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ASTRO 101
Principles of Astronomy
Instructor: Jerome A. Orosz
(rhymes with “boris”)
Contact:
• Telephone: 594-7118
• E-mail: [email protected]
• WWW:
http://mintaka.sdsu.edu/faculty/orosz/web/
• Office: Physics 241, hours T TH 3:30-5:00
Text:
“Discovering the Essential Universe,
Fifth Edition”
by
Neil F. Comins
Course WWW Page
http://mintaka.sdsu.edu/faculty/orosz/web/ast101_fall2012.html
Note the underline: … ast101_fall2012.html …
Also check out Nick Strobel’s Astronomy Notes:
http://www.astronomynotes.com/
Homework/Announcements
• Homework due Tuesday, November 13:
Question 4, Chapter 8 (Describe the three main
layers of the Sun’s interior.)
• Chapter 9 homework due November 20:
Question 13 (Draw an H-R Diagram …)
Next:
How Does the Sun Work?
How Does the Sun Work?
• Some useful numbers:
 The mass of the Sun is 2x1030 kg.
 The luminosity of the Sun is 4x1026 Watts.
 The first question to ask is: What is the energy
source inside the Sun?
Energy Sources
• A definition:
Efficiency = energy released/(fuel mass x [speed of light]2)
• Chemical energy (e.g. burning wood,
combining hydrogen and oxygen to make
water, etc.).
 Efficiency = 1.5 x 10-10
 Solar lifetime = 30 to 30,000 years, depending on
the reaction. Too short!
Energy Sources
• A definition:
Efficiency = energy released/(fuel mass x [speed of light]2)
• Gravitational settling (falling material
compresses stuff below, releasing heat).
 Efficiency = 1 x 10-6
 Solar lifetime = 30 million years. Too short,
although this point was not obvious in the late
1800s.
Energy Sources
• A definition:
Efficiency = energy released/(fuel mass x [speed of light]2)
• Nuclear reactions: fusion of light elements (as
in a hydrogen bomb).
 Efficiency = 0.007
 Solar lifetime = billions of years.
Ways to Transport Energy
Ways to Transport Energy
• Conduction:
direct contact
• Radiation: via
photons
• Convection: via
mass motions
The Phases of Matter
Phases of Matter
•
Matter has three “phases”
1. Solid. Constant volume and constant shape.
2. Liquid. Constant volume but variable shape.
3. Gas. Variable volume and variable shape.
The Gas Phase
• In a gas, the atoms and/or molecules are widely
separated and are moving at high velocities:
– Relatively heavy molecules such as CO2 move
relatively slowly.
– Relatively light molecules like H2 move relatively
quickly.
– The average velocities of the gas particles depend
on the temperature of the gas.
Heating a Gas
• The velocity of a gas particle depends on the mass of
the particle and its temperature.
Image from Nick Strobel (http://www.astronomynotes.com)
Ideal Gas
• For a fixed volume, a hotter gas exerts a higher
pressure:
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
The 4 “Forces” in Nature
The 4 “Forces” of Nature
•
There are 4 “fundamental forces” in nature:
1.
2.
3.
4.
•
Gravity: relative strength = 1, range = infinite.
Electromagnetic: rel. str. = 1036, range = infinite.
“Weak” nuclear: rel. str. = 1025, range = 10-10 meter.
“Strong” nuclear: rel. str. = 1038, range = 10-15
meter.
Gravity is an attractive force between all matter
in the Universe. The more mass something has,
the larger the net gravitational force is.
The 4 “Forces” of Nature
•
There are 4 “fundamental forces” in nature:
1.
2.
3.
4.
•
Gravity: relative strength = 1, range = infinite.
Electromagnetic: rel. str. = 1036, range = infinite.
“Weak” nuclear: rel. str. = 1025, range = 10-10 meter.
“Strong” nuclear: rel. str. = 1038, range = 10-15
meter.
The electromagnetic force can be repulsive (+,+
or -,-) or attractive (+,-). Normal chemical
reactions are governed by this force.
The 4 “Forces” of Nature
•
There are 4 “fundamental forces” in nature:
1.
