What Makes Star A Appear 4 Times Brighter Than Star B?

Apparent Brightness and Distance

When we observe stars from Earth, their apparent brightness can vary due to their distances from us. The apparent brightness of a star is how bright it appears to us from Earth. This brightness is influenced by the star's luminosity (actual brightness) and its distance from us.

Distance and Apparent Brightness Ratio

The apparent brightness of a star decreases as its distance from Earth increases. This relationship is described by the inverse square law, where the apparent brightness decreases with the square of the distance. In the case of Star A and Star B, their distances from Earth play a crucial role in their apparent brightness ratio.

Calculating Brightness Ratio

If Star A is 20 light-years away from Earth and appears 4 times brighter than Star B, which is 40 light-years away, we can calculate the brightness ratio using the formula:

x = (distance of Star A / distance of Star B)^2

By plugging in the given values, we find:

x = (20 / 40)^2 = (1/2)^2 = 1/4

Therefore, Star A appears 4 times brighter than Star B due to being closer to Earth and the influence of distance on apparent brightness.