Energy production in stars

FROM TIME IMMEMORIAL people must have been curious to know what keeps the sun shining. The first scientific attempt at an explanation was by Helmholtz about one hundred years ago, and was based on the force most familiar to physicists at the time, gravitation. When a gram of matter falls to the sun's surface it gets a potential energy where $M = 1.99×1033 gm$ is the sun's mass, $R = 6.96×1010 cm$ its radius, and $G = 6.67×10−8$ the gravitational constant. A similar energy was set free when the sun was assembled from intersellar gas or dust in the dim past; actually somewhat more, because most of the sun's material is located closer to its center, and therefore has a numerically larger potential energy. One‐half of the energy set free is transformed into kinetic energy according to the well‐known virial theorem of mechanics. This will permit us later to estimate the temperature in the sun. The other half of the potential energy is radiated away. We know that at present the sun radiates Therefore, if gravitation supplies the energy, there is enough energy available to supply the radiation for about $1015 sec$ which is about 30 million years.