Size and Luminosity
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Transcript: The Stephan-Boltzmann Law allows us to estimate the size range of stars like the Sun that get their energy from fusion of hydrogen into helium. As a reference, the Sun has a luminosity of 3.8 times 1026 watts, a surface temperature of 5,700 degrees Kelvin, and a radius of 700 thousand kilometers. The Stephan-Boltzmann Law gives a scaling that radius is proportional to the square root of luminosity and the temperature to the minus two power. This means that there are stars 106 times more luminous than the Sun at a temperature of 40 thousand Kelvin that must have sizes of 20 solar radii. At the other end of the energy sequence, there are stars emitting one thousandth the luminosity of the Sun with temperatures of 2,500 Kelvin that are one-fifth the size of the Sun. Thus, there is a factor of a hundred in the size range of stars like the Sun that convert hydrogen into helium by fusion.
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