Standard stars are stars which have had their magnitudes in different filters, measured very carefully by astronomers. By comparing the magnitude of your object with the magnitude of a standard star that you have observed, and knowing its real magnitude, you can calculate the calibrated magnitude of your object. Comparison of different people's data with calibrated magnitudes is then perfectly valid because you are now comparing like with like. Initially, you may choose not to observe a standard star, so the magnitudes you are calculating are not calibrated magnitudes - they are instrumental magnitudes (sometimes called relative or differential magnitudes). This does not affect the shape of any lightcurve that you might produce – it merely affects the numerical values that you might place on the y-axis of your lightcurve. If you were to use calibrated magnitudes, all the data on your plot would be shifted by the same amount in the same direction. This idea also applies to measurements of stars in an open or globular cluster. Measuring all the stars with a set of images from the same telescope using the same software allows us to create a meaningful colour magnitude diagram - standard stars help us define the axes in a way which allows comparisons between clusters.

### The History Behind the Magnitude System

The 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- m= -2.5 * log ( f1/ f) where

m1and mrepresent the magnitudes of two stars and f1and frepresent 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- m= -2.5 * 2 = -5

This implies that star 1 is 5 magnitudes brighter (remember that our magnitude scale is inverse) than star 2.