Question Video: Comparing the Distances of Two Stars from Earth Based on Apparent Brightness Physics

Two stars, A and B, are known to have the same brightness. When observed by an astronomer on Earth, however, star B appears brighter than star A. Which star is farther away from Earth?

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Video Transcript

Two stars, A and B, are known to have the same brightness. When observed by an astronomer on Earth, however, star B appears brighter than star A. Which star is farther away from Earth?

Okay, so in this exercise, we have these two stars, star A over here and star B we’ll say is over here. And an important fact about these two stars that we’re told is that they have the same brightness. In other words, they give off the same amount of light. But then, we’re told that when these two stars are observed by an astronomer on Earth, they don’t appear to have the same brightness. But rather, star B appears brighter than star A. Based on this information, we want to figure out which of these two stars is farther away from Earth.

On one level, the two bits of information we have about these star brightnesses seem to contradict one another. At first, we’re told that they’re the same. But then, we’re told that star B appears brighter than star A. What we need to realise though is that these are two different assessments of the star brightness. The first one that tells us they have the same brightness is a measure of what’s called the absolute magnitude of the brightnesses of these stars.

When we talk about absolute magnitude, we’re describing the brightness of a star in terms of the intrinsic properties of the star all by itself. It’s got nothing to do with how the star is looked at or perceived. So the first sentence of our statement is telling us that, in an absolute sense, regardless of how these stars are looked at, they have the same brightness. They give off the same amount of light. But if we introduce an observer, the astronomer on Earth, then it may not appear that these stars have the same brightness.

Our statement tells us that the astronomer, based on Earth, perceives star B to be brighter than star A. And this makes perfect sense if star B is closer to the astronomer than star A is. In that case, more of the light given off by star B, compared to the light given off by star A, would reach the astronomer’s eye. So then, rather than these two pieces of information about star brightness contradicting one another, they actually give us more information about the space relationships of these stars to the astronomer. Since star B appears brighter than star A, that must mean that star A is farther away from the astronomer. And since the astronomer is on Earth, that must mean that star A is also farther away from Earth than star B.

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