Apparent Magnitude (m)

When we look at the stars in the sky some seem very bright whilst others are just bright enough to be visible. How bright a star appears to be is known as its apparent magnitude (m).

Originally (Hipparchus) the scale was from 1 to 6. The brightest stars were m=1 and the faintest, just barely visible with the naked eye, were m=6. Going from 1 magnitude to another meant an increase or decrease in brightness of about 2 times. This was hardly very scientific.

In 1856 Pogson made things more formal by saying that a magnitude 1 star was 100 times brighter than a magnitude 6 star. The difference between magnitudes is therefore the fifth root of 100 = 2.51, known as Pogson's ratio. So if star A has an apparent magnitude of 5 and star B has an apparent magnitude of 4 then B appears 2.51 x brighter than A.

  
We also need a reference star, a star of known brightness that we can compare all the others by. Various stars have been used for this including Polaris and Vega.

Here are some apparent magnitudes

Bear in mind that the apparent magnitude of a star depends on two things:

How luminous it actually is (its absolute magnitude) and how far away it is.

The Inverse Square Law
Imagine an object, such as a star, which emits light. As the light spreads out it becomes less intense. One can see from the diagram below that if a certain amount of light travels twice as far then it spreads out over an area four times as big. This means that it will be 1/4 of the intensity it was.

The intensity of the light is proportional to 1/r² where r is the distance from the source.

If there were two stars as luminous as each other but one was twice as far away as the other then it would appear 1/4 as bright as the other.

If two stars appeared the same brightness but one was further away we know from the above that it is √ 2 x further than the closer star.