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Astrophysics Internet Course
Unit 1 : Light Phenomenon and its Models
What is the subject of astrophysics? Astrophysics is interested in internal
composition and evolution of stars and galaxies. But how can we learn about
their structure if they are so far away? What kind of information can we obtain to
devise models (Link - Eugenia) of these objects? This information must be
produced by these objects and reach us. Some celestial objects radiate visible
light (http://csep10.phys.utk.edu/astr162/lect/light/spectrum.html )
Some are invisible for our eyes but visible for radio telescopes
(http://csep10.phys.utk.edu/astr162/lect/light/radio.html )
or X-ray telescopes (http://xray.rutgers.edu/dev/trw.html ).
Some radiate cosmic particles
(http://www2.slac.stanford.edu/vvc/applications/morecosmic.html ;
http://zebu.uoregon.edu/~js/glossary/cosmic_rays.html ;
http://www-personal.umich.edu/~ande/cr/cr.html ;
http://www.infoplease.com/ce5/CE012888.html )
The only way to learn about celestial objects is to study what they send us.
Let us start with light. We call it a phenomenon because we can observe it. We
study its properties in experiments. But how do we explain them? In physics,
explanations that we give to the phenomena are called models. The word model
is based on the idea that whatever explanation we devise, it will not comprise all
the complexity of the phenomenon. It will explain some features of it under some
circumstances, and for other circumstances a different model will be called for.
The validity of models is tested in experiments. There are 2 major models that
explain observable light phenomena, such as reflection, refraction, interference,
diffraction, and the radiation and absorption of light. They are a wave model and
a photon model of light.
Mechanical Waves
To understand the wave model of light, you need to refresh your memory
about mechanical waves. Use the following Web page to help you review this
material :
http://www.glenbrook.k12.il.us/gbssci/phys/Class/waves/wavestoc.html
Question Set 1: Mechanical Wave Review
1) What do you need to have if you want to create wave motion?
2) What is called a sinusoidal wave?
3) What are physical quantities that characterize a model of a sinusoidal wave?
4) How can we measure each of them?
5) What do they depend on?
6) What does it mean if the amplitude of a wave in a slinky is 20 cm?
7) What does it mean if the frequency of a wave in a slinky is 2 Hz?
8) What does it mean if the speed of a wave in a slinky is 2 m/s?
9) For the previous conditions, determine the wavelength of the wave and
explain what the number you calculated means.
10) Describe the phenomena of interference and diffraction.
11) Explain the phenomena of interference and diffraction. What modeling
conditions did you use for your explanation?
12) Give examples of wave interference and diffraction that you observed in
everyday life.
Wave Model of Light
Now we can start discussing why a wave model can be used to explain the
behavior of light. Think about light phenomena that resemble different
phenomena that occur with waves. Does light reflect? Refract? Interfere?
Diffract? The following Web pages will help you to answer these questions and
move to the second set of questions in this lesson:
http://www.glenbrook.k12.il.us/gbssci/phys/class/light/lighttoc.html
http://theory.uwinnipeg.ca/physics/light/index.html
Question Set 2 : Wave Model of Light
1) How is light reflected by different surfaces? Are different colors reflected at
the same angle?
2) How is light refracted by different media? Are different colors refracted the
same way?
3) Why do you see a rainbow if white light goes through a prism?
4) How do we know that different colors correspond to different wavelengths of
light?
5) If red light goes from air to water, what changes: its frequency, wavelength or
speed? Why?
6) What will happen if white light goes through two very narrow slits? Why?
7) What will happen if a monochromatic light goes through a system of two very
narrow slits? Why?
8) What will happen if white light goes through a system of many narrow slits?
Why? What do you need to know in order to calculate the separation of slits
using this experiment?
9) Why a diffraction grating should be called an interference grating?
10) What phenomenon is called a spectrum of light?
The Electromagnetic Wave Model of Light
Phenomena of interference and diffraction prove that the wave model can
be applied to study the propagation of light. But what kind of wave is the light
wave? Is it a mechanical wave like a sound wave or a different kind?
(http://www.glenbrook.k12.il.us/gbssci/phys/Class/sound/11l1a.html )
We know that light propagates in a vacuum and sound does not. This means that
light wave is not transmitted by vibrating particles. If this is true, then what is
oscillating in a light wave? Theoretical studies done by J. K. Maxwell
(http://www.bc.cc.ca.us/programs/sea/astronomy/light/lighta.htm ;
http://zebu.uoregon.edu/~js/glossary/maxwell.html ) and experiments carried
out by H. Hertz (http://www.optonline.com/comptons/ceo/02190_A.html )
proved that light is a wave in which electric and magnetic fields oscillate
perpendicular to each other
(http://zebu.uoregon.edu/~js/ast122/lectures/lec04.html ) In order to produce
an electromagnetic wave, an electric charge is accelerated
(http://newton.hanyang.ac.kr/~jhkim/jhdocu5.html ).
