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The Source of Stellar Energy [ch. iv 
other way. Some 3000 tons of oil must be burned to drive a liner across the 
Atlantic ; the same amount of energy could be provided by the annihilation 
of about one-eightieth of an ounce of oil. Over four million tons of coal a 
week are raised to provide for the heating, lighting, power and transport of 
Great Britain alone; the annihilation of a single ton of this coal would 
provide for all these services for a century. And, to carry on the story, the 
total radiation emitted by the sun during the 1500 million years of the 
earth’s existence could be provided by the annihilation of one ten-thousandth 
part of its mass, the result already mentioned in § 101; while the annihila 
tion of the whole of its mass would provide radiation at the present rate for 
15 million million years. This last result not only shews that the annihila 
tion of matter provides an adequate source of stellar energy; it also makes it 
almost certain, as we shall now see, that it provides the actual source. 
A mass of dynamical evidence, which will be brought forward later, 
indicates that the stars as a whole must have existed for millions of millions 
of years. The most direct evidence is perhaps provided by the orbits of 
binary stars. We shall see that, as a consequence of the manner of their 
formation, newly formed binary stars have circular, or nearly circular, orbits. 
Every gravitational pull on a circular orbit tends to make it more elliptical, 
so that the older a binary system is, the more elliptical its orbit ought to 
become. This is found by observation to be the case. But our knowledge of 
the density with which the stars are scattered in space gives us the means 
of calculating the actual rates at which the ellipticities of the orbits of 
binary systems must increase, so that from the observed ellipticities of orbits 
it is possible to calculate the ages of the binary systems. And the answer 
comes out in millions of millions of years. 
We can calculate the total amount of radiation which a star has emitted 
during its life of millions of millions of years. Except in the case of the 
youngest stars, it is found that the total mass of the emitted radiation is 
far greater than the present mass of the star. The original mass of the star 
must have been the sum of the star’s present mass and the mass of all the 
emitted radiation, so that the star must originally have been many times as 
massive as it now is. Indeed we shall shortly find observational evidence that 
young stars, as a class, are many times more massive than old stars. 
The older views of stellar radiation regarded a star’s gravitational potential 
energy and the heat and chemical energy of its molecules as reservoirs from 
which a star’s radiation was drawn. When we look at the matter in terms of 
a time-scale of millions of millions of years, we see that the capacity of all 
these reservoirs is quite negligible; the reservoir in which the star’s future 
radiation is stored is the star’s mass. The time-scale of millions of millions 
of years requires that the energy stored in each gramme of a star’s mass 
shall be of the order of magnitude of 9 x 10 20 ergs, and we know of no way