284 The Origin and Evolution of the Solar System [CH. xn 



at a perihelion distance of I'2xl0 15 cms., this being only 22 per cent, more 

 than the minimum velocity possible. The angular velocity of revolution at 

 closest approach would be 8xlO~ 10 . Let us suppose, again as a rough 

 approximation, that the ejected filament was set in motion so that it rotated 

 as a straight line with an angular velocity equal to half this, say 4xlO~ 10 . 

 Then a point at a distance 9'4x 10 I4 cms. (or 2'1 times the radius of Neptune's 

 orbit) from the sun's centre would have the velocity appropriate to the 

 description of a circular orbit ; planets formed at a distance less than this 

 would describe eccentric orbits which would start by approaching nearer to 

 the sun. 



The innermost planets would describe the most eccentric orbits, for their 

 velocity would differ most from that required for a circular orbit. Traces of 

 this law may perhaps still be found in the solar system in which the eccen- 

 tricity of orbit diminishes on the whole as we recede from the sun, Venus and 

 the earth forming exceptions. See* has shewn that the action of a resisting 

 medium surrounding the sun would be to diminish the eccentricities of the 

 planetary orbits. This is shewn by the analysis already given in 261 ; to 

 study the effects of a resisting medium we need only change the sign of the 

 couple G. We find that the action of a resisting medium diminishes both 

 the eccentricity and the major-axis of the orbit. 



The diminution of eccentricity ought to be greatest nearest the sun ; 

 where the resisting atmosphere may have been supposed to be most dense. 

 This might perhaps account for the smallness of the eccentricities of the 

 orbits of Venus and the earth, but if so that of Mercury remains anomalously 

 large. Similarly the diminution of major-axis ought to be greatest near to 

 the sun. This would be in accordance with the comparative crowding of the 

 planets near to the sun (Bode's Law), and with the corresponding phenomenon 

 in the systems of Jupiter and Saturn. 



304. The distance within which a planet must approach the sun for 

 satellites to be created by tidal break-up depends on the density of the 

 planet. If we are right in supposing that the small planets at the two ends 

 of the series, say Neptune, Uranus, Venus and Mercury, condensed to an 

 almost liquid state immediately after birth, then it seems highly improbable 

 that these bodies can have been broken up tidally by the much less dense 

 mass of the sun. We should expect these planets to have remained without 

 satellites, or at least should expect their satellites not to have been born 

 by tidal interaction with the sun. The high inclinations of the satellites of 

 Uranus and the retrograde motion of the satellite of Neptune seem in any 

 case to suggest some origin other than a tidal encounter with the sun. 

 On the other hand, if we are right in supposing Jupiter and Saturn to have 



* Researches on the Evolution of the Stellar Systems, Vol. n, Chap. VII. See also Poincare, 

 Lemons sur les Hypotheses Cosmogoniques, Chap. VI. 



