407 
379-382] The Birth of Satellites 
progression of increasing mass through Mercury, Venus, Earth, Mars to the 
maximum mass of Jupiter, which is broken only by the anomalous mass of 
Mars; on the descending side the progression through Jupiter, Saturn, 
Uranus, Neptune fails only through Neptune being some 17 per cent, more 
massive than Uranus. Clearly when a tidal filament is drawn out of a break 
ing up star, the matter will be richest near the centre of the filament and 
will tail off at both ends ; this may provide an explanation of the appearance 
of the more massive planets, Jupiter and Saturn, near the centre of the 
planetary sequence, and of the similar phenomenon in the planetary systems. 
381 . So long as the problem is discussed in general terms, it looks as 
though the process might go on for ever, each satellite of each planet pro 
ducing a family of sub-satellites to circle around it, and so on ad infinitum. 
Common sense suggests that there must be a limit somewhere, and calcula 
tion enables us to fix this limit quite definitely. 
The first five satellites of Saturn all have masses of the order of 
10 24 grammes. Formula (3781) shews that for bodies of this mass to be 
formed by gravitational instability out of a gaseous filament, the density of 
the original filament must be many hundreds or thousands of times that of 
water. Such a density is incompatible with the gaseous state, and the obvious 
deduction is that these bodies were not born out of a gaseous filament or, at 
any rate, were not gaseous when born. 
We could have reached the same conclusion in another way. The small 
satellites of Saturn are even now, in their solid states, too small to retain an 
atmosphere; if they were suddenly transformed into gas they would be still 
less able to retain their outer layers of gas and would rapidly dissipate into 
space. This conclusion is entirely independent of any special theories of 
cosmogony; whatever view we hold as to their origin, it is comparatively 
certain that most of the asteroids, the majority of the satellites of the planets, 
and of course the particles of Saturn’s rings have been solid or liquid from 
birth. 
This it is that fixes the limit to the birth of endless generations of satel 
lites. Gaseous bodies below a certain limit of mass cannot hold together 
gravitationally but immediately dissipate into space. A brief reprieve from 
this law is provided by the possibility of the matter liquefying or solidifying 
before the process of dissipation is complete, and it is probably owing to the 
action of this reprieve that most of the satellites of the planets, and possibly 
the smaller planets themselves owe their present existence. But the very 
circumstance which saves the lives of these small individuals prevents their 
giving birth to further generations of astronomical bodies. 
382 . The more liquid a planet was at birth the less likely it would be to 
be broken up tidally by the still gaseous sun. But the discussion of § 379 has