Two stars in our sky have the same apparent brightness.If neither of them is hidden behind gas or dust clouds,then we know that they
A) may be at different distances,in which case the nearest one must have the greater luminosity.
B) may be at different distances,in which case the farther one must have the greater luminosity.
C) must have the same temperature.
D) must be at the same distance away from us.

Question

Quizplus · Accepted Answer

If both stars have the same apparent brightness but are at different distances, the farther one must have a greater luminosity to appear just as bright as the nearer one. This is because the brightness of a star decreases with distance according to the inverse square law (brightness is inversely proportional to the square of the distance). Therefore, if they have the same apparent brightness, they cannot be at the same distance. Choice A is incorrect because the nearest star could have a lower luminosity and still appear to have the same brightness as the more distant star. Choice C is not necessarily true as stars with different temperatures can still have the same apparent brightness. Choice D is also incorrect as we cannot determine their distance from their apparent brightness alone.

Two Stars in Our Sky Have the Same Apparent Brightness