Imagine that the entire surface of the sun is covered with a large black screen, leaving only a small hole through which

Imagine that the entire surface of the sun is covered with a large black screen, leaving only a small hole through which a huge sunspot can be observed. With which of the celestial bodies can you compare its brilliance: the Moon, Venus, Saturn, the pole star? The spot size is equal to one arc minute, the temperature is 4500 K.

Answer: remember that the apparent diameter of the sun is 30 arc minutes, and the temperature of its surface is 5800 K. Thus, the angular area of ​​the visible part of the solar disk will decrease 900 times. In addition, the radiation power is proportional to the 4th power of temperature), and the spot will shine weaker than a portion of the Sun of the same size, but outside the spot by (5800/4500) ^ 4 = 3 times. This means that the total gloss will decrease by a factor of 2700. The corresponding change in magnitude will be approximately 8.6m. The apparent stellar magnitude of the Sun is –26.8 tons, and the brightness of the spot will be –18.2 tons. It is more than a hundred times brighter than the full moon.