Polarization experiments prove that light behaves like a transverse wave
in which electric and magnetic fields (that is why it is called an electromagnetic
wave) are perpendicular to each other and produce each other. It is extremely
important to understand that in the polarization process you will be looking at, it
is the electric field component that is being polarized
(http://www.glenbrook.k12.il.us/gbssci/phys/Class/light/u12l1e.html ).
The transverse wave nature of light can also be proved by the effects that
magnetic field creates on the polarization of light (Link - Eugenia).
We also know that the geometry of experiments done with diffraction
gratings shows that the color of light that we perceive is representative of its
wavelength (and therefore its frequency) (Link - Mike). Frequencies of visible
light range from 4.3 x 10 14 Hz to 7.5 x 1014 Hz. Electromagnetic waves with
frequencies smaller than visible light (known as infrared, microwaves and
radiowaves) as well as those with higher frequencies (ultraviolet, X-rays, gamma
rays) possess the same properties.
Question Set 3 : The Electromagnetic Wave Model of Light
1) What experiments proved that light is an electromagnetic wave?
2) State whether the following forms of electromagnetic radiation radio, TV,
infrared, visible, ultraviolet, X, gamma are listed in order of increasing or
decreasing wavelength, b) increasing or decreasing frequency, c) increasing or
decreasing energy of their photons.
3) For each of the following forms of electromagnetic radiation, state one way
that it is produced in nature, and one way that you might detect the presence of
this form of radiation.
4) What is known about the speed of different forms of radiation in a vacuum?
5) What are the approximate wavelengths of red light, yellow light, blue light,
radio waves, television waves, X-rays?
6) What are two characteristics of sound waves that prove that they are not forms
of electromagnetic radiation?
7) An experiment in which white light is projected through a diffraction grating
onto a screen shows that the red part of the visible spectrum is farther from the
center of the screen than the blue part of the spectrum. Explain how this proves
that red light has a larger wavelength than blue light.
8) How can the polarization of light provide evidence that the wave model of
light works?
9) A student believes that two polarizing filters, aligned perpendicular to each
other, will eliminate any unpolarized light that is passed through both the filters
because one filter removes the electric field and the other filter removes the
magnetic field. Explain how you would correct this student’s ideas about
polarized light.
The Photon Model of Light
At the same time, many experiments cannot be explained if we apply a
wave model to light. Some of these experiments have to do with the photoelectric effect, that is, the absorption of light by metals
(http://theory.uwinnipeg.ca/physics/quant/node3.html ). Still other
experiments are related to radiation of light by hot objects (solids or gases).
Experimental data obtained by studying radiation of light by hot solid objects
can be represented by a curve. One can obtain a similar curve recording the
energy of light at different wavelengths. This information can be obtained if light
from a hot object (such as a filament of an incandescent light bulb or back body)
passes through a diffraction grating and is focused on a screen. With your eyes
you can see a rainbow (spectrum) in which all colors are present. If your eyes
were sensitive to shorter (UV) or longer (infrared) wavelengths, you would see
that the light of these wavelengths is present too, but its intensity is different. The
wavelength at which the maximum intensity that is radiated can be determined
using Wien’s Law, which was obtained experimentally, and the total energy is
given by Stephan-Boltzmann’s Law, which is also the result of experiments.
None of these laws can explain the experimental curve of intensity versus
wavelength, in which light of all frequencies are present but has different
intensity at different wavelengths. This curve is called a continuous spectrum.
The model for the radiation mechanism for the continuous black body spectrum
was provided by Max Planck. The Web pages below should help you to learn
more about the material discussed above as it relates to the photon model of light
: http://zebu.uoregon.edu/~js/glossary/planck_curve.html ;
http://zebu.uoregon.edu/~js/ast122/lectures/lec05.html ;
http://csep10.phys.utk.edu/astr162/lect/light/radiation.html ;
http://theory.uwinnipeg.ca/physics/quant/node2.html
Question Set 4 : The Photon Model of Light
1) What experiments cannot be explained with the wave model of light?
2) What are the main features of the photon model of light?
3) What phenomena can be explained with the help of both models?
What are the explanations (provide at least two examples).
4) What is the difference between red and blue photons?
5) Observations of the light of the stars indicate that they produce a continuous
emission spectrum that is very similar to the black body spectrum. Using these
data, determine the surface temperature of the Sun, assuming that is has yellow
color.
6) Using the datum for the surface temperature from item 5, determine the total
energy radiated by the Sun every second. This rate of energy production is called
the luminosity.
