Transcript Chapter 2: The Sky

Chapter 2:
The Sky
Common Units we will use
Common Conversions
Standard Prefixes
Review Notation
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1,000,000,000 = 109
1,000,000 = 106
1,000 = 103
1 = 100
.001 = 10-3
.000001 = 10-6
.000000001 = 10-9
Celestial Sphere
• When we look at the sky, we see stars but
have no actual clue as to how far away they
are. Therefore it is as if they were all on a
sphere out a long distance from us. This
conceptual device is known as the celestial
sphere.
• Distances between objects then are measured
in angles since all objects appear to be at the
same distance.
• This is an example of the use of a model.
Celestial Sphere Attributes
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North and South Celestial Poles.
Zenith (point directly overhead.
Nadir (point directly below – through earth)
Celestial equator (extension of plane through
the earth at equator and extended to sphere.
The Celestial Sphere
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Zenith = Point on
the celestial
sphere directly
overhead
Nadir = Point on
the c. s. directly
underneath (not
visible!)
Celestial equator
= projection of
the Earth’s
equator onto the
c. s.
North celestial
pole = projection
of the Earth’s
north pole onto
the c.s.
Discussion
• If the Earth did not rotate about its axis, could
we define a celestial sphere as we do now?
• Could we even define a set of poles and
equator?
• What is the difference between a constellation
and an asterism? Examples?
• What does the word apparent mean in the
context of “apparent visual magnitude”?
More discussion
• Where on Earth can you see both the North
and South Celestial poles simultaneously?
Orion
Constellations
Betelgeuse
Rigel
Stars are named by a Greek letter (a, b, g) according to their
relative brightness within a given constellation + the possessive
form of the name of the constellation:
Betelgeuse = a Orionis,
Rigel = b Orionis
The Magnitude Scale
First introduced by Hipparchus
(160 - 127 B.C.)
• Brightest stars: ~1st magnitude
• Faintest stars (unaided eye): 6th magnitude
More quantitative:
Now that we have instrumentation:
• 1st mag. stars appear 100 times brighter than 6th
mag. stars
• 1 mag. difference gives a factor of 2.512 in
apparent brightness (larger magnitude => fainter
object!)
Where did 2.512 come from?
• There are 5 magnitudes difference between
magnitude 1 and magnitude 6 stars.
• The magnitude 1 star is defined to be 100
times as bright as a magnitude 6 star.
• The steps are equal brightness factor.
• Therefore each one of the steps is equal to
(100) 1/5 = 2.512 (fifth root of 100)
Example:
Magn. Diff.
Intensity Ratio
1
2.512
2
2.512*2.512 =
(2.512)2 = 6.31
…
…
5
(2.512)5 = 100
For a magnitude difference of
0.41 – 0.14 = 0.27, we find an
intensity ratio of (2.512)0.27 =
1.28
Betelgeuse
Magnitude = 0.41 mag
Rigel
Magnitude = 0.14 mag
The Magnitude Scale
The magnitude scale system can be extended towards negative
numbers (very bright) and numbers > 6 (faint objects):
Sirius (brightest star in the sky): mv = -1.42
Full moon: mv = -12.5
Sun: mv = -26.5
More standard values
The Celestial Sphere
On the sky, we measure distances between objects as angles:
The full circle has 360o (degrees)
1o has 60’ (arc minutes)
1’ has 60” (arc seconds).