110 The Source of Stellar Energy [ch. iv 
The radioactive contents of rocks provide what must apparently be accepted 
as quite conclusive evidence that the earth’s crust has been solid for at least 
1500 million years*. The age of the sun must, then, be greater than this. 
Speaking very loosely, we may say that the sun must have been generating 
energy for at least 1500 million years at a rate comparable with its present 
rate of T9 ergs per gramme per second. This represents a total energy 
generation of about 9 x 10 16 ergs for each gramme of the sun’s mass. 
It has long been realised that combustion of matter, and chemical action 
in general, are quite inadequate to provide any such amount of energy. The 
formation of one gramme of carbon dioxide by the union of carbon and oxygen 
sets free 2140 calories or 9 x 10 10 ergs, which is only about a millionth part 
of the required output of 9 x 10 16 ergs per gramme. Some chemical reactions 
provide rather more energy per gramme than that just mentioned, but no 
known reaction provides ten times as much, or 9 x 10 u ergs per gramme, so 
that chemical action is unable to provide even one part in 100,000 of the 
energy which the sun has radiated away during the life of the earth. 
Heat energy is equally insignificant. Even in the most favourable case in 
which matter is entirely broken up into its constituent electrons and protons, 
the heat energy of a gramme of matter at a temperature of 30 million degrees 
is only 1*5 x 10 18 ergs. Thus if the sun were merely radiating stored heat 
energy, the 9 x 10 16 ergs per gramme which it must have radiated during the 
life of the earth, would require it to have had a temperature of about 
1800 million degrees when the earth was born. The calculations of stellar 
temperatures which were given in the last chapter enable us to dismiss any 
such temperature as impossibly high. 
In 1854 Helmholtz put forward his famous contraction-hypothesis, accord 
ing to which the shrinkage of the sun under its own gravitational attraction, 
with the accompanying loss of gravitational potential energy, sets free the 
energy which appears as the sun’s radiation. At a point in the sun’s interior, 
the gravitational potential is of the order of magnitude of yM/r, where M is 
the mass and r the radius of the sun, and y is the gravitation constant. On 
inserting numerical values, this quantity is found to be of the order of 2 x 10 15 
in c.G.s. units, so that even if the whole mass of the sun had fallen in from 
infinity, each gramme could only provide about 2 x 10 18 ergs of energy, and it 
appears that the Helmholtz contraction-hypothesis cannot account for more 
than about two per cent, of the energy which has been radiated by the sun 
during the earth’s life. 
Thus neither chemical energy, heat energy, nor gravitational energy are 
anything like adequate to account for the sun’s emission of radiation even 
during the existence of the earth. The only remaining sources of energy are 
of sub-atomic nature, and of these radioactivity provides the only example of 
which we have any direct experience. 
* A. Holmes, The Age of the Earth.