# 10 Measuring The Stars

```Chapter 10
Measuring the
Stars
Chapter 10
Measuring the Stars
Units of Chapter 10
The Solar Neighborhood
Luminosity and Apparent Brightness
Stellar Temperatures
Stellar Sizes
The Hertzsprung–Russell Diagram
Extending the Cosmic Distance Scale
Stellar Masses
Question 1
Stellar parallax
is used to
measure the
a) sizes of stars.
b) distances of stars.
c) temperatures of stars.
d) radial velocity of stars.
e) brightness of stars.
Question 1
Stellar parallax
is used to
measure the
a) sizes of stars.
b) distances of stars.
c) temperatures of stars.
d) radial velocity of stars.
e) brightness of stars.
Parallax can be used to measure
distances to stars accurately to about 200
parsecs (650 light-years).
The Solar Neighborhood
Parallax: Look at
apparent motion of
object against distant
background from two
vantage points;
knowing baseline
allows calculation of
distance:
distance (in parsecs) =
1/parallax (in arc seconds)
1 parsec ~ 3.3 ly
Parallax Exaggeration
Arc sec of movement
Distance in parsecs
Question 2
The angle of
stellar parallax
for a star gets
larger as the
a) distance to the star increases.
b) size of the star increases.
c) size of the telescope increases.
d) length of the baseline increases.
e) wavelength of light increases.
Question 2
The angle of
stellar parallax
for a star gets
larger as the
a) distance to the star increases.
b) size of the star increases.
c) size of the telescope increases.
d) length of the baseline increases.
e) wavelength of light increases.
Astronomers typically make
observations of nearby stars 6 months
apart, making the baseline distance
equal to 2 AU (Astronomical Units).
The Solar Neighborhood
Nearest star to the Sun: Proxima Centauri,
which is a member of a 3-star system: Alpha
Centauri complex 1.3 parsecs or 0.77” of
parallax (1/0.77=1.3) 4.3 ly
Model of distances:
•
Sun is a golf ball, Earth is a grain of sand
orbiting 1 meter away.
• Solar system extends about 50 m from the
Sun; rest of distance to nearest star is
basically empty.
Question 3
You can best model
the size and distance
relationship of our
Sun & the next
nearest star using
a) a tennis ball here, and one on the
Moon.
b) two beach balls separated by 100
city blocks.
c) two grains of sand 100 light-years
apart.
d) two golf balls 270 km apart.
e) two baseballs 100 yards apart.
Question 3
You can best model
the size and distance
relationship of our
Sun & the next
nearest star using
a) a tennis ball here, and one on the
Moon.
b) two beach balls separated by 100
city blocks.
c) two grains of sand 100 light- years
apart.
d) two golf balls 270 km apart.
e) two baseballs 100 yards apart.
The Sun is about one million miles
in diameter.
The next nearest star is about 25
million times farther away.
The Solar Neighborhood
The 30 closest stars to the Sun
Question 4
A star’s proper
motion is its
a) true motion in space.
b) apparent shift as we view from opposite
sides of Earth’s orbit every six months.
c) annual apparent motion across the sky.
d) motion toward or away from us, revealed by
Doppler shifts.
e) orbital motion around the galaxy.
Question 4
A star’s proper
motion is its
a) true motion in space.
b) apparent shift as we view from opposite
sides of Earth’s orbit every six months.
c) annual apparent motion across the sky.
d) motion toward or away from us, revealed by
Doppler shifts.
e) orbital motion around the galaxy.
A star’s “real space motion” combines its apparent proper
motion with its radial motion toward or away from Earth.
The Solar Neighborhood
Barnard’s Star (top) has the
largest proper motion of any –
proper motion is the actual
shift of the star in the sky,
after correcting for parallax.
The pictures (a) were taken 22
years apart. (b) shows the
actual motion of the Alpha
Centauri complex.
Luminosity and Apparent
Brightness
Luminosity, or absolute brightness, is a
measure of the total power radiated by a star.
Apparent brightness is how bright a star
appears when viewed from Earth; it depends on
the absolute brightness but also on the distance
of the star:
apparent brightness  luminosity/distance2
Luminosity and Apparent
Brightness
This is an example of an inverse square law.
Luminosity and Apparent Brightness
Therefore, two
stars that appear
equally bright
might be a closer,
dimmer star and
a farther, brighter
one.
Question 5
In the stellar magnitude
system invented by
Hipparchus, a smaller
magnitude indicates a
_____ star.
a) brighter
b) hotter
c) cooler
d) fainter
e) more distant
Question 5
In the stellar magnitude
system invented by
Hipparchus, a smaller
magnitude indicates a
_____ star.
a) brighter
b) hotter
c) cooler
d) fainter
e) more distant
Luminosity and Apparent Brightness
Apparent luminosity is
measured using a
magnitude scale, which is
related to our perception.
