# The Stefan-Boltzmann Law and Sunspots

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• K. Doc Holiday
In summary, the Stefan-Boltzmann Law has been well tested and found to be accurate in predicting the brightness of the sun's surface. However, there is a discrepancy in the luminosity of sunspots compared to the photosphere, which could be due to other factors such as magnetism. It is important to refer to reliable sources and textbooks on stellar physics rather than making assumptions.

#### K. Doc Holiday

The Stefan-Boltzmann Law

Question: Is this law proven to be true? If so, then what about sunspots?

The surface of the sun is roughly double the temperature of an umbra which means it should be 16 times brighter according to this law. It isn't.

The luminosity of the photosphere is 10,000 times the luminosity (1,000,000%) of a sunspot umbra. That seems like a huge discrepancy. Could something else be at play? Could sunspots be a different element and/or a different state of matter?

I know current theory blames magnetism. In order for that to be the mitigating factor wouldn't sunspots have to generate their own magnetic field? Can hydrogen do that?
Just asking.

Respectfully
Doc Holiday

K. Doc Holiday said:
Is this law proven to be true?
In science you never ”prove” anything. You test your theory by checking whether the predictions it makes match your experimental result. In the case of the Stefan-Boltzmann law, it has been extremely well tested and found accurate.

K. Doc Holiday said:
If so, then what about sunspots?
What about them? The physics of sunspots are also well understood. I suggest reading a textbook on stellar physics rather than making assumptions.

davenn
@K. Doc Holiday could you please provide sources for those numbers so we can tell if you have properly interpreted what you are reading.

## What is the Stefan-Boltzmann Law and how does it relate to sunspots?

The Stefan-Boltzmann Law is a physical law that describes the relationship between the temperature of an object and the amount of thermal radiation it emits. This law states that the total energy emitted by a blackbody (an object that absorbs all radiation that falls on it) is proportional to the fourth power of its absolute temperature. Sunspots, which are cooler regions on the surface of the sun, emit less thermal radiation compared to the surrounding areas due to their lower temperature.

## How was the Stefan-Boltzmann Law discovered?

The law was first derived by Josef Stefan in 1879 and later refined by Ludwig Boltzmann in 1884. They conducted experiments measuring the radiation emitted by various objects at different temperatures and found that the amount of radiation increased exponentially as the temperature increased. This led to the formulation of the Stefan-Boltzmann Law.

## Why is the Stefan-Boltzmann Law important in understanding the sun?

The sun is a blackbody, meaning it absorbs and emits all forms of radiation. Therefore, the Stefan-Boltzmann Law is crucial in understanding the amount of thermal radiation the sun emits and how it varies with changes in temperature. This law also helps us understand the energy balance of the sun and how it affects Earth's climate.

## How do sunspots affect the temperature of the Earth?

Sunspots have a direct impact on the Earth's temperature due to their influence on the amount of thermal radiation emitted by the sun. When there are more sunspots, the sun's overall temperature increases, leading to warmer temperatures on Earth. Conversely, when there are fewer sunspots, the sun's temperature decreases, resulting in cooler temperatures on Earth.

## Can the Stefan-Boltzmann Law be applied to other objects besides the sun?

Yes, the Stefan-Boltzmann Law can be applied to any object that emits thermal radiation, regardless of its size or composition. This law has been used to study various objects in the universe, such as stars, planets, and even everyday objects like light bulbs and human bodies. However, it is most commonly used in the study of celestial bodies, including the sun and other stars.