An Overview of the 13:8 Mean Motion Resonance between Venus and Earth

TL;DR

This paper investigates the orbital dynamics of Venus and Earth near the 13:8 mean motion resonance, revealing potential for chaotic behavior and instability in the inner planetary system through numerical experiments.

Contribution

It provides a detailed analysis of the Venus-Earth system's proximity to the 13:8 MMR and explores how small orbital variations can lead to chaos and potential planetary escapes.

Findings

Venus and Earth are nearly in the 13:8 MMR.

Small changes in Venus's orbit can cause chaos in Mercury's orbit.

Inner planet escapes are possible within short time scales.

Abstract

It is known since the seminal study of Laskar (1989) that the inner planetary system is chaotic with respect to its orbits and even escapes are not impossible, although in time scales of billions of years. The aim of this investigation is to locate the orbits of Venus and Earth in phase space, respectively to see how close their orbits are to chaotic motion which would lead to unstable orbits for the inner planets on much shorter time scales. Therefore we did numerical experiments in different dynamical models with different initial conditions -- on one hand the couple Venus-Earth was set close to different mean motion resonances (MMR), and on the other hand Venus' orbital eccentricity (or inclination) was set to values as large as e = 0.36 (i = 40deg). The couple Venus-Earth is almost exactly in the 13:8 mean motion resonance. The stronger acting 8:5 MMR inside, and the 5:3 MMR outside the 13:8 resonance are within a small shift in the Earth's semimajor axis (only 1.5 percent). Especially Mercury is strongly affected by relatively small changes in eccentricity and/or inclination of Venus in these resonances. Even escapes for the innermost planet are possible which may happen quite rapidly.