What Would We See if the Sun Suddenly Darkened?

[v_pino]

Homework Statement

Explain, as quantitatively as you can, what would be observed from Earth if the Sun's surface instantaneously darkened and hence explain why the brightness of a body cannot significantly alter on time scales significantly less than the light travel time across it.

Homework Equations

Hubble's constant = H
velocity of galaxy = v
distance from Earth = d
d = v / H

redshift = z
speed of light = c
z = v / c

The Attempt at a Solution

The first thing that came to my mind is that it will take ~ 8 minutes for the photons to reach the Earth, meaning that any observation from the Earth would be 8 min after the event. The Sun is still receding from the Earth. However, we will not be able to calculate the redshift.

Am I nowhere near what they are looking for in the answer?

thanks x

 

[Stonebridge]

Think about the fact that the Sun is a sphere (almost!), and that the centre of the visible sphere is nearer to you than the edge.

 

[kerimek]

I would like to add some more details to your answer. Firstly, you are correct in stating that it will take approximately 8 minutes for the photons to reach Earth, as the speed of light is approximately 299,792,458 meters per second. This means that the distance between the Sun and Earth is approximately 149,600,000 kilometers, which is equal to 8 minutes of light travel time.

Now, let's consider what would be observed from Earth if the Sun's surface instantaneously darkened. The first thing that would be observed is a sudden decrease in the brightness of the Sun. This is because the photons that were previously reaching Earth and providing us with light, would no longer be emitted from the Sun's surface. However, this decrease in brightness would not be instantaneous on Earth, as it would still take 8 minutes for the light from the darkened Sun to reach us. Therefore, we would see the Sun gradually getting dimmer over the course of 8 minutes.

Furthermore, the decrease in brightness would not be significant enough to be noticeable on Earth. This is because the Sun's surface area is very large compared to the distance between the Sun and Earth. This means that even if the entire surface of the Sun were to suddenly darken, the decrease in brightness would only be a small fraction of the total amount of light emitted by the Sun. This is why the brightness of a body cannot significantly alter on timescales significantly less than the light travel time across it.

To quantify this, we can use the inverse square law, which states that the intensity of light is inversely proportional to the square of the distance from the source. This means that as the distance between the Sun and Earth increases, the intensity of light decreases. Using this law, we can calculate that if the Sun's surface were to darken, the brightness on Earth would decrease by a factor of approximately 1/64,000,000,000. This is a minuscule decrease that would not be noticeable to the human eye.

In conclusion, if the Sun's surface were to instantaneously darken, the only observable effect on Earth would be a gradual decrease in brightness over the course of 8 minutes. This is due to the large distance between the Sun and Earth and the fact that the decrease in brightness would not be significant enough to be noticeable. This is why the brightness of a body cannot significantly alter on timescales significantly less than the light travel time