On the Condensation of the Planets

Abstract

The main object of the present paper is to consider the condensation of planets in a gaseous disk of material moving in orbital motion about the Sun. The following results are obtained :— (1) Condensations grow in much the same manner as droplets form in a supersaturated atmosphere of water vapour. This process is mainly important for condensations with masses less than about 10 ²³ gm. This mass is attained, by condensations that do not suffer many collisions with other condensations, in a time of order 10 ⁸ years. (2) For condensations with masses greater than 10 ²³ gm. the growth is mainly by accretion. The time taken for the mass to increase from 10 ²³ gm. to a value of order 10 ³⁰ gm. is also about 10 ⁸ years. The final stages of the accretion process are very rapid. Thus a condensation requires only about 10 ⁵ years for growth from 10 ²⁸ gm. to 10 ³⁰ gm. (3) The rapidity of the final stages of growth by accretion means that the first condensations to acquire masses of order 10 ²⁸ gm. will quickly go on to attain masses comparable with the total mass of the planetary material. This result has two important consequences. (i) That a large fraction of the gaseous material will condense into a few bodies of large mass rather than into a swarm of small particles. Thus only a small fraction of the gaseous material remains finally in the form of condensations of small mass. These small condensations are associated with the asteroids. (ii) The terrestrial planets and satellites cannot be formed by condensation. The reason for this is that the mass of a condensation does not stop at a value of order 5 × 10 ²⁷ gm. but must quickly go on to values of the order of the masses of the major planets. This result confirms Lyttleton's theory of the formation of the terrestrial planets and satellites. (4) The axial rotation period of planets of large mass is shown to be of order 5 hours. This result provides further confirmation of Lyttleton's theory, since in this theory it is necessary for the primitive planets to possess rotation periods less than about 7 hours.