2.
3.
4.
•
•
Gravity: relative strength = 1, range = infinite.
Electromagnetic: rel. str. = 1036, range = infinite.
“Weak” nuclear: rel. str. = 1025, range = 10-10 meter.
“Strong” nuclear: rel. str. = 1038, range = 10-15
meter.
The weak force governs certain radioactive
decay reactions.
The strong force holds atomic nuclei together.
The Strong Force.
p = proton, positive charge
n = neutron, no charge
p
n
n
p
• Here is a helium nucleus. The protons are held together by the strong
force.
The 4 “Forces” of Nature
•
There are 4 “fundamental forces” in nature:
1.
2.
3.
4.
•
Gravity: relative strength = 1, range = infinite.
Electromagnetic: rel. str. = 1036, range = infinite.
“Weak” nuclear: rel. str. = 1025, range = 10-10 meter.
“Strong” nuclear: rel. str. = 1038, range = 10-15
meter.
Gravity is the most important force over large
scales since positive and negative charges tend
to cancel.
How to get energy from atoms
• Fission: break apart the nucleus of a heavy
element like uranium.
• Fusion: combine the nuclei of a light element
like hydrogen.
More Nuclear Fusion
• Each atomic nucleus has a
“binding energy” associated
with it. The curve is increasing
as you go up to iron from small
nuclei, and decreasing as you go
down from large nuclei.
• The tendency of Nature is to
increase binding energy, much
like the tendency of water to
flow downhill.
Image from Vik Dhillon (http://www.shef.ac.uk/physics/people/vdhillon/teaching/phy213/phy213_fusion1.html)
More Nuclear Fusion
• Fusion of elements
lighter than iron can
release energy (leads to
higher BE’s).
• Fission of elements
heaver than iron can
release energy (leads to
higher BE’s).
Nuclear Fusion
• Summary: 4 hydrogen nuclei (which are
protons) combine to form 1 helium nucleus
(which has two protons and two neutrons).
• Why does this produce energy?
 Before: the mass of 4 protons is 4 proton masses.
 After: the mass of 2 protons and 2 neutrons is 3.97
proton masses.
 Einstein: E = mc2. The missing mass went into
energy! 4H ---> 1He + energy
Nuclear Fusion
• Summary: 4 hydrogen nuclei (which are
protons) combine to form 1 helium nucleus
(which has two protons and two neutrons).
• Extremely high temperatures and densities are
needed!
Images from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Nuclear Fusion
• Summary: 4 hydrogen nuclei (which are
protons) combine to form 1 helium nucleus
(which has two protons and two neutrons).
• Extremely high temperatures and densities are
needed! The temperature is about 15,000,000K
at the core of the Sun.
More Nuclear Fusion
• Fusion of elements lighter than iron can release energy (leads to
higher BE’s).
• As you fuse heavier elements up to iron, higher and higher
temperatures are needed since more and more electrical charge
repulsion needs to be overcome.
–
–
–
–
Hydrogen nuclei have 1 proton each
Helium nuclei have 2 protons each
Carbon nuclei have 6 protons each
…..
• The Sun is presently only fusing hydrogen since it is not
hot enough to fuse helium.
Nuclear Fusion
• Summary: 4 hydrogen nuclei (which are
protons) combine to form 1 helium nucleus
(which has two protons and two neutrons).
• Why does this produce energy?
 Before: the mass of 4 protons is 4 proton masses.
 After: the mass of 2 protons and 2 neutrons is 3.97
proton masses.
 Einstein: E = mc2. The missing mass went into
energy! 4H ---> 1He + energy
Nuclear Fusion
• Summary: 4 hydrogen nuclei (which are
protons) combine to form 1 helium nucleus
(which has two protons and two neutrons).
• The details are a bit complex:
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Nuclear Fusion
• Summary: 4
hydrogen nuclei
(which are
protons) combine
to form 1 helium
nucleus (which
has two protons
and two
neutrons).
