this, a sophisticated theory of music was developed, one can read about it for example in the book:
B. L. van der Waerden, Science awakening. Mathemarics of ancient Egypt, Babylon and Greece, Appendix: Pythagorean teaching on harmony. (Was earlier published as a separate paper in Math. Ann., 118 (1941)).
Remark. This competes with Babylonian mathematical astronomy, but one can argue whether Babylonian astronomy belongs to physics or not. Anyway, this discovery is more ancient than Greek astronomy.
Remark 2. Since Pythagoreans was a secret society, the exact details of this discovery and its date are not known. But surely this predates the first well-documented discoveries in physics which are due to Archimedes (floating bodies, the rues of the lever etc.)
The Almagest, written in the second century contains a mathematical description of the Universe (and, in particular, of the solar system), which is expressed mathematically. Its contents were almost certainly already known to (and copied from) Hipparchus of Nicaea, who lived in he second century BC. In fact, the kind of research that led to this began already at the time of Plato (fifth century BC).