Predicting the Orbit of TRAPPIST-1i

TL;DR

This paper uses resonance and Titius-Bode law arguments to predict the orbital period of TRAPPIST-1i, aiming to test the predictive power of these methods in compact resonant planetary systems.

Contribution

It introduces a novel approach combining resonance chain analysis and Titius-Bode law to predict unknown planetary orbits in the TRAPPIST-1 system.

Findings

Predicted two possible periods for TRAPPIST-1i: 25.345 and 28.699 days.

Validated the method by accurately predicting TRAPPIST-1h's period.

Proposed the approach as a basis for future planet predictions in similar systems.

Abstract

The TRAPPIST-1 system provides an exquisite laboratory for advancing our understanding exoplanetary atmospheres, compositions, dynamics and architectures. A remarkable aspect of TRAPPIST-1 is that it represents the longest known resonance chain, where all seven planets share near mean motion resonances with their neighbors. Prior to the measurement of 1h's period, Luger et al. (2017) showed that six possible and highly precise periods for 1h were expected, assuming it also participated in the resonant chain. We show here that combining this argument with a Titius-Bode law fit of the inner six worlds narrows the choices down to a single precise postdiction for 1h's period, which is ultimately the correct period. But a successful postdiction is never as convincing as a successful prediction, and so we take the next step and apply this argument to a hypothetical TRAPPIST-1i. We find two possible periods predicted by this argument, either 25.345 or 28.699 days. If successful, this may provide the basis for planet prediction in compact resonant chain systems. If falsified, this would indicate that the argument lacks true predictive power and may not be worthwhile pursuing further in our efforts to build predictive models for planetary systems.