Formation of the Solar System - Rawal, J. J. (Research Advances in Environment, Geography and Earth Science Vol. 10, 2024)
The solar system stretches outward from the sun, passing the four inner planets, through the asteroid belt, past the four gas giants, and continues to the disk-shaped Kuiper Belt, extending even further to the teardrop-shaped heliopause. Rawal [1-16] studied the contraction of the Solar Nebula in order to understand the formation of the Solar System and to derive Planetary Distance Law. He took the view that the Solar Nebula contracted in steps of Roche Limit. Roche Limit is defined above eq. (9), (10) and (11). In his paper entitled "Contraction of the Solar Nebula", Rawal [3] took the assumption that the ratio of the density of the primary (\(ρ_p\)) to the density of the secondary (\(ρ_s\)), which appears in the formula of Roche Limit, is of the order unity, that is, \(ρ_p\) / \(ρ_s\) = 1. In order to get a closer look at the contraction of the Solar nebula, here, in this paper, we would like to remove this restriction on the ratio ( \(ρ_p\) / \(ρ_s\) ) and take it to be 0.7,0.8,0.9 or 1.1,1.2,1.3 and derive the distances of outer and inner edges of the gaseous rings, which one by one, go to form secondaries around the primary (here, the Sun), out of which planets were formed. This may give us a closer look at the contraction of the Solar Nebula which is going to form the Solar System, giving rise to the form of Planetary Distance Law, consistent with a 2/3-stable Laplacian Resonance Relation, which may be closer to reality. After going through this exercise, it is found, here, that if the assumption that ( \(ρ_p\) / \(ρ_s\) ) = 1 to be relaxed and if it is less than 1, the system is shrunk and if it is more than 1 the system expands, only the scale parameters change, and the structure remains similar. However, in all these cases, resonance necessarily will not be stable 2/3-Laplacian resonance. For stable 2/3-Laplacian resonant orbits, the ratio ( \(ρ_p\) / \(ρ_s\) ) = 1 is utmost necessary. One, therefore, concludes that the orbits in the Solar System are stable because the ratio ( \(ρ_p\) / \(ρ_s\) ) involved in the Roche Limit, is of the order unity. This theory is also valid for all satellite systems. Other aspects of the Solar System/Satellite System are also discussed. This means that when the density of the secondary equals that of primary, then only the ring gets detached and Laplace Resonance is attained.