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It is known that Jupiter is mostly made of hydrogen, but that it is not massive enough to start nuclear fusion. In other words, Jupiter is not a star, but could be a star if someone added hydrogen to the planet.

How can the critical mass, where there is sufficient thermal energy at the core to start nuclear fusion, be calculated?

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    $\begingroup$ Related: physics.stackexchange.com/q/776 $\endgroup$ – user139561 Dec 19 '16 at 11:20
  • $\begingroup$ I look forward to people's answers, but to my knowledge there isn't a good way to calculate the value from first principles. Observationally it seems to be between about $0.5-0.1 M_\odot$, with the lower end of the range (seemingly) favored more strongly as of late. $\endgroup$ – DilithiumMatrix Dec 19 '16 at 22:25
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Yes, your logic is correct, if we kept adding hydrogen to jupiter, it could eventually become a star.

See: http://www-star.st-and.ac.uk/~kw25/teaching/stars/STRUC5.pdf

So long as you understand the basic thermodynamics in there then you will be able to follow through to the end, if not, and you are not interested, then the critical mass for collapse into a star is approximately 0.08 * (Mass of Sun).

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