In astronomy, magnitude is a logarithmic measurement of observed
brightness. The logarithmic nature of magnitudes comes from the fact
that the response of the human eye to light is logarithmic. The
magnitude units devised by ancient Greek astronomers correspond to
equal flux ratios, or

f(a)
m(a) - m(b) = const * log ------ (1)
f(b)

implying a logarithmic scale. Five magnitudes corresponds to a factor of 100
difference in flux, which makes the constant in the equation above equal
to -2.5.

Magnitudes are typically measured with reference to an astronomical
standard, usually the star Vega which has a magnitude of 0.0.
*Increasing*
magnitudes denote *fainter* objects, thus a star with a magnitude of
-1.0 is *brighter* than a star with a magnitude of +1.0.
The unaided human eye can detect objects with magnitudes as faint as
approximately 6.0. The deepest telescopic image -- the Hubble Deep Field --
detected objects as faint as 28.0 to 29.0, more than a thousand million times
fainter.

The apparent magnitude of an object, usually denoted by a lower case *m*,
is the perceived brightness of an object.
Thus The Sun has an *apparent magnitude* of -26.7, but only
because it is nearby, cosmically speaking.

The absolute magnitude of an object, denoted by an upper case *M* is the apparent magnitude an object
*would* have if we were observing it from a distance of ten parsecs.
The absolute magnitude of the Sun is around +4.75, while the apparent magnitude
of an average galaxy would be about -19.5.

The apparent and absolute magnitudes of an object (if both are known) can
be used to determine the distance to an object, using the formula

m - M = ( 5 * log(D) ) - 5 + A (2)

where D is the distance in parsecs, and A is a fudge factor which accounts
for extinction by dust and gas between us and the object. *m* is
usually straightforward to measure, but *M* requires that you know
something about the object in advance.

Magnitudes are often measured in specific wavelengths or filters, and
many filter sets have been defined for specific uses. Often, objects are
described in terms of their color, which is the difference in observed
magnitudes in different filters. For example,

(B - V) = m(B) - m(V) (3)

where

*B* and

*V* are filters in the

Johnson filter set, measuring

blue and

green-

yellow light, respectively. By equation (1), this
corresponds to a ratio of fluxes observed in the different filters. The
color can, for example, tell you the

temperature of an object, or tell you
the amount of

interstellar reddening.
You may also see

bolometric magnitude, which is the sum of all emitted
radiation from

radio waves to

gamma rays, used to measure the total

luminosity of an object.