7) Compare this value for the luminosity of the Sun with the value that you
obtain from the amount of energy that 1/2 of the Earth’s surface receives from the
Sun. (Note : the Solar constant, which is the rate at which each square meter of
the earth receives energy from the sun, is 1.37 x 103 Watts/m2)
The Doppler Effect
Another phenomenon that can be explained with the wave model of light
is the Doppler Effect. Although many people are familiar with the Doppler Effect
as it relates to sound, it is also a fundamental tool in the analysis of stellar
phenomena. To begin learning about it, visit these Web pages:
http://www.glenbrook.k12.il.us/gbssci/phys/class/waves/u11l3b.html
http://csep10.phys.utk.edu/astr162/lect/light/doppler.html
http://zebu.uoregon.edu/~js/ast122/lectures/lec04.html
The mathematical expression for the Doppler Effect for light is different from the
expression that you may be familiar with for sound. The derivation of the
expression for the Doppler Effect for light can be found here (Link - Mike).
After reviewing all of the links above, you will be prepared to answer the next
question set.
Question Set 5 : The Doppler Effect for Light
1) Suppose a source is monochromatic yellow light. How does the appearance of
the source change as the source (a) approaches the observer, or (b) recedes from
the observer.
2) Suppose the observed wavelength of the sodium line in a star is 5891 A,
whereas in the laboratory the wavelength is 5890 A.
(a) At what speed is the star moving relative to us?
(b) Is the star approaching or receding?
3) Describe in words how the sun’s rotation can be determined from an analysis
of the spectra of light coming from various parts of the disk.
4) Explain how the earth’s orbital speed can be determined from observations of
the spectrum of a star.
5) Light from a galaxy in the Constellation Virgo is observed to be 0.4% longer
than corresponding light that has a wavelength of 656 nm when measured in the
laboratory. What is the radial speed of this galaxy with respect to the earth? Is it
approaching or receding?
6) The period of rotation of the sun at its equator is about 24.7 days; its radius is 7
x 105 km. What Doppler wavelength shift is expected for light with wavelength
550 nm emitted fom the edge of the sun’s disk?
Unit 2 : The Ideal Gas Model
Many phenomena occurring to celestial objects can be explained with the
help of another model... the model of ideal gas. This model is connected to the
Kinetic Molecular Theory. The following Websites will help you to review the
major parts of this theory/model :
http://www.bcpl.lib.md.us/~kdrews/kmt.html
http://www.chem.ualberta.ca/~plambeck/che/p101/p01051.htm
http://www.chem.ualberta.ca/~plambeck/che/p101/p01061.htm
http://www.chem.ualberta.ca/~plambeck/che/p101/p01062.htm
http://www.chem.ualberta.ca/~plambeck/che/p101/p01063.htm
http://www.chem.ualberta.ca/~plambeck/che/p101/p01065.htm
Question Set 6 : The Ideal Gas Model
1) What is gas? What do we know about its properties? How do we know what
we know (What experimental observations give us the evidence for these
statements? What theoretical assumptions we use and why?)
2) What is ideal gas? What is the difference between real gas and ideal gas?
3) When can we say that real gas behaves like ideal? When can’t we say this?
4) What are physical quantities that describe the behavior of ideal gas? What are
their units? What is the relationship between them? How do we know that these
laws are true?
5) Can we use the model of ideal gas for the gas in a typical classroom?
Approximately how much energy does it possess?
6) What is the difference between words temperature, heat energy and heat?
7)Calculate the speed of air molecules in this room.
8) How often do molecules collide? (calculate the number of collisions per
second).
9) The best vacuum that can be produced in the laboratory is about 10-15 atm.
How many molecules still exist in one cubic centimeter of space at this pressure
and temperature 0°C?
10) Why does the Moon have no atmosphere?
Unit 3: The Structure of Atoms
As we understand now, our knowledge of stars come from the studies of
electromagnetic waves that they radiate. But how do they radiate light? How do
stars radiate UV radiation, or X-rays? This section will help you to understand
how stars produce visible and UV radiation.
By the middle of the 19th century scientists learned how to analyze light radiated
by hot gases. For example, the studies of hydrogen by Johann Balmer that atomic
hydrogen does not radiate white light, but light of only certain wavelength. For
example, he observed light of the following wavelengths: 656 nm, 486 nm, and
434 nm. The same phenomenon was observed for all gases at low density.
Scientists were curious about the mechanisms that could lead to this kind of
radiation. To explain the mechanism they needed to devise a model of the inner
structure of atoms that would account for their stability, lack of total electric
charge and their radiation spectra.
The first step in this work was the discovery of the electron in the studies of
cathode rays . After this J.J.Thomson proposed his “plum-pudding model”, and
E. Rutherford came up with the planetary model
(http://wine1.sb.fsu.edu/chm1045/notes/Atoms/AtomStr1/Atoms02.htm ;
http://www.phys.virginia.edu/classes/252/rays_and_particles.html ).
Unfortunately none of them accounted for all of the observed properties. This
prompted N. Bohr to devise a new model which was later called the “Bohr
hydrogen atom”. The following set of questions will help you to understand the
features of this model and the limitations of the previous ones.
Question Set 7 : Models of Atoms
1) What are cathode rays and what properties they have?
2) Describe the main features of Thomson model of atoms and the experimental
facts that it accounts for.
3) What experimental facts cannot be explained with Thomson’s model?
