16 PART 1^ |^ EXPLORING THE SKY
allows modern astronomers to measure and report the brightness
of stars to high precision while still making comparisons to
observations of apparent visual magnitude that go back to the
time of Hipparchus.The Sky and Its Motion
The sky above seems to be a great blue dome in the daytime and
a sparkling ceiling at night. It was this ceiling that the fi rst astrono-
mers observed long ago as they tried to understand the night sky.The Celestial Sphere
Ancient astronomers believed the sky was a great sphere sur-
rounding Earth with the stars stuck on the inside like thumb-
tacks in a ceiling. Modern astronomers know that the stars are
scattered through space at diff erent distances, but it is still con-
venient to think of the sky as a great starry sphere enclosing
Earth.
Th e Concept Art Portfolio The Sky Around You on
pages 18–19 takes you on an illustrated tour of the sky.
Th roughout this book, these two-page art spreads introduce new
concepts and new terms through photos and diagrams. Th ese
concepts and new terms are not discussed elsewhere, so examine
the art spreads carefully. Notice that Th e Sky Around You intro-
duces you to three important principles and 16 new terms that
will help you understand the sky:
Th e sky appears to rotate westward around Earth each day,
but that is a consequence of the eastward rotation of Earth.
Th at rotation produces day and night. Notice how reference
points on the celestial sphere such as the zenith, nadir, hori-
zon, celestial equator, and the north celestial pole and south
celestial pole defi ne the four directions, north point, south
point, east point, and west point.
Astronomers measure angular distance across the sky as
angles and express them as degrees, arc minutes, and arc sec-
onds. Th e same units are used to measure the angular diam-
eter of an object.
What you can see of the sky depends on where you are on
Earth. If you lived in Australia, you would see many constel-
lations and asterisms invisible from North America, but you
would never see the Big Dipper. How many circumpolar
constellations you see depends on where you are. Remember
your Favorite Star Alpha Centauri? It is in the southern sky
and isn’t visible from most of the United States. You could
just glimpse it above the southern horizon if you were in
Miami, Florida, but you could see it easily from Australia.
Pay special attention to the new terms on pages 18–19. You need
to know these terms to describe the sky and its motions, but
don’t fall into the trap of just memorizing new terms. Th e goal of2-2
1
2
3
Th is allows you to compare the brightness of two stars. If
they diff er by two magnitudes. they will have an intensity ratio of
2.512 2.512, or about 6.3. If they diff er by three magnitudes,
they will have an intensity ratio of 2.512 2.512 2.512,
which is 2.512^3 or about 6.3, and so on (■Table 2-1).
For example, suppose one star is third magnitude, and
another star is ninth magnitude. What is the intensity ratio? In
this case, the magnitude diff erence is six magnitudes, and the
table shows the intensity ratio is 250. Th erefore light from one
star is 250 times more intense than light from the other star.
A table is convenient, but for more precision you can express
the relationship as a simple formula. Th e intensity ratio IA/IB is
equal to 2.512 raised to the power of the magnitude diff erence
mB mA:
__IIA
B (2.512)(mB^ ^ mA)If, for example, the magnitude diff erence is 6.32 magnitudes,
then the intensity ratio must be 2.5126.32. A pocket calculator
tells you the answer: 337. One of the stars is 337 times brighter
than the other.
On the other hand, when you know the intensity ratio of
two stars and want to fi nd their magnitude diff erence, it is con-
venient to rearrange the formula above and write it as
mB mA 2.5 log ( __IIA
B(^) )
For example, the light from Sirius is 24.2 times more intense
than light from Polaris. Th e magnitude diff erence is 2.5 log(24.2).
Your pocket calculator tells you the logarithm of 24.2 is 1.38, so
the magnitude diff erence is 2.5 × 1.38, which equals 3.4 magni-
tudes. Sirius is 3.4 magnitudes brighter than Polaris.
Th e modern magnitude system has some big advantages. It
compresses a tremendous range of intensity into a small range of
magnitudes, as you can see in Table 2-1. More important, it
16 PART 1PART^1 || EXPLORING THE SKYEXPLORING^ THE^ SKY
Pay
to k
don
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■ Table 2-1 ❙ Magnitude and IntensityMagnitude Difference Approximate Intensity Ratio
0 1
1 2.5
2 6.3
3 16
4 40
5 100
6 250
7 630
8 1600
9 4000
10 10,000
15 1,000,000
20 100,000,000
25 10,000,000,000