(a) How far away from the Earth it is and
(b) How bright the star really
is
(a) It is easy to see why the distance from the Earth affects how bright the star
appears. Imagine looking at a candle flame a metre away from you and then looking at the
same candle flame when it is 100 m away. Although the amount of light energy coming from
the candle does not change the amount of this energy getting into your eye from the candle
when it is close to your eye is much greater than that when it is further away (See Figure
1)
(b) The other thing that affects how bright a star appears is of course how bright it really is. Think about our candle again and this time compare it with a car headlight. If the car is, say, a mile away the headlight might look about as bright as the candle does when it is a metre away although of course the car headlight is really very much brighter. It is just the same with stars. A star that is very bright but very far away will appear to us to be the same brightness as a fainter star which is closer to the Earth.