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show that the star Altair is relatively close to Earth, while the star Deneb is relatively...

show that the star Altair is relatively close to Earth, while the star Deneb is relatively far away from Earth. Despite their large difference in distance to Earth, both stars have relatively similar brightnesses (i.e. magnitudes) when viewed from Earth. What physical property must be different between the two stars in order to explain why they have similar brightnesses? (Hint: Think in terms of the “Inverse-square law for brightness” equation

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Answer #1

Initially we should take a look at the inverse-square law of brightness which states that

This simply means that the brightness observed for a source at a distance d is inversely proportional to the square of this distance (d) from the source for the observer.

And as per the brightness-luminosity relationship we have:

Now, for the given case in order for Altair and Deneb to have smiliar apparent brightness observed values the Luminosity of the far away star that is Deneb must have a very large value as compared to Altair so as to compensate for the large distance.

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