On the formation of planets from a solar nebula

The development of planets within a solar nebula of both gas and dust is shown to occur in two main stages. First, in a time comparable with the orbital period at any distance the dust comes to move with Keplerian motion in a thin plane disc. This is an essential prerequisite since the volume-density in such a disc is amply sufficient for the self-gravitation of condensations to overcome the differential action of the Sun. By such means small solid planets can form independently of the gaseous component of the nebula. Second, the range-of- influence of a planet (of mass m moving at distance R ) out to which its gravitation dominates over that of the Sun is |$(m/3{M})^{1/3}\,R$| . At any stage material within this distance can be captured, and the growth of bodies to mass of lunar order requires about 10 4 yr. It seems probable that many small bodies would begin to form separately, and then themselves combine by collisions to yield larger bodies fewer in number. The vorticity associated with the motion of the disc round the Sun will reappear as angular momentum of the bodies and give them initial rotation-periods of about 4–5 hr, but collisions would tend to give the later larger masses longer periods of rotation. The energy of infall to the surface would be sufficient to melt the material for bodies as large as the Moon, but it would arrive only at an equatorial band because of the thinness of the dust-disc, and flow of molten material polarwards would produce a condition highly conducive to cooling. If larger masses than of lunar order result mainly from collisions, it seems probable that initially only all-solid planets would be formed. The great outer planets must also start their growth within the dust-disc as small solid bodies and thereafter they would continue growth by capture of gaseous material from the nebula. Only for Jupiter is capture of gas in accordance with thermal accretion likely to have occurred, since only for it could the accretion-radius ever exceed the range of gravitational influence.