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Classification of Stars By
Luminosity
Apparent Magnitude
Hipparchus of Rhodes (aound 160 BC)
Developed a system to compare the
apparent brightness of stars in the sky
with which he recorded the relative
brightness of the stars in a catalogue
listing 850 stars.
This system with modifications is
still used today.
He called the brightest stars in the sky
first magnitude and the dimmest
visible to the naked eye sixth
magnitude. Stars of intermediate
brightness were given intermediate
values.
THE EXTENDED
APPARENT
MAGNITUDE
SCALE
Apparent magnitude
• Apparent magnitude is not necessarily
related to the amount of light actually
produced by the star but is simply a
measure of how bright it appears to be
from Earth.
• (Some bright stars are simply close
neighbours while other giant stars may
appear equally bright but are also very
distant.)
The systemisation of apparent
magnitude
In the nineteenth century systems were developed for measuring exactly
how much light was arriving from a star. The intensity of the light (the
energy arriving every second per metre 2 at Earth) was calculated. This is
sometimes referred to as the apparent brightness of the star
Astronomers were able to show that a first magnitude star was about
100x as intense as a sixth magnitude star.
As a result apparent magnitude was redefines to so that a magnitude
difference of 5 EXACTLY corresponds to a factor of 100 in the light energy
received
1
100x
brighter
2
3
4
5
6
The difference in apparent
brightness
1
2
3
5
4
6
x 2.512
x 2.512
x 2.512
x 2.512
x 2.512
brighter
than 2
brighter
than 3
brighter
than 4
brighter
than 5
brighter
than 6
So it takes about 2 ½ third magnitude stars to be as bright as 1 second
magnitude star
So it becomes apparent that eye is a logarithmic detector, and the magnitude
system is based on the response of the human eye, it follows that the
magnitude system is a multiplicative (logarithmic scale).
Apparent brightness
The actual apparent brightness of a star (its Intensity at Earth) actually
obeys the inverse square law:
P
I
2
4d
Where P is the power produced by the star and d is the distance
from the Earth.
Apparent magnitude
• By itself the apparent magnitude of a star
does not give us enough information to
calculate how bright a star really is.
• To do this we need to know the distance to
the star.
Units of distance
• Although we could measure distances
simply in metres it is useful to have a
larger distance unit:
the light year is the distance travelled by
light in 1 year = 9.46 x1015km.
The parsec
The parsec is the distance at which parallax
of an object would be 1 second of arc
The observed ellipse is tiny even for nearby stars
θ
1 parsec = 3.26ly
When the
angle θ is 1
second of arc
(1/3600
degree) the
distance x is
1 parsec
x
Absolute Magnitude
• Imagine that you could bring every star in the
sky to the exact distance of 10 parsecs.
• We could then directly compare their true
brightness.
• The absolute magnitude of a star is defined as
the apparent magnitude it would have at a
distance of 10 parsecs.
• If the Sun were moved to a distance of 10
parsecs its apparent magnitude would be +4.8
therefore the absolute magnitude of the Sun is
4.8.
The relationship between absolute
magnitude and apparent magnitude
d
m  M  5 log
10
Where m is the apparent magnitude
M is the absolute magnitude
d is the star’s distance in parsecs