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.
