Closer Look at the Contracting Solar Nebula

Rawal [1 to 11] 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 as the three dimensional distance on entering which the secondary body breaks into pieces due to tidal forces of the primary. Alternatively, it is the three-dimensional distance within which the primordial matter which is left behind around the primary, after its formation, does not get condensed into a secondary, due to tidal forces of the primary. In his paper entitled “Contraction of the Solar Nebula”, Rawal (afore-mentioned papers) took the assumption that the ratio of the density of the primary to the density of the secondary , which appears in the formula of Roche Limit, is of the order unity, that is, ( . In order to get closer look in the contraction of the Solar nebula, here, in this paper, we would like to remove this restriction on the ratio ( 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 closer look of 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 2/3-stable Laplacian Resonance Relation, which may be closer to reality. After going through this exercise, it is found, here, that the assumption that ( = 1 may be relaxed. If it is less than 1, the system is shrunk and if it is more than 1 the system expands, only the Scale-parameter changes, 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 ( is utmost necessary. One, therefore, concludes that the orbits in the Solar System are stable because the ratio ( ) involved in the Roche Limit, is of the order unity.