The existence of the temperature gradient requires a flow and release of energy (luminosity) at the surface of the star. If the star is to remain stable the energy loss at the surface must be balanced by new energy from within. But what is the origin of this energy ? For a simple model of the energy source we might suppose that the heat output occurs solely because the central regions of a star are hotter than the outer ones. However, a very important calculation shows that this cannot be sufficient, at least for the Sun. There is reliable geological evidence that the amount of solar radiation received at the Earth has changed only a little during the 4.5 X 109 years that the Earth has existed. Therefore we can legitimately use the present value for the solar luminosity in calculating an estimate of the total amount of energy radiated by the Sun during the lifetime of the Earth. Once the estimate is made, we may ask if the heat (or thermal) energy of the Sun, caused by the cooling of the hot central regions is sufficient to account for the estimated output. To make this calculation we must remember that, as the central regions cool, the Sun will have to contract a little in order o keep up on the gas pressure. A cooler gas has to be compressed into a smaller volume if its pressure is to remain constant. Now it turns out that the total amount of heat energy that the Sun could have acquired in contracting to its present radius is given by its present gravitational potential energy. This latter quantity is roughly GM02/R0, where G is the universal gravitational constant, M0 the solar mass and R0 the present radius. This calculation was first made by Lord Kelvin and H.Helmholtz in the nineteenth century. The lifetime of this energy source radiating at the rate of the solar luminosity, L0, is therefore roughly GM02/ROLO, which turns out to be about ten million years. Hence we see that the thermal energy source in the Sun is sufficient to power it for only about 0.2 per cent of its known lifetime. Such a source is clearly insufficient and this line of reasoning led Eddington to suggest that there should be another energy producing mechanism in stars, namely a nuclear energy source.

Before considering a nuclear source of energy, however, it is instructive to inquire if any known terrestrial sources of energy would be sufficient to power the Sun. Think, for example, of coal which still supplies a significant amount of the annual energy budget of Europe and North America, and let us suppose that the bulk of the Sun is made up of coal or of some similar source of chemical energy. A simple calculation shows that a coal-burning Sun might last for about 10 thousand years falling short of the observed requirements by a factor of nearly a million. The need for a sub-atomic nuclear source is therefore clear.

We stress in passing that the lack of a nuclear source does not mean a lack of energy for the star; it simply means lack of sufficient energy. There are indeed stages in the life of a star when no nuclear reactions are occurring. In such cases a star still radiates energy, but it draws it from its thermal energy account which is, in turn, derived ultimately from its gravitational potential energy. The star releases gravitational energy by contraction; some of the energy goes in radiation and some into heating up the whole star.

The question of whether stars are a suitable place for nuclear transmutations to occur was hotly debated in the 1920s. From the equations that describe the structure of a star it is possible to make order of magnitude estimates of the physical conditions near the centre of a star. These conditions turn out to be roughly: central temperature 107K, central pressure 1016 Nm-2, density 105kgm-3. Even at these high densities and pressures the high temperature ensures that the material is completely gaseous. The principle question facing physicists in the 1920s was simply whether or not nuclear reactions would work under such physical conditions. The main problem at the time was that since nuclear physics was in its infancy the exact reactions were unknown. However general arguments led scientists to believe that it would be difficult to conceive of a nuclear transmutation of elements occurring, simply became of the substantial amount of kinetic energy required to fuse hydrogen nuclei together. This is because of the strong electrical repulsion between the positive charges of the hydrogen nuclei. It was clear that a high temperature, with which high collision speeds would be associated was required. The question was how high, and it was this that persuaded Eddington to suggest ironically to his colleagues that they find a hotter place than the centres of the stars. New quantum mechanical calculations by G.Gamow on the prob¬ability of two nuclei penetrating their repulsive barriers and the proposal by H.Bethe and C.von Weizsacker of specific reactions were the final ingredients in the story. Indeed we now know that in the Sun about one in 1022 collisions give rise to a nuclear reaction.

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