409 
382-384] Effects of a Resisting Medium 
Jeffreys* has studied the rate at which the eccentricities of planetary 
orbits would be reduced by the action of such a medium, and finds that the 
orbit of Mercury would be reduced to its present eccentricity in a period of 
the order of 3000 million years, a time which agrees well with other estimates 
of the age of the solar system. It is quite likely that this primitive resisting 
medium has not yet been wholly absorbed by the sun and planets, and the 
particles which scatter the zodiacal light may well form the last surviving 
vestiges of it. 
The Frequency of Planetary Systems in Space. 
384 . It appears to be clearly established that, whatever structure we 
assign to a primitive sun, a planetary system cannot come into being merely 
as the result of the sun’s rotation. If a sun, rotating alone in space, is 
not able of itself to produce its family of planets and satellites, it becomes 
necessary to invoke the presence and assistance of some second body. This 
brings us at once to the Tidal Theory. But our analysis has shewn that the 
passage of this second body will have no permanent effect on the sun unless 
the centre of the second body passes with a distance of some 2 or 3 stellar 
radii of the centre of the sun. The limit is not very much greater than 
the distance at which a physical collision takes place. Now in § 286 we 
calculated that, with the present distribution of stars in the neighbour 
hood of the sun, a given star is only likely to meet with actual collision once 
in 6 x 10 17 years. Its chance of a tidal encounter of sufficient intensity to 
break it up into a planetary system is somewhat, but not much, greater. We 
may perhaps suppose that the chance is twice as great, but we must also 
take into account that not every encounter of the requisite closeness can be 
expected to form a planetary system. 
At a rough estimate we may suppose that a given star’s chance of forming 
a planetary system is one in 5 x 10 17 years. Allotting an average age of 5 x 10 12 
years to the stars, we find that only about one star in 100,000 can have 
formed a planetary system in the whole of its life, so that only about one star 
in 100,000 is at present surrounded by planets. Planetary systems must then 
be of the nature of “freak-formations”; they do not appear in the normal 
evolutionary course of the normal star. 
To a rough approximation we may regard the stars of the galactic system 
as consisting of about 100 million stars packed approximately as closely as 
the stars in the neighbourhood of the sun, and a far greater number 
scattered far more sparsely in space. In the former group of 100 million stars 
planetary systems must form at the rate of about one per 5 x 10 9 years; in the 
latter the stars are so sparse that the chance of planetary systems coming into 
being may be almost neglected. We may conclude that in the whole of the 
galactic system planetary systems only come into being at the rate of about one 
J 
* M.N. lxxviii. (1918), p. 424.