It is a logarithmic scale; a
change of 5 in magnitude
corresponds to a change
of a factor of 100 in
apparent brightness.
It is also inverted – larger
magnitudes are dimmer.
Magnitude 5 to 30
•
•
•
•
•
5 to 10 = 100 times dimmer
10 to 15 = 100 x 100 = 10,000
15 to 20 = 100 x 10,000 = 1,000,000
20 to 25 = 100 x 1,000,000 = 100,000,000
30 = 100 x 100,000,000 = 10,000,000,000
times dimmer than magnitude 5
Question 6
A star’s apparent
magnitude is a number
used to describe how
our eyes measure its
a) distance.
b) temperature.
c) brightness.
d) absolute luminosity.
Question 6
A star’s apparent
magnitude is a number
used to describe how
our eyes measure its
a) distance.
b) temperature.
c) brightness.
d) absolute luminosity.
Question 7
The absolute magnitude
of a star is its brightness
as seen from a distance
of
a) one million km.
b) one Astronomical Unit.
c) one light-year.
d) ten parsecs.
e) ten light-years.
Question 7
The absolute magnitude
of a star is its brightness
as seen from a distance
of
a) one million km.
b) one Astronomical Unit.
c) one light-year.
d) ten parsecs.
e) ten light-years.
Astronomers use a distance of 10 parsecs (about
32 light-years) as a standard for specifying and
comparing the brightnesses of stars.
Stellar Temperatures
The color of a star is indicative of its
temperature. Red stars are relatively cool,
whereas blue ones are hotter.
Stellar Temperatures
The radiation from stars is blackbody radiation; as
the blackbody curve is not symmetric, observations
at two wavelengths are
enough to define
the temperature.
Question 8
Wien’s law tells us that the
hotter an object, the _____
the peak wavelength of its
emitted light.
a) longer
b) more green
c) heavier
d) shorter
e) more constant
Question 8
Wien’s law tells us that the
hotter an object, the _____
the peak wavelength of its
emitted light.
a) longer
b) more green
c) heavier
d) shorter
e) more constant
Wien’s law states that
hotter stars appear more blue in color,
and
cooler stars appear more red in color.
Stellar Temperatures
Stellar spectra are much more informative than
the blackbody curves.
There are seven general categories of stellar
spectra, corresponding to different
temperatures.
From highest to lowest, those categories are:
OBAFGKM
Question 9
We estimate the
surface temperature
of a star by using
a) its color.
b) the pattern of absorption lines in its
spectrum.
c) Wien’s law.
d) differences in brightness as measured
through red and blue filters.
e) All of the above are used.
Question 9
We estimate the
surface temperature
of a star by using
a) its color.
b) the pattern of absorption lines in its
spectrum.
c) Wien’s law.
d) differences in brightness as measured
through red and blue filters.
e) All of the above are used.
Stellar Temperatures
The seven
spectral types
Emission
Question 10
Which spectral classification
type corresponds to a star
like the Sun?
a) O
b) A
c) F
d) G
e) M
Question 10
Which spectral classification
type corresponds to a star
like the Sun?
a) O
b) A
c) F
d) G
e) M
The OBAFGKM classification scheme is based on absorption lines.
Question 11
The key difference
between the
spectra of B stars
and G stars is
a) B stars show strong hydrogen lines;
G stars show weaker hydrogen lines.
b) B stars show few metal lines; G stars
show many.
c) B stars have no metal atoms.
d) G stars have no hydrogen atoms.
e) Both a and b are true.
Question 11
The key difference
between the
spectra of B stars
and G stars is
a) B stars show strong hydrogen lines;
G stars show weaker hydrogen lines.
b) B stars show few metal lines; G stars
show many.
c) B stars have no metal atoms.
d) G stars have no hydrogen atoms.
e) Both a and b are true.
The original OBAFGKM sequence was arranged alphabetically by
the strength of hydrogen absorption lines.
B stars had strong hydrogen lines, G stars had weak lines.
Stellar Temperatures
The different spectral classes have distinctive
absorption lines.
Question 12
What are the two
most important
intrinsic properties
for classifying stars?
a) distance and surface temperature
b) luminosity and surface temperature
c) distance and luminosity
d) mass and age
e) distance and color
Question 12
What are the two
most important
intrinsic properties
for classifying stars?
a) distance and surface temperature
b) luminosity and surface temperature
c) distance and luminosity
d) mass and age
e) distance and color
The H–R diagram plots stars
based on their luminosities and
surface temperatures.
Stellar Sizes
A few very large, very close stars can be imaged
directly; this is Betelgeuse.
Stellar Sizes
For the vast majority of stars that cannot be
imaged directly, size must be calculated knowing
the luminosity and temperature:
luminosity  radius2  temperature4
Giant stars have radii between 10 and 100
times the Sun’s.
