Dynamical Calculations Relating to the Origin of the Solar System

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Abstract
The dynamical aspects of certain hypotheses for the formation of planets are shown to be capable of close representation by a restricted three-body system, and accurate machine integrations of the equations of motion have been carried out on such a basis to test the hypotheses. It is first shown that the collisional and tidal mechanisms as applied to the Sun could not result in any particles going into orbital motion outside the Sun at however small at distance. The calculations also show that in a two-body collision of stars only a negligible quantity of material is likely to escape from both stars and be available for capture by the Sun; the amount could rise to planetary order only if the relative speed of the colliding stars when widely separated were several hundred kms per sec. Rotational break-up of a companion star to the Sun might fulfil such a condition. The rotational instability of a primitive planet growing gradually from a disk of material in motion round the Sun would probably result in disruption into two main pieces with high mass-ratio and separating with hyperbolic speed. The motion of small particles formed in the stream of material drawn out between the separating main masses can also be investigated by means of a restricted three-body analogy, and in this way it is shown that satellite orbits are possible as a result of the great elongation that the last Jacobi figure possesses together with the high relative velocity of the separating pieces. It is suggested that the rotational stability of the great planets has been reached in this way and by the same means their principal satellites produced. The smaller main pieces resulting from the break-up would have sufficient terminal speed to escape entirely from the solar system.

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