In the 19th century, J. Herschel called the question of the source of the Sun’s energy “the great secret.” Among the first scientific

In the 19th century, J. Herschel called the question of the source of the Sun’s energy “the great secret.” Among the first scientific hypotheses was the assumption that our daylight is a hot, cooling body or is a chemically burning body. Julius Robert Meyer showed in the middle of the 19th century that even if the Sun were made of pure coal, it would burn out in a historically short period of time. Make an estimate of this time.
Hint. The mass of the Sun is M = 2 * 10 ^ 30 kg, the luminosity of the Sun is L = 3.8 * 10 ^ 26W, the specific heat of combustion of coal q = 2.7 * 10 ^ 7J / kg.

The burning time of coal with a mass equal to the mass of the Sun with a burning power equal to the luminosity of the Sun can be easily found by the formula t = qM / L. Hence the burning time of the “coal” Sun is about 5000 years. In addition, combustion would require a large amount of oxygen, which is not found in such quantities in the solar system. Already Mayer himself showed that to maintain the luminosity of the Sun, a constant fall on the luminary of a large amount of matter is required – about two masses of the Moon per year. And since the motion of the planets indicates the constancy of the mass of the Sun, this hypothesis required the same intense outflow of matter from it, which is not observed. Further research yielded other counter-arguments:
– the amount of meteoric matter in the space around the sun would be depleted very quickly, and its intensive renewal from outside the solar system is unlikely;
– if a powerful stream of meteorites fell on the Sun, then from their impacts the Earth would have a very high temperature, and geological strata would largely consist of meteoric matter