Question

What started as a fun exercise really annoys me because I cannot see where I got it wrong.

I initially wanted to see how many photons hit a pixel of a camera on the ISS pointed at the Earth - but I kept getting less than one at 1/250 shutter speed which would be invisible so now I'm just trying to get a number that makes some sense. Even the Earth as seen from the Moon is 40 times brighter than the Moon is from Earth, and the Moon can be captured at 1/250 shutter speed with cameras with the same pixel size I'm using here (5µm). What did I do wrong?

Answer 1

The amount of light reaching a camera on the ISS pointed at the Earth is reduced due to the distance between them, resulting in less than one photon at a 1/250 shutter speed. This is caused by the inverse square law, which states that the increase in the area that light must cover is proportional to the square of the distance that the light has traveled.

Step-by-step explanation:

The reason you are getting less than one photon at a 1/250 shutter speed when calculating how many photons hit a pixel of a camera on the ISS pointed at the Earth is due to the distance between the Earth and the ISS. As the distance between the camera and the subject increases, the amount of light reaching the camera decreases. This phenomenon is known as the inverse square law. The increase in the area that the light must cover is proportional to the square of the distance that the light has traveled.

For example, if you stand twice as far from the light source, you will intercept four times less light. Therefore, even though the Earth appears brighter from the Moon than the Moon does from Earth, the distance between the ISS and the Earth is much greater, reducing the amount of light reaching the camera sensor.