Long-term stability of planetary orbits between Jupiter and Saturn

Abstract

We extend our two previous studies on the existence of stable orbits in the Solar System by examining the domain between Jupiter and Saturn. We place (1) a massless object, (2) a Moon-mass object, (3) a Mars-mass object, (4) an Earth-mass object, and (5) a Uranus-mass object in the said region. Note that these objects are considered separately in the framework of our simulations. Our goal is to explore the orbital stability of those objects. We employ the Lie-integration method, which is fast and well established, allowing us to solve the respective differential equations for the $N$-body system. Hence, we consider the celestial bodies spanning from Jupiter to Neptune, including the aforementioned test object, the main focus for our model simulations. The integrations indicate that in some models the test objects placed in the region between Jupiter and Saturn reside in that region for more than 600 Myr. Between 5 and 10 au, mean-motion resonances (MMRs) take place acting upon the test objects akin to simulations of Paper I and II. Our models indicate relatively small differences for the long-term stability of the five test objects notwithstanding their vastly different masses. Generally, it is found that between $a_{\text{ini}}=7.04$ and 7.13 au the orbits become unstable mostly within 5 million years and further out, that is, up to $a_{\text{ini}}=7.29$ au, the duration of stability lengthens to up to hundreds of millions of years.