Final answer:
Star A appears 4 times brighter than Star B.
Step-by-step explanation:
Star A and Star B have different apparent brightnesses but identical luminosities. If Star A is 20 light-years away from Earth and Star B is 40 light-years away from Earth, we can determine which star appears brighter by comparing their distances. The apparent brightness of a star decreases as its distance from Earth increases. Since Star A is closer to Earth than Star B, it will appear brighter.
The apparent brightness of a star decreases with the square of the distance. If Star A is 20 light-years away and appears brighter than Star B, which is 40 light-years away, by a factor of x, then the brightness ratio can be calculated using the equation:
x = (distance of Star A / distance of Star B)^2
Plugging in the given values, we have:
x = (20 / 40)^2 = (1/2)^2 = 1/4
Therefore, Star A appears 4 times brighter than Star B.