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A means of measuring the brightness of a star or other body: the lower the body's magnitude value, the brighter it appears in the sky. A star of magnitude +5.0 is dim, and hardly visible to the naked eye, while a star with a magnitude close to 0.00 (such as Vega in Lyra) is very bright indeed.
The system of stellar magnitudes is more than two thousand years old. Its first known use was by the Greek astronomer Hipparchus in about 120 BCE, whose informal system classified stars as first magnitude for the brightest down to sixth magnitude for the faintest.
Especially with the advent of the telescope, this kind of informal approach proved inadequate, and in the middle of the nineteenth century, standards for the calculation of magnitudes were introduced. According to these standards, which are still in use today, a difference in brightness of five magnitudes is equivalent to factor of 100. For example, Alpha Centauri or Rigil Kentaurus (with a magnitude of very nearly 0.00) is one hundred times brighter than Marsic in Hercules, one of the faintest named stars with a magnitude of almost exactly +5.00. It follows from this that a difference of one magnitude corresponds to a difference in brightness of a little over 2½ times.
The magnitude scale is calibrated to the brightnesses of about a hundred specific stars, all lying within a few degrees of the Northern Celestial Pole and thus termed the North Polar Sequence. By coincidence, the North Polar constellation, Ursa Minor, provides a useful 'key' to stellar magnitudes. The four stars that form the rectangular 'bowl' of the Little Dipper each represent a different level of brightness. Kochab, the brightest, has a magnitude of +2.05; Pherkad is magnitude +3.02, Alifa al Farkadain is +4.28, and the faintest, Anwar al Farkadain, has a magnitude of +4.96.
+6.5 is conventionally regarded as the limit of visibility with the naked eye. The actual limit, of course, will depend on the observer, but few people can see objects fainter than this value. Since the magnitude scale works by the relative brightness of objects, though, it can continue below this threshold of visibility. Objects of magnitude +6.00 are 2½ times fainter than those of magnitude +5.00, and so on. At the time of writing, for example, the dwarf planet Pluto has a magnitude of +13.8, which is far, far too faint to be seen with the naked eye, but calculable as about 400,000 times fainter than Alpha Centauri.
A few very bright stars and certain objects within the Solar System exceed magnitude 0.00, and therefore need negative numbers to describe their brightness. There are three stars with negative magnitudes: Sirius (-1.44), Canopus (-0.62) and Arcturus (-0.05), while Alpha Centauri comes extremely close to the zero magnitude mark at +0.01. Within the Solar System, all of the planets visible to the naked eye have negative magnitudes for at least some of the time. The brightest objects of all are the Moon (which can reach magnitude -13.0 or brighter) and, of course, the Sun, whose magnitude value varies around an extreme -26.7.
To a great extent, the brightness of objects in the sky depends on their position in space. Sirius is the brightest star in the sky, but it belongs to the dwarf classification, and is not particularly luminous in stellar terms - it appears brilliant because it is less than nine light years away. By comparison, the star Deneb in Cygnus appears much fainter than Sirius in the sky, but is actually a supergiant thousands of times more luminous than Sirius - it appears fainter because it is up to three thousand light years away, or about three hundred and fifty times farther from Earth.
For this reason, the brightness of objects as they appear in the sky is properly referred to as their apparent magnitude. A separate scale exists - absolute magnitude - to describe the intrinsic luminosity of an object, irrespective of the location of its observer. This concept is discussed in its own entry on this site.
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