• The details are a
bit complex:
Nuclear Fusion
• Summary: 4 hydrogen nuclei (which are
protons) combine to form 1 helium nucleus
(which has two protons and two neutrons).
• The details are a bit complex:
 In the Sun, 6 hydrogen nuclei are involved in a
sequence that produces two hydrogen nuclei and
one helium nucleus. This is the proton-proton chain.
Nuclear Fusion
• Summary: 4 hydrogen nuclei (which are
protons) combine to form 1 helium nucleus
(which has two protons and two neutrons).
• The details are a bit complex:
 In the Sun, 6 hydrogen nuclei are involved in a
sequence that produces two hydrogen nuclei and
one helium nucleus. This is the proton-proton chain.
 In more massive stars, a carbon nucleus is involved
as a catalyst. This is the CNO cycle.
Nuclear Fusion
• The CNO cycle (left) and pp chain (right) are outlined.
Nuclear Fusion
• Summary: 4 hydrogen nuclei (which are
protons) combine to form 1 helium nucleus
(which has two protons and two neutrons).
• Why doesn’t the Sun blow up like a bomb?
There is a natural “thermostat” in the core.
Controlled Fusion in the Sun
Controlled Fusion in the Sun
• First, note that the rate of the p-p chain or CNO
cycle is very sensitive to the temperature.
Controlled Fusion in the Sun
• First, note that the rate of the p-p chain or CNO
cycle is very sensitive to the temperature.
 Rate ~ (temperature)4 for p-p chain.
Controlled Fusion in the Sun
• First, note that the rate of the p-p chain or CNO
cycle is very sensitive to the temperature.
 Rate ~ (temperature)4 for p-p chain.
 Rate ~ (temperature)15 for the CNO cycle.
Controlled Fusion in the Sun
• First, note that the rate of the p-p chain or CNO
cycle is very sensitive to the temperature.
 Rate ~ (temperature)4 for p-p chain.
 Rate ~ (temperature)15 for the CNO cycle.
 Small changes in the temperature lead to large
changes in the fusion rate.
Controlled Fusion in the Sun
• First, note that the rate of the p-p chain or CNO
cycle is very sensitive to the temperature.
 Rate ~ (temperature)4 for p-p chain.
 Rate ~ (temperature)15 for the CNO cycle.
 Small changes in the temperature lead to large
changes in the fusion rate.
• Suppose the fusion rate inside the Sun increased:
Controlled Fusion in the Sun
• First, note that the rate of the p-p chain or CNO
cycle is very sensitive to the temperature.
 Rate ~ (temperature)4 for p-p chain.
 Rate ~ (temperature)15 for the CNO cycle.
 Small changes in the temperature lead to large
changes in the fusion rate.
• Suppose the fusion rate inside the Sun increased:
 The increased energy heats the core and expands the
star. But the expansion cools the core, lowering the
fusion rate. The lower rate allows the core to shrink
back to where it was before.
Models of the Solar Interior
•
The interior of the Sun is relatively simple
because it is an ideal gas, described by three
quantities:
1. Temperature
2. Pressure
3. Mass density
Models of the Solar Interior
•
The interior of the Sun is relatively simple
because it is an ideal gas, described by three
quantities:
1. Temperature
2. Pressure
3. Mass density
•
The relationship between these three quantities
is called the equation of state.
Ideal Gas
• For a fixed volume, a hotter gas exerts a higher
pressure:
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Hydrostatic Equilibrium
• The Sun does not collapse on itself, nor does it
expand rapidly.
Hydrostatic Equilibrium
• The Sun does not collapse on itself, nor does it
expand rapidly. Gravity and internal pressure
balance:
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Hydrostatic Equilibrium
• The Sun does not collapse on itself, nor does it
expand rapidly. Gravity and internal pressure
balance. This is true at all layers of the Sun.
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Hydrostatic Equilibrium
• The Sun (and other
stars) does not collapse
on itself, nor does it
expand rapidly. Gravity
and internal pressure
balance. This is true at
all layers of the Sun.
• The temperature
increases as you go
deeper and deeper into
the Sun!
Models of the Solar Interior
• The pieces so far:
 Energy generation (nuclear fusion).
