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

TL;DR

This study simulates transit timing observations of our solar system to determine the limits of characterizing planetary masses and orbits, highlighting the potential and challenges of future exoplanet surveys.

Contribution

It introduces an analytic model for TTV analysis of solar system analogues, assessing detection thresholds and parameter retrieval for multiple planets with realistic noise and observation durations.

Findings

Venus and Earth+Moon masses and orbits can be robustly retrieved.

Jupiter can be detected at high significance with sufficient baseline and timing precision.

Mars detection at 5 sigma requires long baselines and high timing accuracy.

Abstract

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 analogue, 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 the Earth+Moon (EM) -- influenced by the other solar system 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 2, 3, and 4 planets. For various observing baselines, we can robustly retrieve the masses and orbits of Venus and EM; detect Jupiter at high significance (for < 90-second timing error and baseline $\leq$ 15 yrs); and detect Mars at 5 $\sigma$ confidence (with < 20-second timing error and baseline $\geq$ 27 yrs) using TTVFaster. We also find that the 3-planet model is generally preferred, and provide equations to estimate the mass precision of Venus/Earth/Jupiter-analogues. 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 multi-planetary systems. Our findings are comparable to theoretical limits based upon stellar variability and may eventually be possible.