4) Describe the main features of Rutherford’s planetary model of atoms and the
experimental facts that it accounts for.
5) What experimental facts cannot be explained with Rutherford’s planetary
model?
6) In his model, Bohr modified planetary model for hydrogen to account for all
experimental observations. The electron was still orbiting the nucleus but Bohr
postulated that:
• there are certain stationary states (radii) in which the electron even moving in
a circular orbit does not radiate electromagnetic waves. In these states the
angular momentum of the electron is quantized: the magnitude of the orbital
angular momentum (mvr) equals a positive integer multiple of Planck’s
constant (h) divided by 2
mvr = nh/(2)
(n=1,2,3,...).
• Radiation is emitted by the atom when the electron undergoes a transition
from one stationary state to another.
• This energy is emitted in a form of a photon, which frequency is determined
by the difference in energies of the states:





E = hf
Using these postulates, your knowledge about the energy of the electron in each
state (taking into account that it has kinetic energy and electric potential energy
due to Coulomb’s force of its interaction with the nucleus) and applying
Newton’s laws to the motion of the electron, find out from what level to what
level transitions were made to produce light of the wavelengths observed by
Balmer (656 nm, 486 nm, and 434 nm) in the spectrum of hydrogen. All necessary
constants are in the table (link to the table of constants here).
7) Calculate the energy of a photon that can ionize the atom of hydrogen.
8) Calculate the temperature of hydrogen at which all atoms are ionized.
9) Imagine that you have white light produced by the hot filament (remember, it
produces a continuous spectrum), what will happen if this light goes through a
cloud of cold hydrogen? Hot hydrogen? Ionized hydrogen?
10) If you look at the Sun through a spectroscope
(http://infoplease.lycos.com/ce5/CE049035.html ), you will see a continuous
spectrum with the brightest part around yellow light and dark stripes. The
wavelengths at which there is no radiation coming can be easily recorded. Some
of them are the same as the wavelengths of spectral lines radiated by different
elements in the laboratory conditions (for example ionized Fe, Mg, Ca, Na, or
atomic H). How can you explain this phenomenon?
Unit 4 : Stellar Parameters
Stellar parameters are physical characteristics of the stars that astronomers
use to classify stars and study their evolution. It is important to not only know
what these characteristics are but also how to determine them.
These parameters are:
1) Stellar luminosities. The luminosity of the star is the total amount of energy it
radiates every second. It is measured in J/s and depends on the surface
temperature and the size of the star.
(http://www.bc.cc.ca.us/programs/sea/astronomy/starprop/strpropb.htm )
Surface temperatures can be determined from the analysis of the spectrum of the
star but the sizes of stars are very hard to measure. One method that is used for it
is lunar occultations. The moon occults a star when it passes in front of the star as
viewed from the Earth. The observer makes very rapid measurements of the
star’s light as the Moon occults it. The diameter of the star can be determined
from the time of the occultation because the angular speed of the Moon is well
known. Unfortunately this is not a very precise method. Another way of
determining sizes of the stars comes from knowing the next parameter.
2) Stellar magnitudes (absolute and apparent)
(http://csep10.phys.utk.edu/astr162/lect/stars/magnitudes.html
http://zebu.uoregon.edu/~js/ast122/lectures/lec09.html ). As you understand,
apparent magnitude can be determined from observations but absolute cannot.
To determine the absolute magnitude, one must know the distance to the stars.
One of the methods to measure distances is called “parallax”
(http://csep10.phys.utk.edu/astr162/lect/distances/parallax.html
http://zebu.uoregon.edu/~js/ast122/lectures/lec09.html ).
The relationship between apparent and absolute magnitude allows astronomers
to determine the luminosities of stars even when they do not know their radii.
It is important to know that the luminosity as we defined it before is
related to electromagnetic energy in all wavelengths. As you already know,
according Wien’s Law, the amount of energy that hot objects radiate at different
wavelengths depends on their surface temperatures. That is why astronomers
distinguish luminosities in different parts of the spectrum and bolometric
luminosities.
3) Stellar spectra. The studies of stellar spectra in the 19th century demonstrated
that though stars’ spectra look different
(http://instruct1.cit.cornell.edu/courses/astro101/lec13.htm
http://csep10.phys.utk.edu/astr162/lect/stars/spectra.html ;
http://csep10.phys.utk.edu/astr162/lect/sun/spectrum.html
http://zebu.uoregon.edu/~js/ast122/lectures/lec10.html ), they can be
classified. We will use Harvard spectral classification
(http://csep10.phys.utk.edu/astr162/lect/stars/harvard.html ). The studies of
stellar spectra allow astronomers to determine chemical composition of stars,
their surface temperatures, density of the atmospheres, their motion, whether
they belong to binary systems, and their age.