 Ideal gas law (relation between temperature,
pressure, and volume.
 Hydrostatic equilibrium (gravity balances pressure).
Models of the Solar Interior
• The pieces so far:
 Energy generation (nuclear fusion).
 Ideal gas law (relation between temperature,
pressure, and volume.
 Hydrostatic equilibrium (gravity balances pressure).
 Continuity of mass (smooth distribution throughout
the star).
Models of the Solar Interior
• The pieces so far:
 Energy generation (nuclear fusion).
 Ideal gas law (relation between temperature,
pressure, and volume.
 Hydrostatic equilibrium (gravity balances pressure).
 Continuity of mass (smooth distribution throughout
the star).
 Continuity of energy (amount entering the bottom of
a layer is equal to the amount leaving the top).
Models of the Solar Interior
• The pieces so far:
 Energy generation (nuclear fusion).
 Ideal gas law (relation between temperature,
pressure, and volume.
 Hydrostatic equilibrium (gravity balances pressure).
 Continuity of mass (smooth distribution throughout
the star).
 Continuity of energy (amount entering the bottom of
a layer is equal to the amount leaving the top).
 Energy transport (how energy is moved from the
core to the surface).
Models of the Solar Interior
• Solve these equations on a computer:
 Compute the temperature and density at any layer, at
any time.
 Compute the size and luminosity of the star as a
function of the initial mass.
 Etc…….
Solar Structure Models
Solar Structure Models
• Here is the model of the structure of the Sun.
Solar Structure Models
• The Sun is mostly hydrogen and helium.
Solar Structure Models
• Here is the model
of the structure of
the Sun.
• Next: Characterizing Stars
The Sun and the Stars
• The Sun is the nearest example of a star.
• Basic questions to ask:
– What do stars look like on their surfaces? Look
at the Sun since it is so close.
– How do stars work on their insides? Look at
both the Sun and the stars to get many
examples.
– What will happen to the Sun? Look at other
stars that are in other stages of development.
Stellar Properties
• The Sun and the stars are similar objects.
• In order to understand them, we want to try and
measure as many properties about them as we
can:





Power output (luminosity)
Temperature at the “surface”
Radius
Mass
Chemical composition
Observing Other Stars
• Recall there is basically no hope of spatially
resolving the disk of any star (apart from
the Sun). The stars are very far away, so
their angular size as seen from Earth is
extremely small.
• The light we receive from a star comes from
the entire hemisphere that is facing us. That
is, we see the “disk-integrated” light.
Observing Other Stars
• To get an understanding of how a star works,
the most useful thing to do is to measure the
spectral energy distribution, which is a plot of
the intensity of the photons vs. their
wavelengths (or frequencies or energies).
• There are two ways to do this:
 “Broad band”, by taking images with a camera and
a colored filter.
 “High resolution”, by using special optics to
disperse the light and record it.
Broad Band Photometry
• There are several
standard filters in use
in astronomy.
• The filter lets only
light within a certain
wavelength region
through (that is why
they have those
particular colors).
Color Photography
• The separate images are digitally processed to
obtain the final color image.
Color Photography
Color Photography
Broad Band Photometry
• Broad band photometry has the advantage in
that it is easy (just need a camera and some
filters on the back of your telescope), and it is
efficient (relatively few photons are lost in the
optics).
• The disadvantage is that the spectral resolution
is poor, so subtle differences in photon energies
are impossible to detect.
High Resolution Spectroscopy
• To obtain a high resolution spectrum, light from a star is
passed through a prism (or reflected off a grating), and
focused and detected using some complicated optics.
High Resolution Spectroscopy
• Using a good high resolution spectrum, you
can get a much better measurement of the
spectral energy distribution.
• The disadvantage is that the efficiency is lower
(more photons are lost in the complex optics).
Also, it is difficult to measure more than one
star at a time (in contrast to the direct imaging
where several stars can be on the same image).
Stellar Properties
• The Sun and the stars are similar objects.
