The apparent magnitude of
a star is a measure
of its apparent brightness.
The brightest stars that can
be seen by the naked-eye are defined as “first magnitude”. Slightly fainter
stars are called "second magnitude". This scale continues down to
“sixth magnitude”, that are he faintest stars we can see (naked-eye) in very
good conditions (no light pollution, no Moon).
This is how the Greek astronomer
Hipparcos (in Latin: Hipparchus) ranked stars in the 2nd century
B.C. His important star catalog can be considered the first notable
writing in scientific astrometry. In the 2nd Century A.D. the
astronomer and astrologer Ptolemy adopted the Hipparcos scale in his own star catalog.
However, Ptolemy differentiated between some of the stars
that were listed as having the same magnitude (eg. slightly brighter, slightly
For the newcomer to astronomy,
it can be confusing that (for example) a star of magnitude 2 is fainter
(instead of brighter) than a star of magnitude 1. One would expect that as the
brightness of a star increases, the number would. This is not the case of
magnitudes: this system works “backwards”.
The first important change to
the six-magnitude system came with Galileo's telescopic observations. He could
see a large number of stars fainter than those that were classed as 6th
magnitude, and in 1610 he suggested that the brighter of these newly seen stars
should be classed as 7th magnitude.
Since then, the scale has
continued to grow. Astronomers discovered that 1st magnitude stars were
around 100 times brighter than 6th magnitude stars. This ratio (100) may seems too much, but it
is due to the “logarithmic” features of our eyes (the same can be said for our
ears: the decibel scale, that measures the power of sounds, is logarithmic either).
So in 1856 the astronomer
Norman Pogson proposed a scientific definition of magnitude, based on the real
ratio of physical luminosity for a difference of five magnitudes, that he
defined as a brightness ratio of exactly 100 to 1. Accordingly, a 1 magnitude
difference equates to a brightness of the 5th root of 100, approximately 2.512
times. In mathematical terms, magnitude is a logarithmic measure of brightness,
with base 2.512.
The faintest stars that can be seen under given conditions (naked-eye or telescope, light-pollution or not, bright Moon or not,
and so on) determine the “limiting magnitude”.
With small binoculars (such as
the popular 8x30) a dark sky enables us to see the 9th magnitude, and with regular
binoculars (such as the popular 10x50) the 10th magnitude can be reached.
A small telescope (3-inch-diameter) can reach
11m stars, and an average telescope for amateurs (6-inch-diameter) will let us
seek out 13m stars (or other 13m astronomical objects). Largest amateur telescopes (such as 20-inch-diameter
Dobsonian) allows us to see 16m stars.
The larger your optics, the
fainter you see. Every time the diameter is doubled, 1.5m are gained.
Photography enables fainter stars to be captured.
Earth-bound telescopes can record images approaching 24m, while Hubble Space Telescope pictures can reach
Each magnitude can be divided
into decimals: for example the bright stars Castor and Pollux (in the
constellation Gemini) have magnitudes 1.2 and 1.6 respectively.
A number of so-called
"first magnitude" stars showed to be much brighter than others that
were also classed as first magnitude. Then astronomers, rather than downgrade
all the other stars in magnitude, extended the scale. Thus, the star Vega in
the constellation Lyra is around 0.00m. The brightest star in the
night sky, Sirius, has a magnitude of -1.46m: so the scale allowed
negative numbers to include brighter celestial bodies. The closest star to the
real "first magnitude" is Spica, which is 0.98m.
The planets Mars, Jupiter and
Venus often appear even brighter than Sirius: Mars and Jupiter can be brighter
than –2 and Venus can reach a peak of –4.4. The full Moon reaches an overall
magnitude of –12.5 and the Sun of –26.7.
About photography, it was noticed
in the 1800s that some stars that were of the same brightness visually,
appeared to be of different brightness when seen on photographic film, and vice
versa. Photography turned out to be more sensitive to blue light, and less to
Two magnitude terms were
therefore employed. Visual magnitude, abbreviated as mv, refers to
how the star looks to our eye, while photographic magnitude, abbreviated as mp,
refers to the brightness of stars on "blue-sensitive black and white
film". The difference between these magnitudes is termed the colour index,
and is a measure of the colour of the star. The more negative the value, the
more blue the star is.
Limiting magnitude by the naked-eye
Many people believe that they can
see million stars by the naked eyes: this is unrealistic. The fainter magnitude
that can be seen by normal eyes in a dark sky (under perfect conditions) is 6.5m.
There are 8000 stars that are 6.5m or brighter. However, at a given
time, from a single point on Earth, we can see half sky (half the celestial
sphere) so we can actually see 4000 stars.
Unfortunately the “limiting
magnitude” is often lower than 6.5m and this dramatically reduces
the number of stars that can be seen. Here are 3 examples of very good sky
conditions, that can be reached in a mountain or desert area (with no light-pollution and no Moon), with limiting magnitude between 6.5 and 6.0:
In such good conditions, the
Milky Way structure is clearly visible (by the naked eyes), the nebula M42 in Orion
actually looks as a small nebula, and the galaxy M31 in Andromeda actually
looks like a small oblong galaxy.
Of course, if conditions are not
so good, fewer stars can be seen. Examples:
Rural area (low light-pollution)
Limiting Magnitude (LM) = 5m
Theoretical number of stars visible (naked eye): 1500
Actually visible at a given time: 750
Milky Way is barely visible; M42 and M31 look like small nebular objects rather than stars.
Sub-urban area (moderate/mild light-pollution)
Limiting Magnitude (LM) = 4m
Theoretical number of stars visible (naked eye): 500
Actually visible at a given time: 250
Urban area (severe light-pollution)
Limiting Magnitude (LM) = 3m
Theoretical number of stars visible (naked eye): around 160
Actually visible at a given time: around 80
Let's sum up in a single table:
The difference is striking: from a city you are likely to see around 80 stars in the sky, while in a mountain area you may see 4000 stars!
Of course these limiting magnitudes refer to the naked eyes. Binoculars and telescopes allow to see fainter stars,
depending on the diameter of their main lens (or their primary mirror in the
case of “reflecting telescopes”). Small binoculars (such as the popular 8x30) allows us
to gain more than 2 magnitudes while regular binoculars (such as the popular 10x50) allows us
to gain more than 3 magnitudes.
The gain allowed by binoculars or telescopes can be calculated upon the ratio between the diameter or the main lens (or primary mirror)
and the diameter of the eye's pupil: multiply 5 by the decimal logarithm of this ratio and that's the gain in magnitude.
Viewing in dark conditions, the diameter of the pupil is around 7 millimeters (several minutes are needed before our eyes adapt to dark conditions and our pupils enlarge).
So, if our binoculars or telescope diameter is D millimeters, the formula becomes: gain = 5 * log(D/7) magnitudes.
Apparent brightness is not equal to actual brightness: of course an extremely bright object may appear quite
dim, if it is far away (the rate at which apparent brightness changes, as the
distance from an object increases, is calculated by the inverse-square law.
The absolute magnitude,
M, of a star or galaxy is the
apparent magnitude it would have if it were 10 parsecs away (1 parsec is around 300,000,000,000,000
kilometres or 32.6 light years).
For comparison, the Sun
has an absolute visual magnitude of 4.83 (it also serves as a reference point)
and Sirius of 1.4.
Absolute magnitudes of stars generally range from -10 to +17,
that means that stars can be very, very different in brightness.
For an object with a given absolute magnitude,
5 is added to the apparent magnitude for every tenfold increase in the distance
to the object.
Thanks for your interest!
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