Energy Production in the Sun

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What sort of energy generation requirement has observation placed on the Sun?

• The Luminosity of the Sun is 4 x 10²⁶ Watts
• The Earth (and Solar System and hence the Sun) is 4.6 billion years old and it appears that the Sun was roughly the same brightness over this time span.

  The combination of these two things says that the Sun must have produced a huge amount of energy over its lifetime -- 6 x 10⁴³Joules. Note--the book will sometimes consider another measure of energy known as the erg. An erg is related to the Joule as 1 Joule = 10⁷ ergs. So, in ergs, the Sun radiates ~ 6 x 10⁵⁰ ergs in its lifetime.

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There were four ideas proposed to power the Sun:

• The Sun was formed hot and has since been cooling off. This leads to a lifetime of 10s of millions of years.
• The Sun is slowly shrinking because of gravity and has been producing heat through this gravitational contraction (compression). Lord Kelvin worked out this problem in the 1800s and showed that the Sun could shine for only 20-30 million years or so at its current rate.
• The Sun produces energy through ordinary chemical burning . Coal has a heat of combustion of ~ 35 million Joules per kilogram ===> 7x10³⁷ Joules is available if the Sun were pure coal! ===> lifetime of 6,000 years.
• The Sun is a huge nuclear reactor. Nuclear energy is efficient enough to power the Sun for up to 100 billion years.

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