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What would be the effects on Earth if the sun was half its current diameter, but retained the same mass?

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  • $\begingroup$ at our suns end of life this exact thing will happen. $\endgroup$ Commented Apr 16 at 4:58

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The power output of the sun is given by the Stefan-Boltzman equation:

$$P = \sigma T^4 A$$ where $\sigma$ is Stefan-Boltzman constant, T is the temperature, and A is the surface area. The surface area of the sun is $A = 4\pi R^2$ where R is the radius of the sun so

$$P = 4\pi\sigma T^4 R^2$$

If the Sun was half its diameter with the same mass and temperature, the power output would be reduced by a factor of 4. The earth would receive less energy/time and be considerably cooler.

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  • $\begingroup$ If the sun's mass was compacted into half its current size, does this necessarily cause the temperature output to decrease? It would seem temperature would increase even though luminosity would decrease. $\endgroup$
    – JP_7
    Commented Apr 18 at 17:36

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