300-303] The Tidal Theory 283 



matter must have begun. The rate of ejection of matter would be slow at 

 first, it would increase to a maximum when the passing star was at its distance 

 of closest approach, and would subsequently diminish to zero. The result 

 ought to be a filament of matter of which the line density would be zero at 

 each end and would increase to a maximum near the middle. 



As this filament lost heat by radiation, the ends would experience the 

 greatest fall of temperature, for the ratio of surface to mass would be greatest 

 here. Thus liquefaction ought to commence near the ends, and after a time the 

 ends of the filament might be mainly liquid while the middle region was still 

 almost entirely gaseous. During this process of condensation, gravitational 

 instability would result in the formation of furrows, leading to ultimate 

 fission into separate masses. 



We have already noticed ( 217) that, when fission of this kind occurs, 

 small masses- are formed out of dense matter, and conversely. Thus those 

 planets which formed near the ends of this filament, being formed out of 

 dense matter, would be those of smallest mass, while the planets formed near 

 the middle, mainly from uncondensed gas, would be of greatest mass. In 

 this way the tidal theory readily explains the great inequality between the 

 masses of Jupiter, Saturn and the other planets, while explaining at the 

 same time why the two largest planets occur in the middle of the chain. The 

 theory indicates that the smaller planets must have been mainly liquid or 

 solid from their birth, while Jupiter and perhaps also Saturn may have always 

 been almost entirely gaseous. We have already seen that the masses of these 

 two larger planets are quite consistent with this view of their origin. 



303. It is impossible to trace the early life of the planets with any pre- 

 cision. If it were not for the tangential velocity which they must have 

 acquired from the gravitational attraction of the passing star, they must have 

 all fallen back into the sun. If they were endowed with only a small tan- 

 gential velocity, they would describe highly eccentric orbits; some would 

 pass through the outer layers of the sun at perihelion and perhaps finally 

 become merged in the sun's mass, others would pass near to the sun's surface 

 while escaping actual collision. The tidal forces exerted on these planets by 

 the sun might result in the creation of systems of satellites encircling the 

 planets. This hypothesis accounts at once for the directions of revolution of 

 the majority of the satellites, and explains why their orbital planes are, for 

 the most part, close to the orbital planes of the corresponding planets. 



We have already noticed that the least velocity that the tide-generating 

 mass can have is that due to a fall from infinity, and this is \/2 times the 

 velocity for a circular orbit. Considerations of probability make it unlikely 

 that the velocity was much greater than this minimum, for a much higher 

 velocity would require an improbably close encounter. As an approximation, 

 let us suppose that the tide-generating mass had a velocity of 10 kms. a second 



