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```Charles Hakes
Fort Lewis College
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Chapter 10
Measuring the Stars
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Fort Lewis College
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Outline
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Telescope lab next Monday, Thursday?
Constellation sign-ups (will be on door)
Magnitudes
Parallax
Colors
Sizes
H-R diagrams
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Fort Lewis College
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Chapter 10
Parallax
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Fort Lewis College
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Figure P.12
Parallax Geometry
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Fort Lewis College
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Figure P.11
Parallax
Recall information
from Chapter 0
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Fort Lewis College
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Figure 10.1
Stellar Parallax
distance (pc) =
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Fort Lewis College
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parallax angle
(arc sec)
Distance Analogy
• If the Sun is a marble…
• The Earth is a grain of sand 1 m
away.
• The solar system is ~100 m in
diameter
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Fort Lewis College
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Distance Analogy
• If the Sun is a marble…
• The Earth is a grain of sand 1 m
away.
• The solar system is ~100 m in
diameter
• The next star is in Albuquerque!
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Fort Lewis College
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Figure 10.2
Sun’s
Neighborhood
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Fort Lewis College
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Parallax Measurements
• Earth-based measurements can typically be made
to 0.03”, or to a distance of ~30 parsecs (pc)
• Distances to several thousand stars are known
this way.
• The Hipparcos satellite extends the distance to
~200 pc, so distances to nearly one million stars
can be measured with parallax.
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Fort Lewis College
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Figure 10.3
Real Space Motion - Barnard’s Star 22 years apart
• Nearby stars also show
proper motion, or
transverse velocities.
• Only a few hundred
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Fort Lewis College
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If a star has a parallax of 0.05”, then its
distance must be
A) 5 light years.
B) 5 parsecs
C) 20 light years.
D) 20 parsecs.
E) 200 parsecs
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Fort Lewis College
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If a star has a parallax of 0.05”, then its
distance must be
A) 5 light years.
B) 5 parsecs
C) 20 light years.
D) 20 parsecs.
E) 200 parsecs
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Fort Lewis College
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Chapter 10
Magnitudes
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Fort Lewis College
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If Venus is magnitude -4.4, and
Sirius is magnitude -1.4, then
A) Sirius is ~15.8x brighter than Venus
B) Sirius is ~3x brighter than Venus
C) Venus is ~15.8x brighter than Sirius
D) Venus is ~3x brighter than Sirius
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Fort Lewis College
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If Venus is magnitude -4.4, and
Sirius is magnitude -1.4, then
A) Sirius is ~15.8x brighter than Venus
B) Sirius is ~3x brighter than Venus
C) Venus is ~15.8x brighter than Sirius
D) Venus is ~3x brighter than Sirius
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Fort Lewis College
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More Precisely 10-1
More on the Magnitude
Scale
• Absolute magnitude
is how bright a star
would appear at
10pc. (a very
arbitrary distance)
• The Sun’s absolute
magnitude is +4.8
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Fort Lewis College
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Magnitudes
• Apparent Magnitude
• how bright it looks
• depends on distance
• brightness depends on distance2
• Absolute Magnitude
• Only depends on Luminosity (how much energy
is being produced)
• Does not change with distance
• At 10pc, Apparent magnitude= Absolute
magnitude
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Fort Lewis College
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Magnitudes and Distance
• Example:
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2 flashlights have the same luminosity
flashlight A = apparent “brightness” 4.0 units
flashlight B = apparent “brightness” 2.0 units
Which is closer and by how much?
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Fort Lewis College
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Magnitudes and Distance
• Example:
•
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2 flashlights have the same luminosity
flashlight A = apparent “brightness” 4.0 units
flashlight B = apparent “brightness” 2.0 units
Which is closer and by how much?
• Calculate brightness ratio
• Star A is 2.0x brighter
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Fort Lewis College
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Magnitudes and Distance
• Example:
•
•
•
•
2 flashlights have the same luminosity
flashlight A = apparent “brightness” 4.0 units
flashlight B = apparent “brightness” 2.0 units
Which is closer and by how much?
• Calculate brightness ratio
• Star A is 2.0x brighter
• Calculate distance ratio
• Star B = sqrt(2.0) = 1.41 times farther away
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Fort Lewis College
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Magnitudes and Distance
• Example:
• 2 stars, both have Absolute magnitude = 3.0
• Star A = apparent magnitude 4.0
• Star B = apparent magnitude 7.5
• Calculate magnitude difference
• Difference of 3.5 magnitudes
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Fort Lewis College
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Magnitudes and Distance
• Example:
• 2 stars, both have Absolute magnitude = 3.0
• Star A = apparent magnitude 4.0
• Star B = apparent magnitude 7.5
• Calculate magnitude difference
• Difference of 3.5 magnitudes
• Calculate brightness difference
• Brightness difference of 2.512(3.5) = 25.1x
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Fort Lewis College
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Magnitudes and Distance
• Example:
• 2 stars, both have Absolute magnitude = 3.0
• Star A = apparent magnitude 4.0
• Star B = apparent magnitude 7.5
• Calculate magnitude difference
• Difference of 3.5 magnitudes
• Calculate brightness difference
• Brightness difference of 2.512(3.5) = 25.1x
• Calculate distance difference
• Star B = sqrt(25.1) = 5 times farther away
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Fort Lewis College
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Two stars both have parallaxes of 0.023”. Star A is
magnitude +2.3 and star B is magnitude +7.3
A) star A must be 10x closer.
B) star B must be 10x more luminous.
C) star A is both 100x brighter and more luminous.
D) star A is both 100x brighter and larger.
E) we can conclude nothing.
