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. The Geological Orrery is a network of geological records of orbitally paced climate designed to address the inherent limitations of solutions for planetary orbits beyond 60 million years ago due to the chaotic nature of Solar System motion. We use results from two scientific coring experiments in Early Mesozoic continental strata: the Newark Basin Coring Project and the Colorado Plateau Coring Project. We precisely and accurately resolve the secular fundamental frequencies of precession of perihelion of the inner planets and Jupiter for the Late Triassic and Early Jurassic epochs (223–199 million years ago) using the lacustrine record of orbital pacing tuned only to one frequency (1/405,000 years) as a geological interferometer. Excepting Jupiter’s, these frequencies differ significantly from present values as determined using three independent techniques yielding practically the same results. Estimates for the precession of perihelion of the inner planets are robust, reflecting a zircon U–Pb-based age model and internal checks based on the overdetermined origins of the geologically measured frequencies. Furthermore, although not indicative of a correct solution, one numerical solution closely matches the Geological Orrery, with a very low probability of being due to chance. To determine the secular fundamental frequencies of the precession of the nodes of the planets and the important secular resonances with the precession of perihelion, a contemporaneous high-latitude geological archive recording obliquity pacing of climate is needed. These results form a proof of concept of the Geological Orrery and lay out an empirical framework to map the chaotic evolution of the Solar System.