Dwarf stars have radii equal to, or less
than, the Sun’s.
Supergiant stars have radii more than 100
times the Sun’s.
Stellar Sizes
widely.
Question 13
Astronomers
can estimate
the size of a
star using
a) apparent brightness.
b) direct observation of diameter.
c) temperature.
d) distance to the star.
e) a, b, and c are all true.
Question 13
Astronomers
can estimate
the size of a
star using
a) apparent brightness.
b) direct observation of diameter.
c) temperature.
d) distance to the star.
e) a, b, and c are all true.
Brightness and temperature are
used to plot the star on an H–R
diagram, and indicate its
approximate size.
Some stars are large enough to
measure directly.
The Hertzsprung–Russell Diagram
The H–R diagram plots
stellar luminosity
against surface
temperature.
This is an H–R
diagram of a few
prominent stars.
The Hertzsprung–Russell Diagram
Once many stars are plotted on an H–R diagram, a
pattern begins to form:
These are the 80 closest
stars to us; note the dashed
lines of constant radius.
The darkened curve is called
the main sequence, as this
is where most stars are.
Also indicated is the white
dwarf region; these stars are
hot but not very luminous,
as they are quite small.
The Hertzsprung–Russell Diagram
An H–R diagram of the 100 brightest stars looks
quite different.
These stars are all more
luminous than the Sun.
Two new categories
appear here – the red
giants and the blue giants.
Clearly, the brightest stars
in the sky appear bright
because of their enormous
luminosities, not their
proximity.
Compare Near to Bright
Near
Bright
The Hertzsprung–Russell Diagram
This is an H–R plot of
The main sequence
is clear, as is the red
giant region.
About 90 percent of
stars lie on the main
sequence; 9 percent
are red giants and 1
percent are white
dwarfs.
H-R Diagram
Extending the Cosmic Distance
Scale
Spectroscopic parallax: Has nothing to do with
parallax, but does use spectroscopy in finding
the distance to a star.
1. Measure the star’s apparent magnitude and
spectral class.
2. Use spectral class to estimate luminosity.
3. Apply inverse-square law to find distance.
Extending the Cosmic Distance
Scale
Spectroscopic parallax can extend the cosmic
distance scale to several thousand parsecs.
Andromeda
Sun
Extending the Cosmic Distance
Scale
The spectroscopic parallax calculation can be
misleading if the star is not on the main sequence.
The width of spectral
lines can be used to
define luminosity
classes.
Extending the Cosmic Distance
Scale
In this way, giants and supergiants can be
distinguished from main-sequence stars.
Question 14
Eclipsing binary
stars are very
useful for
determining the
a) ages of stars.
b) absolute luminosities of stars.
c) masses of stars.
d) distances to stars.
e) rotation rates of stars.
Question 14
Eclipsing binary
stars are very
useful for
determining the
a) ages of stars.
b) absolute luminosities of stars.
c) masses of stars.
d) distances to stars.
e) rotation rates of stars.
Analysis of the light curve
of an eclipsing binary star
system can reveal the
masses of the stars.
Stellar Masses
Many stars are in binary
pairs; measurement of
their orbital motion allows
determination of the
masses of the stars. Orbits
of visual binaries can be
observed directly; Doppler
shifts in spectroscopic
binaries allow
measurement of motion;
and the period of eclipsing
binaries can be measured
using intensity variations.
Stellar Masses
Mass is the main
determinant of
where a star will
be on the main
sequence.
Stellar Masses
Stellar mass distributions
– there are many more
small stars than large
ones!
Question 15
What is the single most
important characteristic
in determining the
course of a star’s
evolution?
a) density
b) absolute brightness
c) distance
d) surface temperature
e) mass
Question 15
What is the single most
important characteristic
in determining the
course of a star’s
evolution?
a) density
b) absolute brightness
c) distance
d) surface temperature
e) mass
A star’s mass determines how fast it
forms, its luminosity on the main
sequence, how long it will shine, and
its ultimate fate.
Lifetime of a Star
• A redwood tree might live
2000 years. How would we
ever know what it looked
like at 1 year or 10 years or
100years?
•We do the same thing with
stars.
•This is millions to trillions
of years for stars
depending on the type.
Summary of Chapter 10
• Distance to nearest stars can be measured by
parallax.
• Apparent brightness is as observed from
Earth; depends on distance and absolute
luminosity.
• Spectral classes correspond to different
surface temperatures.
• Stellar size is related to luminosity and
temperature.
Summary of Chapter 10, cont.
• H–R diagram is plot of luminosity vs.
temperature; most stars lie on main sequence.
• Distance ladder can be extended using
spectroscopic parallax.
• Masses of stars in binary systems can be
measured.
• Mass determines where star lies on main
sequence.
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