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Level of extremeness. As something increases in size or the amount, magnitude increases.

The magnitude of a vector can be found by the following equation.

Assume V= ai+bj+ck
Then: ||V|| = (a^2+b^2+c^2)^1/2

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.

Mag"ni*tude (?), n. [L. magnitudo, from magnus great. See Master, and cf. Maxim.]

1.

Extent of dimensions; size; -- applied to things that have length, breath, and thickness.

Conceive those particles of bodies to be so disposed amongst themselves, that the intervals of empty spaces between them may be equal in magnitude to them all. Sir I. Newton.

2. Geom.

That which has one or more of the three dimensions, length, breadth, and thickness.

3.

Anything of which greater or less can be predicated, as time, weight, force, and the like.

4.

Greatness; grandeur.

"With plain, heroic magnitude of mind."

Milton.

5.

Greatness, in reference to influence or effect; importance; as, an affair of magnitude.

The magnitude of his designs. Bp. Horsley.

Apparent magnitude Opt., the angular breadth of an object viewed as measured by the angle which it subtends at the eye of the observer; -- called also apparent diameter. -- Magnitude of a star Astron., the rank of a star with respect to brightness. About twenty very bright stars are said to be of first magnitude, the stars of the sixth magnitude being just visible to the naked eye. Telescopic stars are classified down to the twelfth magnitude or lower. The scale of the magnitudes is quite arbitrary, but by means of photometers, the classification has been made to tenths of a magnitude. <-- the difference in actual brightness between magnitudes is now specified as a factor of 2.512, i.e. the difference in brightness is 100 for stars differing by five magnitudes. -->

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