Introductory Astronomy: Apparent Brightness (or Flux)
When we look at a bright light, our eyes respond to the visual wavelength energy falling on the eye's retina, which tells us how bright the object looks. Brightness, therefore, is related to how much energy is entering our eyes. We describe the amount of energy entering our eyes per second as the Flux. Flux is simply the amount of energy which falls on a certain area (like our eyes) each second. A very bright object has a large flux, or a lot of energy falling on our eyes; a faint object has a small flux. We can see this in the diagram (right).
Greek Astronomers spent a lot of time looking at the stars and comparing how bright stars are in order to learn more about them. They developed a system of numbers which describe the relative brightnesses of different stars. In their system, the brightest stars were called "Magnitude 1" and the faintest were called "Magnitude 6". They did this because, to the Greeks, 1 was the perfect number, 2 was less perfect than 1, and so on.
The Greeks classified the stars they could see according to this system. However, since then we have developed telescopes which can see much farther than the eye. To include these fainter stars, scientists have expanded the Greek system to include higher numbers (remember that the higher the number, the fainter the star!). Also, the Greeks did not realize that the Sun is just another star. Because the Sun appears so bright to the eye, scientists had to expand the Greek system in the other direction (to numbers less than 1) to include the Sun. This meant they had to include negative numbers. So, the Sun was given an apparent magnitude of -26. (For comparison, the full Moon has an apparent brightness of -12.5 and Venus at its brightest has a magnitude of -4.4.) Today the scale extends from -26 (the Sun) to 29 (a faint quasar seen by the Hubble Space Telescope). The Sun appears to be the brightest object to our eyes, and stars with apparent magnitudes of 6 and greater are too faint to even be seen without a telescope!
How do these magnitudes relate to Flux? Modern astronomers have fixed the scale so that a star which is 5 magnitudes brighter than another star will have 100 times more flux. For example, the full Moon has an apparent magnitude of about -12.5 and Mars, at its brightest has an apparent magnitude of about -2.8. This means that the full Moon is about 10 (-12.5 - (-2.8)) magnitudes brighter than the maximum brightness of Mars. Each five magnitudes means 100 times more flux. Since 10 = 5 x 2, about 10,000 (100^(2)) times more flux reaches our eyes from the full Moon than from Mars.
Magnitudes are not hard. You just need to remember that smaller numbers mean brighter stars than larger numbers and that negative numbers are smaller than positive numbers!!