Is the Sun on fire?

Where does the energy production of the Sun come from?

Maybe it is burning.

Any intelligent child might ask this question. A child doesn't have the knowledge base to answer it, but now we do.

• Consider an example of burning methane (natural gas):
  C H₄ + 2 O₂ --> C O₂ + 2 H₂ O
• Laboratory measurements show that burning methane releases an amount of energy per kg of ingredients equal to
  E/M = 1.1 x 10⁷ J/kg
  (Recall that a watt is a joule (J) per second).
• The mass of the Sun is
  M = 2 x 10³⁰ kg
• So if the whole Sun were made of methane and oxygen, the energy that could be released by burning all of it would be E = (E/M) x M = (1.1 x 10⁷ J/kg) x (2 x 10³⁰ kg) = 2.2 x 10³⁷J
  
• That's a lot. But the Sun is radiating energy at a rate of L= 4 x 10²⁶ J/s
• Burning methane at that rate, it would last for a time t = E/L = 2.2 x 10³⁷J / (4 x 10²⁶ J/s) ~ 6 x 10¹⁰s
  
• There are 3 x 10⁷ seconds in a year, so this time is t ~ (6 x 10¹⁰s) /( 3 x 10⁷ s/yr) ~ 2000 years
  
• Since the Earth has been around, and reasonably warm, much longer than that, we may conclude that the source of the Sun's energy is not burning methane.
• And it can't be any other chemical process either, since the energy available in any chemical process is roughly the same as for burning methane.

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Updated 3 October 2007