4) Chemical composition. Stellar spectra exhibit absorption lines that can be
used to identify chemical elements whose atoms could absorb recorded
frequencies. At the same time this information can be deceiving because the
conditions for absorption vary with temperature. Most of the stars are made of
the same chemical elements : 70% H and about 25% He
(http://csep10.phys.utk.edu/astr162/lect/sun/composition.html ). Chemical
composition changes slightly as the star evolves.
5) Stellar masses. This parameter can be determined rather accurately for binary
stars (http://csep10.phys.utk.edu/astr162/lect/binaries/binaries.html ;
http://csep10.phys.utk.edu/astr162/lect/binaries/visual.html ) through
observations of their orbital periods and speeds. One needs to know Kepler’s
laws to understand this method
(http://csep10.phys.utk.edu/astr162/lect/binaries/astrometric.html ). For
single stars that are on the Main Sequence, the experimental relationship between
mass and luminosity (called the Mass-Luminosity Relation ) is used to determine
their masses (http://csep10.phys.utk.edu/astr162/lect/binaries/masslum.html
).
Question Set 8 : Stellar Parameters
1) Determine the Solar luminosity using two methods: a) data about its surface
temperature and radius; b) data about the energy that every square meter of the
Earth receives every second (Solar constant). How will the luminosity of the sun
change if the observer moves away from it twice the distance between the Earth
and the Sun? How will the Solar constant change it this happens? Explain.
2) Use the table shown below to derive the relationship between two apparent
magnitudes and stars’ brightness.
Difference in apparent magnitude
0.0
0.5
0.75
1.0
1.5
2.0
2.5
3.0
4.0
5.0
6.0
10.0
15.0
20.0
25.0
Ratio of Brightness
1:1
1.6 : 1
2:1
2.5 : 1
4:1
6.3 : 1
10 : 1
16 : 1
40 : 1
100 : 1
251 : 1
10,000 : 1
1,000,000 : 1
100,000,000 : 1
10,000,000,000 : 1
3) Can two stars have the same apparent magnitudes but different absolute
magnitudes? Give an example. Explain.
4) Can two stars have the same absolute magnitudes but different apparent
magnitudes? Give an example. Explain.
5) At what distance one half of the Earth’s orbit would have a parallax of
1 arcsec?
6) If a star’s parallax is 0.04 arcsec, what is its distance in parsecs, in light years,
in astronomical units, in kilometers? (25 pc, 81.5 LY, 5.16 x 106 au,
7.7 x 1014 km)
7) The smallest parallaxes that can be measured are about 0.01 arcsec what is the
maximum distance that can be measured by the method of stellar parallax? (d=
1/0.01=100 parsecs)
8) What would be the advantages of measuring stellar parallaxes from Mars
rather than from Earth? (Mars’ orbit is 50% larger than the Earth’s, so all
parallaxes will be 50% larger, we will be able to measure the distances to the stars
that we can do from Earth)
9) Derive the relationship between the apparent, absolute magnitude and the
distance to between the star and the observer.
10) Derive the relationship between the absolute magnitude of the star and its
luminosity.
11) Why is the star’s apparent magnitude not a good indication of the star’s
energy output?
12) Why is the star’s absolute visual magnitude not an accurate measure of a
starís total energy output?
13) Which kinds of stars are expected to emit large amounts of ultraviolet
radiation?
14) Which kinds of stars would be expected to emit large amounts of infrared
radiation?
15) Which characteristics of a star can be determined by one night’s observing
with a naked eye?
16) Which characteristics of a star can be determined by one night of telescopic
observations, including auxiliary instruments?
17) What characteristic determines the color of the star?
18) Two stars of equal luminosity. Star B is blue, star Y is yellow-orange. Which
star appears brighter to the eye? Which star appears brighter on the photo?
19) The spectral class of the star depends on which two properties of the star?
20) List the following stars in order of increasing surface temperature: A0, B3, F2,
M3, G2, O8.
21) Determine the color and approximate surface temperature of the following
stars:
Sirius A1
Centauri
G2
Arcturus
K2
Rigel
B8
Betelgeuse M2
Crucis B0
22) Three stars are observed to put out their maximum light at the following
wavelength. Estimate the spectral class of each.
2.6 x 10-7m
5.0 x 10-7m
9.7 x 10-7m
23) In which stellar spectral class is each of the following most likely to be found
in the spectrum?
(a) Strong hydrogen lines
(b) Lines of neutral metals
(c) lines of neutral helium.
24) How do astronomers estimate the chemical compositions of stars?
25) How do astronomers estimate stellar rotation rates?
26)What different kinds of information can be obtained from the analysis of
stellar spectra?
