Can an Earth-mass planet exist between Jupiter and Saturn? A numerical experiment

Motivated by previous studies about asteroids situated between Jupiter and Saturn, where long-term stable orbits with small eccentricities and low inclinations have been identified, we extend this research by placing an Earth-mass planet in the region between Jupiter and Saturn. We pursued numerical integrations of the equations of motions for the outer solar system encompassing Jupiter, Saturn, Uranus, and Neptune, as well as the additional Earth-mass planet. This 6-body system has been integrated with the Lie method for up to 500 Myr. The default initial stable zone for the Earth-mass planet has been assumed between 7.04 and 7.31 au based on the results from previous studies by our group. We explored each region separately for 360 Earth-mass planets (assuming different mean anomalies) and inspected the respective escape times (ETs). The overall picture shows that the most stable orbits occur between 7.12 and 7.28 au. Furthermore, the mean of the ETs for all 360 mean anomalies between 7.24 and 7.12 au gradually decreases from ET = 11 to 0.9 Myr, although smaller values are obtained for the median due to outliers. To check the role of stability of the Earth-mass planet depending on its initial inclination, we focused on three regions (i.e., 7.23, 7.24, and 7.25 au) in terms of their ETs assuming i = 1 degrees, 3 degrees, and 5 degrees however, no significant differences were found. Hence, the general possibility of an Earth-mass planet situated between Jupiter and Saturn in the Solar System's distant past is highly notable, although it would have been a transient event.