Modeling the Solar System. I. Characterization Limits from Analytic Timing Variations

Planetary systems with multiple transiting planets are beneficial for understanding planet occurrence rates and system architectures. Although we have yet to find a solar system (SS) analog, future surveys may detect multiple terrestrial planets transiting a Sun-like star. In this work, we simulate transit-timing observations of our system based on the actual orbital motions of Venus and Earth + Moon (EM)—influenced by the other SS objects—and retrieve the system’s dynamical parameters for varying noise levels and observing durations. Using an approximate coplanar N -body model for transit-time variations, we consider test configurations with two, three, and four planets. For various observing baselines, we can robustly retrieve the masses and orbits of Venus and EM, detect Jupiter at high significance (for <90 s timing error and baseline ≤15 yr), and detect Mars at 5 σ confidence (with <20 s timing error and baseline ≥27 yr) using TTVFaster . We also find that the three-planet model is generally preferred, and we provide equations to estimate the mass precision of Venus/Earth/Jupiter analogs. The addition of Mars—which is near a 2:1 mean-motion resonance with Earth—improves our retrieval of Jupiter’s parameters, suggesting that unseen terrestrials could interfere in the characterization of multiplanetary systems. Our findings are comparable to theoretical limits based on stellar variability and may eventually be possible.