More About Magnitudes
The History Behind the Magnitude SystemThe first ever star catalogues were compiled by the Greek astronomer Hipparchus around 2200 years ago. His scale turns out to be logarithmic – although to the human eye, a first magnitude star appears twice as bright as a second magnitude one, it turns out that it’s actually 2.512 times as bright. A difference of two magnitudes corresponds to a difference of 2.512 squared (i.e. about 6.3 times) as bright. We therefore have Hipparchus to thank for our reverse logarithmic scale! This scale is also known as the Pogson scale after Norman Pogson who determined, in 1856, that a difference of 5 magnitudes equates to a brightness ratio of 100:1 (i.e. 2.512 to the power of 5).
The Maths of the Magnitude System
The maths of magnitudes can be summed up in the equation m1- m2 = -2.5 * log ( f1/ f2 ) where
m1and m2 represent the magnitudes of two stars and f1and f2 represent their relative fluxes
By way of an example, imagine two stars visible in the night sky, one of which is 100 times brighter than the other. This value of 100 represents the ratio of the fluxes (f1/ f2)
Since the log of 100 is 2, we can conclude that m1- m2 = -2.5 * 2 = -5
This implies that star 1 is 5 magnitudes brighter (remember that our magnitude scale is inverse) than star 2.
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