• In order to understand them, we want to try and
measure as many properties about them as we
can:





Power output (luminosity)
Temperature at the “surface”
Radius
Mass
Chemical composition
The Distance
• How can you measure the distance to
something?
 Direct methods, e.g. a tape measure. Not good
for things in the sky.
 Sonar or radar: send out a signal with a known
velocity and measure the time it takes for the
reflected signal. Works for only relatively
nearby objects (e.g. the Moon, certain
asteroids).
The Distance
• How can you measure the distance to
something?
 Direct methods, e.g. a tape measure. Not good
for things in the sky.
 Sonar or radar: send out a signal with a know
velocity and measure the time it takes for the
reflected signal. Works for only relatively
nearby objects (e.g. the Moon, certain
asteroids).
 Triangulation: the use of parallax.
The Parallax
• Parallax is basically the apparent shifting of
nearby objects with respect to far away
objects when the viewing angle is changes.
• Example: hold out your finger and view it
with one eye closed, then the other eye
closed. Your finger shifts with respect to
the background.
The Parallax
• Example: hold out your finger and view it
with one eye closed, then the other eye
closed. Your finger shifts with respect to
the background.
The Parallax
• A better example: place an object on the
table in front of the room and look at its
position against the back wall as you walk
by. In most practical applications you will
have to change your position to make use of
parallax.
Triangulation
• Triangulation is based
on trigonometry, and
is often used by
surveyors.
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Triangulation
• Triangulation is based
on trigonometry, and
is often used by
surveyors.
• The length B and the
angle p can be
measured, so the
distance can be
computed: d=B/tan(p)
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Triangulation
• Triangulation is based
on trigonometry, and
is often used by
surveyors.
• This technique can be
applied to nearby
stars.
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Triangulation
• Triangulation is based
on trigonometry, and
is often used by
surveyors.
• Here is another
diagram showing the
technique. This
technique can be
applied to other stars!
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Triangulating the Stars
• The largest baseline one can obtain is the orbit of the
Earth!
• When viewed at 6 month intervals, a relatively nearby
star will appear to shift with respect to distant stars.
Triangulating the Stars
• The largest baseline one can obtain is the orbit of the
Earth!
• When viewed at 6 month intervals, a relatively nearby
star will appear to shift with respect to distant stars.
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Triangulating the Stars
• The largest baseline one can obtain is the orbit of the
Earth!
• When viewed at 6 month intervals, a relatively nearby
star will appear to shift with respect to distant stars.
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Triangulating the Stars
• Here are two neat Java tools demonstrating parallax:
http://www.astro.ubc.ca/~scharein/a310/Sim.html#Oneover
http://spiff.rit.edu/classes/phys240/lectures/parallax/para1_jan.html
Triangulating the Stars
• When viewed at 6 month intervals, a relatively nearby
star will appear to shift with respect to distant stars.
• The angle p for the nearest star is 0.77 arcseconds.
One can currently measure angles as small as a few
thousands of an arcsecond.
Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)
Triangulating the Stars
• For very tiny angles, use the approximation that
tan(p)=p, when p is in radians.
• Then d=B/tan(p) becomes d=B/p.
Triangulating the Stars
• For very tiny angles, use the approximation that
tan(p)=p, when p is in radians.
• Then d=B/tan(p) becomes d=B/p.
• B=1 “astronomical unit” (e.g. the Earth-Sun distance).
Define a unit of distance such that d=1/p, if the angle p
is measured in arcseconds.
Triangulating the Stars
• For very tiny angles, use the approximation that
tan(p)=p, when p is in radians.
• Then d=B/tan(p) becomes d=B/p.
• B=1 “astronomical unit” (e.g. the Earth-Sun distance).
Define a unit of distance such that d=1/p, if the angle p
is measured in arcseconds.
• This unit is the parsec, which is 3.26 light years.
Distances and Brightness
• What do we do with the distance
measurement?
Distances and Brightness
• What do we do with the distance
measurement? We need the distance to
compute the star’s luminosity.
• Note the distinction between how bright a
star appears and how luminous it actually is.
• Let’s review how to quantify brightness…