Hertzshprung-Russel Diagram
After we established the system of stellar parameters, it would be interesting to
find out, if there is any relationship between different parameters of the stars. For
example, do stars of the same spectral class have different luminosities, or the
same spectrum leads to the same luminosity? To answer this question, one must
examine observational data from different stars. We offer you data on 65 stars:
Star
Proper
name
Sheratan
Arietis
 Bootis
A
 Bootis
B

Cassiope
iae A

Cassiopi
ae B
Centau
ri
 Centi
Eridan
yC
VZ
Hydrae
Hydri
Lac 9352
 Leonis Denebola
70
Ophiuch
iA
70
Ophiuch
iB

Luminosi
ty
20
0.5
Mas
s
2.5
0.8
Radius
Color
1.8
0.9
Temper
ature
8800
5300
White
Yellow
Spectral
Class
A5 V
G8 V
0.19
0.6
0.8
4400
Orange
K4 V
1.2
1.1
1.1
6000
Yellow
GO V
0.05
0.4
0.6
3700
Red
MO V
2900
11
6
19000
Blue
B2 V
0.7
0.02
0.9
0.3
0.9
0.4
5600
3300
Yellow
Red
G5 V
M4 V
3.5
1.5
1.2
7200
Green
F5 V
7
0.04
27
1.8
0.4
2.7
1.4
0.6
1.8
7400
3400
9000
White
Red
White
FO V
M2 V
A3 V
0.4
0.8
0.9
5200
Orange
KO V
0.12
0.66
0.7
4200
Orange
K6 V
3.0
1.4
1.2
6300
Green
F6 V
Orionis
Persei
Scorpii
 Ursae
Majoris

Virginis
Ophui
uchi




Ursae
Mejoris
 Austrini
Algol
Dschubb
a
Alkaid
Spica
Archerna
r
Regulus
Vega
Merak
200
12000
5.2
17
3
7.6
12000
28000
Blue
Blue
B8 V
BO V
1100
8
4
15000
Blue
B5 V
4
1.5
1.3
7100
Green
F2 V
16000
19
8
30000
Blue
O9.5 V
1800
720
14
10
7
5
23000
17500
Blue
Blue
B1 V
B3 V
164
55
70
5.5
3.8
3.6
3.2
2.6
2.43.6
13000
1000
9900
Blue
White
White
B7 V
AO V
A1 V
3.0
2.0
9000
White
A3 V
1.81
1.9
8800
12
3.0
2.1
1.12
1.5
1.05
8100
6200
White
Green
A7 V
F7 V
1.0
0.95
1.05
5800
Yellow
G2 V
0.44
0.51
0.8
0.78
0.9
0.89
5300
5100
yellow
Orange
G8 V
KO V
0.04
0.58
0.6
3600
Red
M1 V
0.3
3300
Red
M3 V
Formalha 20
ut
WW
Aurigae
A
 Aquilae
VZ
Hydrae
UV
Leonis
 Ceti

Herculis
YY
Geminor
ium
Krueger
60 A
 Crusis

Centauri
Orionis
Cygni A
 Carenae
Altair
Castor C
0.01
A5 V
Beta
Crusis
Hadar
6000
21
10
28000
Blue
B0.5 V
10400
15
10
23000
Blue
B1 III
Rigel
Deneb
Canopus
60000
60000
1500
43
42
15
22
44
60
11200
9300
7400
Blue
White
white
B8 I
A2 I
Fo I-II
 Ursae
Minoris

Aurigae
Polaris
6000
14
90
5300
Yellow
G8 III
Capella
150
4
13
5300
Yellow
G8 III
Geminoru
m
 Cephei
Pollux
34
4
15
4600
Orange
KO III
 Bootis
 Tauri
Arcturus
Aldebara
n
9200
115
160
16
4
5
220
18
45
5000
4400
3900
Orange
Orange
Orange
K1 I
K2 III
K5 III
300
6
50
3300
Red
M1 III
Antares
9500
Betelgeus 15000
e
Sheat
700
24
27
600
750
3200
3200
Red
Red
M1.5 I
M2 I
7
100
3000
Red
RasAlgethi
1600
9
100
2700
Red
M2 IIIII
M5 II
1
1.0
1
1.0
1
1
5800
5800
Yellow
yellow
G2 V
G2 V
 Centauri
B
 Centauri
C
0.2
0.6
0.8
4400
Orange
K4 V
0.01
0.2
0.3
3000
Red
M5 V
Baranar
ds Star
Wolf 359
Lalande
21185
0.004
0.2
0.3
2500
Red
M5 V
0.001
0.1
0.2
2400
3400
Red
Red
M8 V
M2 V
28
2.7
1.8
9900
White
A1 V
0.0027
1.1
0.02
9300
White
0.005
0.3
0.18
0.15
0.7
0.6
0.25
0.85
0.7
2800
4800
4400
Red
Orange
Orange
White
Dwarf
M6 V
K2 V
K5 V
0.08
0.5
0.7
4000
Orange
K7 V
7
1.8
2.2
6500
Green
F5 IV-V
Ophiuc
hi
 Scorpii
 Orionis
 Pegasi
 Herculis
Sun
Centauri
A
 Canis
Majoris A
 Canis
Majoris B
Rigil
Kent

Sirius
UV Ceti
 Eridani
61 Cygni
A
61 Cygni
B
Procyon
 Canis
Minoris
A
 Canis
Minoris
B
0.0006
0.7
0.01
9100
White
White
Dwarf
To find the patterns in this data, you need to graph it. We suggest that you
obtain log paper (desirable for 6 - 8 orders of magnitude) and graph the data
from the table for luminosity and temperature. Because luminosity of stars varies
so much, it is convenient to graph the log of the ratio of the star’s luminosity and
the Sun’s luminosity (y axis) versus temperature (x axis). Notice, that
traditionally astronomers graph temperatures backwards : the highest are closest
to the beginning of the axis and the lowest are at the right end. After you are
done with graphing, compare your graph with the graph conventionally known
as Hertzshprung-Russel diagram
(http://zebu.uoregon.edu/~js/ast122/lectures/lec12.html ;
http://instruct1.cit.cornell.edu/courses/astro101/lec13.htm ;
http://www.bc.cc.ca.us/programs/sea/astronomy/starprop/strpropd.htm )
Question Set 9 : The H-R Diagram
1) For the stars in the table:
Which star has the hottest surface?
