Significance The Solar System is chaotic, and precise solutions for the motions of the planets are limited to about 60 million years. Using a network of coring experiments that we call the Geological Orrery (after 18th century planetaria), we recover precise and accurate values for the precession of the perihelion of the inner planets from 223- to 199-million-year-old tropical lake sediments, circumventing the problem of Solar System chaos. Extension of the Geological Orrery from 60 million years ago to the whole Mesozoic and beyond would provide an empirical realm to constrain models of Solar System evolution, further test General Relativity and its alternatives, constrain the existence of additional past planets, and provide further tests of gravitational models.