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Fort Lewis College
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Two stars both have parallaxes of 0.023”. Star A is
magnitude +2.3 and star B is magnitude +7.3
A) star A must be 10x closer.
B) star B must be 10x more luminous.
C) star A is both 100x brighter and more luminous.
D) star A is both 100x brighter and larger.
E) we can conclude nothing.
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Fort Lewis College
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Distance calculations
• Absolute magnitude is the apparent magnitude if
the object is 10 parsecs away.
• Absolute magnitude and luminosity refer to the
same thing.
• Sun absolute magnitude is 4.8
• Sun luminosity is 1 solar luminosity.
• If you know the luminosity, how exactly do you find
the distance?
m - M = 5 log10 (r/10pc)
r = 10pc x 10(m-M)/5
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Fort Lewis College
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Chapter 10
Star Temperatures
(Colors)
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Fort Lewis College
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Figure 10.7
Star Colors – Orion (20°) and the Milky Way Center (2’)
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Fort Lewis College
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Which star would be the hottest?
A) Blue
B) White
C) Yellow
D) Orange
E) Red
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Fort Lewis College
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Which star would be the hottest?
A) Blue
B) White
C) Yellow
D) Orange
E) Red
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Fort Lewis College
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Star Temperatures
• Recall Wien’s Law –
lmax =
0.29 (cm K)
T (K)
(peak frequency  Temperature)
• You do not need to measure the intensity
at many wavelengths to find the peak.
• Because you know the shape of the curve
(~Blackbody) you only need two points.
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Fort Lewis College
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Figure 10.8
Blackbody
Curves
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Fort Lewis College
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Element Spectra
• Note - The spectrum of an element can
“change” as the temperature changes.
• Line locations do NOT change
• The intensity of different lines can change.
• Historical Classification of star types
• According to the intensity of the H lines
• Labeled A,B,C,D,...
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Fort Lewis College
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Figure 10.9
Stellar
Spectra
• Very hot stars
• Most H ionized
(weak spectrum)
• He spectrum
stronger
• Medium T stars
• stronger H lines
• Cooler stars
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Fort Lewis College
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• Lines from heavier
elements
• Some molecular
lines
Star Spectral Classification
• Modern Classification of star types
• According to star temperature
• Historical labels kept (A,B,C,D,...), but
order changed
• New order, from hottest to coldest is:
O, B, A, F, G, K ,M.
• Other letters removed from
classification
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Fort Lewis College
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Star Spectral Classification
• New order is: O, B, A, F, G, K ,M.
• Remember the order...
• Oh, Be A Fine Girl/(Guy) Kiss Me
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Fort Lewis College
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Chapter 10
Star Sizes
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Fort Lewis College
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Star Sizes
• The luminosity of a star depends on
the stars diameter as well as its
temperature.
• When radius is combined with
Stefan’s Law:
( means proportional to)
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Fort Lewis College
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Star Sizes
• The luminosity of a star depends on
the stars diameter as well as its
temperature.
• When surface area is combined with
Stefan’s Law:
luminosity = 4r2 T4
(= means equal)
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Fort Lewis College
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Star Sizes
• Can directly measure the radius on
very few stars. (~dozen)
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Fort Lewis College
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Figure 10.10
Betelgeuse
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Fort Lewis College
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Star Sizes
• Can directly measure the radius on
very few stars. (~dozen)
• Can calculate the radius if you know
the luminosity and the temperature.
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Fort Lewis College
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Figure 10.11
Stellar Sizes
between 10x
and 100x solar
• Supergiants larger (up to
1000x)
comparable to
or smaller than
the sun.
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Fort Lewis College
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Chapter 10
HR Diagrams
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Fort Lewis College
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Figure 10.12
H–R Diagram
of Well-Known Stars
• Plot the
luminosity vs.
temperature.
• This is called a
HertzsprungRussell (H-R)
diagram
• Need to plot
more stars!
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Fort Lewis College
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Figure 10.15
Hipparcos H–R Diagram
Charles Hakes
Fort Lewis College
• Plot many stars
and notice that
90% fall on the
“main
sequence”.
and now have
• luminosity
• temperature
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Figure 10.14
H–R Diagram
of 100 Brightest Stars
• Most very bright
stars are also
distant
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Fort Lewis College
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Figure 10.13
H–R Diagram
of Nearby Stars
• Most close stars
are very dim
• Best estimate
now is that 80%
of stars are red
dwarfs
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Fort Lewis College
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Three Minute Paper
• Write 1-3 sentences.
• What was the most important thing
you learned today?
• What questions do you still have
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Fort Lewis College
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Review
• What was the most important thing you
learned?
• Absolute magnitude is how bright a star would
appear at 10 parsecs
• A difference of 5 magnitudes corresponds to
exactly a factor of 100 in brightness
• …take the difference in magnitudes and use it
in an exponential equation:
brightness = (100.2)mag
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Fort Lewis College
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Group Exercise
• Given that:
• one magnitude is a factor of 1000.2 = 2.511886
• Venus magnitude is -4.6
• Faintest stars visible in Durango ~+6.5
• (Approximately) How Much brighter is Venus than
the dimmest star visible in Durango?
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Fort Lewis College
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Group Exercise
• Given that:
• one magnitude is a factor of 1000.2 = 2.511886
• Venus magnitude is -4.6
• Faintest stars visible in Durango ~+6.5
• (Approximately) How Much brighter is Venus than
the dimmest star visible in Durango?
• What is the magnitude difference?
• How does this difference relate to brightness?
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Fort Lewis College
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Three Minute Paper
• Write 1-3 sentences.
• What was the most important thing
you learned today?
• What questions do you still have