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Could there have been a planet with the mass of Earth between Jupiter and Saturn?

Author(s): Calvin Neel

 We expand on this research by putting an Earth-mass planet in the zone between Jupiter and Saturn. This research was inspired by earlier studies of asteroids located between Jupiter and Saturn, where long-term stable orbits with tiny eccentricities and low inclinations have been observed. We worked on numerical integrations of the motion equations for the outer solar system, which includes Jupiter, Saturn, Uranus, Neptune, and one more planet with an Earth-mass. For up to 500 Myr, this 6-body system has been combined with the Lie technique. Based on the findings of earlier research by our team, the default initial stable zone for the Earth-mass planet has been estimated to be between 7.04 au and 7.31 au. Assuming differing mean anomalies, we searched each area independently for 360 Earthmass planets and looked at the corresponding Escape Times (ETs). The overall image reveals that between 7.12 au and 7.28 au, the orbits are the most stable. Additionally, although lesser values are obtained for the median due to outliers, the mean of the ETs for all 360 mean anomalies between 7.24 au and 7.12 au steadily falls from ET=11 Myr to 0.9 Myr. We concentrated on three areas (7.23 au, 7.24 au, and 7.25 au) in terms of their ETs to test the stability of the Earth-mass planet based on its initial inclination, assuming I=1, 3, and 5; however, no discernible variations were identified. Therefore, even though it would have been a brief occurrence, the potential of an Earth-mass planet being located between Jupiter and Saturn in the early history of the Solar System is very remarkable

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