Which star has the coolest surface?
Which star is the nearest?
Which star is the farthest?
Which are the largest stars?
Which are the smallest stars?
Which star is bluest?
Which are the reddest?
Which star is most like the Sun?
Which stars do not follow the intuitive temperature-brightness relationship for
stars?
2) Why were you asked to find the relationship between luminosity and
temperature, not between color and temperature, temperature and spectral class?
3) Is there a relationship between stars’ luminosities, temperatures and radii?
Chose several stars from the table to prove your answer qualitatively.
4) What is the theoretical model that will allow you to determine the radius of a
star when its temperature and luminosity are known? Test it quantitatively using
the data from the table for several stars.
5) H-R diagram is used to determine distances for the stars. Can you offer a
method to do it?
6) What is the difference between different groups of stars represented on H-R
diagram? Why, do you think they are so different?
7) What does it mean if most of the stars are located on the region called “The
Main Sequence”?
8) What does it mean if only very few stars are “white dwarfs”, i.e., hot and tiny
stars.
9) Why are some luminosities in the table rather estimates that measured
quantities.
Unit 5 : Stellar Structure, Composition, and Evolution.
H-R diagram shows that stars spend most of their life on the Main Sequence. Our
sun is on the Main Sequence too. It means that it is going through the longest
phase of its evolution. What do we know about the Sun that might help us to
learn about its interior? We know its color, its size, the energy that is sends in all
directions every second and its approximate age : this can be deduced from the
age of the Earth that is estimated to be at least 4.5 billion years. Let us try to
figure out how the Sun maintains its tremendous luminosity for billions of years
and what is the source of its energy.
Question Set 10 : Energy of the Sun
1) How old is our Sun?
2) Will it shine forever? Why not?
3) What affects the length of time the Sun can shine? How would you express its
life time in terms of the energy that it possesses and the energy it loses every
second?
4) How long can it shine using its heat energy? To calculate the heat energy of
the Sun, estimate that it is made of hydrogen, and the average temperature of the
Sun is 50,000 K. In what state (gas or plasma) is hydrogen at this temperature?
How do you know? (The mass of the Sun is listed in the data table).
5) How long can it shine using its gravitational potential energy?(Link - Mike)
Assume that half of the total GPE can be radiated as electromagnetic radiation if
the Sun shrinks to a point.
6) What other sources of energy might it have? Can it use chemical energy? Why
not?
7) What is fusion? How much energy is radiated when a nucleus of helium is
produced in a fusion reaction?
8) How many protons (in terms of mass in kg) should fuse to maintain the
present luminosity of the sun for 5 billion years? Is this number reasonable for
the Sun?
9) What conditions are necessary so that fusion might take place in the core of the
Sun?
10) Calculate the temperature at which two protons can come close enough for
nuclear attraction forces to start acting on them. Why can’t they come close at
lower temperatures? References to nuclear forces can be found at
(http://csep10.phys.utk.edu/astr162/lect/energy/reactions.html ;
http://zebu.uoregon.edu/~js/ast122/lectures/lec06.html ;
http://www.scri.fsu.edu/~jac/Nuclear/whatis/forces.html
http://library.advanced.org/tq-admin/month.cgi )
11) How does this relate to the possibility of fusion in the core of the Sun? The
temperature in the core of the Sun is estimated to be 10 million degrees K. Does it
mean that fusion is impossible?
12) What is a p-p cycle? What is a CNO cycle?
(http://csep10.phys.utk.edu/astr162/lect/energy/ppchain.html ;
http://csep10.phys.utk.edu/astr162/lect/energy/cno.html ;
http://csep10.phys.utk.edu/astr162/lect/energy/cno-pp.html )
13) What might be an indicator of the presence of the fusion in the core of the
Sun? Estimation show that it takes 100 million years for a photon radiated in the
fusion reaction in the core of the Sun to reach the surface (because of absorption,
reemission, and scattering). It means that the photons that we are seeing on the
surface of the Sun now, were born very long time ago. What particle that is
emitted in fusion reactions, does not get absorbed on its way out?
