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## The Question

(Submitted March 02, 1998)

How did scientists determine the starting point for the magnitude scale? I am in eighth grade and have a fair background in astronomy. I understand that brighter stars may have negative numbers on this scale, but how did someone determine "zero" on this scale?

The magnitude system goes back to the second century B.C. when the Greek astronomer Hipparchus divided stars into six classes. The number one stood for the brightest and six was the faintest. In 1856, Norman Pogson replaced this system with one based on mathematics, but he tried to match the old system as closely as he could. He used the formula:

m = -2.5 * log (F/Fstand)

Now if you don't understand this formula, I'll help you through it. First I'll define the terms:

m - the magnitude
F - is the flux from our star
Fstand - is the flux from a standard star

By the way, flux is basically the amount of energy arriving at earth from the star. Now the tricky part of this is the "log". That is a function that tells you home many powers of ten are in a number. For example:

log(1000) = 3
log(100) = 2
log(10) = 1
log(1) = 0
log(.1) = -1
log(.01) = -2
log(.001) = -3

So with a little knowledge of the log function, we can tell where the zero point of the magnitude system is. When the flux of the star is the same as the standard, then we have:

m = -2.5 log(1)
m = -2.5 * 0
m = 0

So when our star has the same flux as the standard star its magnitude is zero. Now a negative magnitude would be when a star is brighter than the standard star. Most likely this will happen when we calculate the absolute magnitude. This is when we correct for distance. We pretend that all the stars were moved to some standard distance and then we determine what the magnitude would be. Sometimes when the star is "closer", it is brighter than the standard and the absolute magnitude is negative.

In modern use, the star Vega defines magnitude 0.0.

Hope this helps,

Jeff Silvis
For Ask an Astrophysicist

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