Further Considerations on Contracting Solar Nebula
Abstract
Prentice (1978a) in his modern Laplacian theory of the origin of the solar system has established the scenario of the formation of the solar system on the basis of the usual laws of conservation of mass and angular momentum and the concept of supersonic turbulent convection that he has developed. In this, he finds the ratio of the orbital radii of successively disposed gaseous rings to be a constant ∼ 1.69. This serves to provide a physical understanding of the TitiusBode law of planetary distances. In an attempt to understand the law in an alternative way, Rawal (1984) starts with the concept of Roche limit. He assumes that during the collapse of the solar nebula, the halts at various radii are brought about by the supersonic turbulent convection developed by Prentice and arrives at the relation: R _{p}= R_{☉}a^{p}, where R _{p}are the radii of the solar nebula at various halts during the collapse, R _{☉}the radius of the present Sun and a = 1.442. ‘a’ is referred here as the Roche constant. In this context, it is shown here that Kepler's third law of planetary system assumes the form: T _{p} = T _{0}(a^{3/2})^{p}, where T _{p} are the orbital periods at the radii R _{p}, T _{0} ∼ 0.1216d ∼ 3 h, and a the Roche constant. We are inclined to interpret ‘T _{0}’' to be the rotation period of the Sun at the time of its formation when it attained the present radius. It is also shown that the oribital periods T _{p}corresponding to the radii R _{p}submit themselves to the Laplace's resonance relation.
 Publication:

Earth Moon and Planets
 Pub Date:
 January 1986
 DOI:
 10.1007/BF00054038
 Bibcode:
 1986EM&P...34...93R
 Keywords:

 Planetary Evolution;
 Solar Corona;
 Solar System;
 Collapse;
 Kepler Laws;
 Resonance;
 Ring Structures;
 Roche Limit;
 Rotation;
 Astrophysics