The star $\alpha$ Centauri C and the star Groombridge 34 B have the same apparent magnitude, but $\alpha$ Centauri C is 1.3 pc away from Earth and Groombridge 34 B is 3.5 pc away. What is the luminosity of Groombridge 34 B compared with $\alpha$ Centauri C?
A) 2.7 times brighter
B) 7.2 times fainter
C) 2.7 times fainter
D) 7.2 times brighter

Question

Quizplus · Accepted Answer

The luminosity of a star compared to another can be determined by the inverse square law of light, which states that the intensity (or apparent brightness) of light is inversely proportional to the square of the distance from the source. Since both stars have the same apparent magnitude but different distances, we can compare their luminosities by squaring their distance ratios. The ratio of distances squared is $(3.5/1.3)^2$, which equals approximately 7.2, meaning Groombridge 34 B is 7.2 times brighter than F1F1F1S1αF1F1F10 Centauri C to have the same apparent magnitude at a greater distance.

The Star α\alphaα Centauri C and the Star Groombridge 34 B Have the B

The Star $\alpha$ Centauri C and the Star Groombridge 34 B Have the B