<p>The power output of the sun is given by the Stefan-Boltzman equation:</p>
<p><span class="math-container">$$P = \sigma T^4 A$$</span> where <span class="math-container">$\sigma$</span> is Stefan-Boltzman constant, T is the temperature, and A is the surface area. The surface area of the sun is <span class="math-container">$A = 4\pi R^2$</span> where R is the radius of the sun so</p>
<p><span class="math-container">$$P = 4\pi\sigma T^4 R^2$$</span></p>
<p>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.</p>

CC BY-SA 4.0
2024-04-18T17:36:26.997Z
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.
JP_7
CC BY-SA 4.0
2024-04-14T16:37:00.273Z
2024-04-14T16:37:00.273Z
Stevan V. Saban
<p>What would be the effects on Earth if the sun was half its current diameter, but retained the same mass?</p>

CC BY-SA 4.0
2024-04-16T04:58:47.370Z
at our suns end of life this exact thing will happen.
trond hansen
<climate-models><astronomy><geobiology>
What would be effects if sun was smaller, but had same mass?
JP_7
# What would be effects if sun was smaller, but had same mass?

(Asked by: username_0 on 2024-04-06)

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

**Tags:** climate-models, astronomy, geobiology

> **Comments:**
> **username_1**: at our suns end of life this exact thing will happen.  

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## 1 answers

### Answer by username_2 on 2024-04-14. Score: 1

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.

> **Comments:**
> **username_0**: 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.  

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