http://nobelprize.org/nobel_prizes/phys ... index.html
However, I found this part really amusing:
It's funny how close this analogy is to the flaw of the CURRENT model of the Sun and how close it is to a realization...What was wrong with Kelvin's analysis? An analogy may help. Suppose a friend observed you using your computer and tried to figure out how long the computer had been operating. A plausible estimate might be no more than a few hours, since that is the maximum length of time over which a battery could supply the required amount of power. The flaw in this analysis is the assumption that your computer is necessarily powered by a battery. The estimate of a few hours could be wrong if you computer were operated from an electrical power outlet in the wall. The assumption that a battery supplies the power for your computer is analogous to Lord Kelvin's assumption that gravitational energy powers the sun.
Neutrino rates lower than predicted, has some explanations and needs further investigations:The discovery of radioactivity opened up the possibility that nuclear energy might be the origin of solar radiation. (...) What was the connection between Einstein's equation and the energy source of the sun? (...) The idea that nuclear fusion powers stars is one of the cornerstones of modern astronomy and is used routinely by scientists in interpreting observations of stars and galaxies.
By the middle of the twentieth century, nuclear physicists and astrophysicists could calculate theoretically the rate of nuclear burning in the interiors of stars like the sun. But, just when we thought we had Nature figured out, experiments showed that fewer solar neutrinos were observed at earth than were predicted by the standard theory of how stars shine and how sub-atomic particles behave.