Further considerations on contracting solar nebula

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 Titius-Bode 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= Ra^p, where R _pare 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 _pcorresponding to the radii R _psubmit themselves to the Laplace's resonance relation.     

A hypothesis on the Oort clouds of planets

Although, we have no quantitative arguments to prove, but we have good reasoning to believe that the Oort clouds existed surrounding the planets. The short period comets, Apollo-Amor-Toro-asteroids and such other objects may be the relics of the Oort clouds that had existed surrounding the planets long ago.     

Physical significance and the role of Lagrangian points and the Oort clouds of planets in the Solar System

Here, the role played by Lagrangian points and the Oort clouds of planets in the evolution and structure of the Solar System has been discussed. It is revealed that the Lagrangian points are not mere isolated points in space associated with the orbit of a planet at which the resultant gravitational force of the system of three bodies is zero as thought previously to be, but their existence has much deeper physical significance as regards the origin of the Solar System and those of satellite systems of planets.     

A study of dissolution and water-bearing characteristics of the restricted platform dolomite facies in the karst areas of Guizhou,China

The restricted platform facies dolomites are widely distributed in the northern and northeastern Guizhou, China, and they are the main lithology of karst groundwater and a primary target for locating drinking water resources in the province of Guizhou. The geological history and deposition environment of the restricted platform dolomite facies vary significantly across the province, making it more difficult to evaluate the dissolution and water-bearing capacity of karstic dolomites. This paper explores a quantitative approach to assessing the solubility of four typical geological strata using analytical hierarchy process (AHP) modeling. Properties including CaO/MgO, clast content, porosity, permeability and fracture density are investigated and used as the major criteria in the AHP analysis to render the rankings for solubility among the studied formations. Hydrogeological characteristics are also discussed. Overall the presented results demonstrate the feasibility of AHP as a modeling tool to provide a quantitative approach when a wide range of properties need to be considered. The explored approach can have strong implications for the exploitation and utilization of karst groundwater in Guizhou, China.     

Contraction of the solar nebula

The concept of Roche limit is applied to the Laplacian theory of the origin of the solar system to study the contraction of a spherical gas cloud (solar nebula). In the process of contraction of the solar nebula, it is assumed that the phenomenon of supersonic turbulent convection described by Prentice (1978) is operative and brings about the halt at various stages of contraction. It is found that the radius of the contracting solar nebula follows Titius-Bode law R _p = Ra^p, where R is the radius of the present Sun and a = 1.442. We call a the Roche's constant. The consequences of the relation are also discussed. The aim, here, is an attempt to explain, on the basis of the concept of Roche limit, the distribution of planets in the solar system and try to understand the physics underlying it.     

Planetary distance law

A general form of the planetary distance law has been proposed in this paper.     

The boundary to the solar system as set by a hypothetical Solar companion

If a binary companion to the Sun exists as proposed by Davis et al. and Whitmire and Jackson, then one can consider a planet/comet-Sun-solar companion system and use King-Innanen's formula to calculate the limiting direct and retrograde orbits around the Sun. The limiting retrograde orbit could be considered as the boundary to the Solar System. We study the problem for the companion having a mass in the range 0.005M –0.3M and find the corresponding boundary to the Solar System.     

Contractions of subsolar nebulae

The present paper attempts to study the contractions of subsolar nebulae along the lines with contraction of the solar nebula.     

A new light on the L 1, L 2 Lagrangian points

The relation between the locations of L ₁, L ₂ Lagrangian points and the boundary to their respective satellite system is brought forth, in that, the Lagrangian points L ₁, L ₂ are seen to lie just on the boundary to their respective satellite system.     

Possible satellites of Mercury and Venus

On the basis of works of King and Innanen, the limiting direct and retrograde orbits around the planets Mercury and Venus have been calculated. Synthesizing this concept with the concept of synchronous orbits around the planets and tidal drags acting within them it is shown that Venus may not have retained any satellite direct or retrograde but Mercury may have retained a retrograde satellite at a distance between 225000 and 252700 km from its center. It is urged that this satellite may be investigated observationally.