The Geological Orrery is a network of archives of geochronological and orbitally-paced climate proxy data created to address inherent limitations of orbital solutions for planetary orbits beyond 60 Ma due to the chaotic nature of Solar System motion (1). We use results from two NSF-ICDP-funded coring experiments in early Mesozoic continental strata, the Newark Basin Coring Project (2) plus new Hartford basin data (N-H) and the Colorado Plateau Coring Project (3), to precisely and accurately resolve the secular frequencies of the precession of perihelion of the inner planets and Jupiter for the Late Triassic and Early Jurassic epochs, using the lacustrine record of orbital pacing as a geological interferometer. The results are robust, reflecting both an independent U-Pb-based age model based on CPCP zircon U-Pb dates and paleomagnetic polarity correlations and tuning the N-H data to the Venus-Jupiter cycle of 405 ky. MultiTaper Method (MTM) and Frequency Map Analysis (FMA) yield the same results within 0.05% for the 22 Myr-long Triassic-Jurassic window for Mercury, Venus, Earth, and Mars. The overdetermined system of Solar System frequencies are faithfully recorded in the N-H climate proxy data with 16 linear combinations yielding deviations from the measured frequencies (FMA) of only <0.04%. Furthermore, while not indicative of a correct solution, LA2010d (4) yields a much closer match to the Orrery results than LA2010a (4). We estimate the probability of these results being due to chance to be 10^-8 to 10^-11. By comparison, the difference between the LA2010d model and the N-H measurement for the precession of perihelion for Mercury is nearly an order of magnitude less than the Newtonian prediction and present observation for that planet. To determine the secular frequencies of the precession of the nodes of the planets and their important secular resonances with the precession of perihelion, a contemporaneous high-latitude geological archive recording obliquity pacing of climate will be needed. These results form a proof-of-concept of the Geological Orrery interferometer and lay out an empirical framework to map the chaotic evolution of the Solar System.