Sky & Telescope - May 2023 - 73

AKIRA FUJII
wrote in his 1610 work Sidereus nuncius,
" we may designate of the seventh
magnitude. "
That was just the beginning of how
deep into the night sky we could see, of
course. As optics improved, astronomers
observed stars and other objects bearing
ever fainter magnitudes. Modern
50-mm binoculars will reach stars of
about 9th magnitude, while a 6-inch
telescope will show those down to
around 13th magnitude. The Hubble
Space Telescope, for its part, can reach
as deep as magnitude 30 or fainter.
An Exact System
Even as late as the mid-1800s, however,
assigning stellar brightness was still a
judgment call. What one astronomer
might consider a 1st-magnitude star,
another might deem 2nd magnitude.
Astronomers needed a more exact way
to define the magnitude scale. So, in
1856, English astronomer Norman
Pogson proposed that astronomers
define a difference of five magnitudes
as a brightness ratio of exactly 100 to 1.
Thus, one magnitude corresponds to a
brightness difference of the fifth root of
100 (
√100), which is roughly 2.5.
5
Don't worry about the math. Just
know that the scale is logarithmic, so
a 1st-magnitude star is about 2.5 times
brighter than a 2nd-magnitude star,
approximately 2.52 times brighter than
a 3rd-magnitude star, around 2.53 times
brighter than a 4th-magnitude star, and
so on. The scale gives us an idea of just
how staggering the differences in the
brightness of stars in the night sky truly
are. So, while a difference of five magnitudes
(from, say, 1st to 6th magnitude)
translates to a ratio in brightness of 100
to 1, a difference of 10 magnitudes is a
ratio of 10,000 to 1, and of 20 magnitudes
is 100,000,000 to 1!
Though astronomers quickly adopted
Pogson's system, another problem
remained: Some 1st-magnitude stars are
brighter than other 1st-magnitude stars.
And, of course, there's the Sun, which
to us is obviously far brighter than any
other star. What to do? The unavoidable
solution was to continue the scale into
negative numbers.
ζ
3.4
ε
Thus, while the stars Vega, Rigel,
and Arcturus are around magnitude 0
(that is, brighter than magnitude 1),
Sirius shines at magnitude -1.5, Venus
at its brightest gleams at -4.9, and the
Sun blinds at -26.7. Going the other
way, into fainter magnitudes, 14.3 is
Pluto's current magnitude, while 16.5 is
roughly the faintest magnitude visible
using a 20-inch amateur telescope.
The Sickle asterism, or star pattern,
in Leo provides a handy way to
visualize stellar magnitudes (see image
below). Starting with Regulus, or Alpha
(α) Leonis, at magnitude 1.4, we move
one magnitude fainter to Algieba,
or Gamma (γ) Leonis, then another
magnitude class each to Zeta (ζ), Mu
(μ), and Kappa (κ) Leonis, respectively.
(For why we use Greek letters in star
charts, see Beginner's Space in the
February issue.) Note that a magnitude
class brackets the whole number, so a
5th-magnitude star can lie anywhere
between magnitude 4.5 and 5.4. Thus,
Kappa Leonis is a 5th-magnitude star.
Apparent versus Absolute
Magnitude
One last point: So far we've been talking
about apparent magnitude - how
bright objects appear from Earth. But
to determine how bright a star actually
is, we need to factor in its distance. For
this, astronomers use the absolute magnitude
scale, which indicates true stellar
luminosity. A star's absolute magnitude
is how bright it would appear if viewed
at a distance of 10 parsecs. (A parsec is a
standard distance unit astronomers use
and is approximately 3.26 light-years, so
10 parsecs is 32.6 light-years.)
Observed from this distance, the Sun
would shine at a mere 4.8 in absolute
magnitude. Meanwhile, Rigel, the blue
supergiant in Orion, would blaze at a
dazzling -8. If we could put them side
by side at a distance of 10 parsecs, our
Sun would appear positively dim in
comparison to Rigel. As with so much
in astronomy, the seemingly straightforward
question at the start of this
article doesn't have a simple answer. ¢
μ
3.9
κ
4.5
γ
2.4
S i c k l e o f L e o
Algieba
α
1.4
STELLAR MAGNITUDES AT A GLANCE In this image of the Sickle asterism in the constellation
Leo, the Lion, magnitudes of stars go up by one magnitude fainter from 1st-magnitude Regulus
all the way out to 5th-magnitude Kappa Leonis (a star not part of the Sickle proper).
sk yand tele scope .o r g * MAY 2023 73
Regulus

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