14) What are the results of Solar Neutrino experiments?
15) What is your conclusion about the sources of stellar energy?
The next step in our understanding of stars will be learning about their
evolution. This deals with the question such as: Where do stars come from? Do
they change over the years? What will their life path depend on? Do they ever
die? What happens to stars after death? How do we know this?
Essentially, the evolution of a star involves 6 stages : “birth”, “childhood”,
“adulthood”, “old age”, “death”, and “life after death”. For a good overview of
these stages, carefully read lectures 14, 15, 16, 17, 18, 20, 21, and 23 at the
University of Oregon Astronomy website (http://zebu.uoregon.edu/~js/ast122
). Another good overview is the entire “Lives and Deaths of Stars” section at the
Bakersfield College Astronomy website
(http://www.bc.cc.ca.us/programs/sea/astronomy/evolutn/evolutna.htm )
Novae, supernovae, and supernovae remnants are part of the last two stages in
the life of a star. In addition to the previously recommended sites, more can be
learned about these phenomena, as well as open (galactic) and globular clusters
by
(1) clicking on the Novae and Supernovae chapters at “The Death of Stars” site
at the University of Tennessee
(http://csep10.phys.utk.edu/guidry/violence/death.html ). The UTenn site also
has a good illustration of a Type 1A Supernova
(http://csep10.phys.utk.edu/astr162/lect/supernovae/type1.html ) , as well as
information about star clusters
(http://csep10.phys.utk.edu/guidry/violence/starclusters.html
(2) clicking on lectures 19, 22, and 23 at the Cornell University Astronomy
101/103 website (http://instruct1.cit.cornell.edu/courses/astro101/index.htm )
(3) clicking on a site provided by NASA
http://imagine.gsfc.nasa.gov/docs/introduction/supernovae.html
Finally, there is a type of star called the Cepheid variable, which plays an
important role in determining distances to stars. Read more about Cepheid
variables at these sites:
http://zebu.uoregon.edu/~soper/MilkyWay/cepheid.html
http://annie.astro.nwu.edu/labs/m100/measdist.html
http://www.ast.cam.ac.uk/~mjp/cepheids.html
http://imagine.gsfc.nasa.gov/docs/science/mysteries_l1/cepheid.html
Question Set 11 : Stellar Evolution
1)What is a proto-star? How do they form? Why doesn’t every gas/dust
interstellar cloud becomes a proto-star?
2)Where in the Galaxy are likely places to search for proto-stars? What is the
observational evidence for the model of a proto-star?
3)What kind of radiation would a proto-star be expected to emit?
How do the main sequence stars contribute to the content of heavy elements in
the interstellar medium?
4)Why is it that we can know so much about the formation of stars, which are so
far away, whereas we know so little about the formation of planets, one of which
is just outside the door?
5)What is the predominant energy source for each of the following kinds of stars:
(a) pre-, (b) main sequence, (c) red giant, (d) white dwarf?
6)Once the proton-proton reaction begins in the core of the star, why isnít all
hydrogen converted to helium instantly?
7)When hydrogen is converted to helium plus energy inside stars, where does
the energy come from?
8) A main sequence star of 20 solar masses is about 10,000 times more luminous
than the Sun. assuming the star to be pure hydrogen, how long would it take for
the star to convert all its hydrogen into helium?
9) When a main sequence star exhausts its hydrogen fuel in its core,
(a)what happens to the core of the star? (b) what happens to the starís outer
layers?
10) What two reactions are believed to occur in red giants, and where in the star
do they occur?
11) What property of a star determines where it is located on the main sequence?
12) Describe the basic differences between: a) a main sequence A0 star and a
white dwarf A0 star; b) a main sequence M2 star and a red giant M2 star.
13) Why is it believed that stars spend the major portion of their lives on the
main sequence?
14) Why do upper main sequence stars (O & B) spend much less time on the
main sequence than do lower main sequence stars?
15) Describe and explain the differences between H-R diagrams for a typical
globular cluster and a typical open cluster.
16) What are possible end stages for stars?
17) What property of a star determines how it will end?
18) What will be the fate of the Sun?
19) How is it known that dwarfs are dying stars, and not stars at some active
stage of evolution? What is believed to be inside a whit dwarf? How do we know
that this is true?
20) What are neutron stars and how are they detected?
21) Why is it difficult to detect black holes in space, if they exist?
22) If black holes do exist but emit no electromagnetic radiation, then how might
they be detected?
23) Why doesn’t a proto-star just continue to collapse until it becomes a planet or
a black hole?
24) What will happen if fusion reactions start in the degenerate gas?
25) Why does fusion occurs peacefully in the stars on the main sequence but
leads to explosions in Novae stars? Supernovae Stars? Or on Earth? (hint: the
reasons are the same in principle but different in details).
26) Describe the phenomenon of a Nova star.
27) Provide possible explanation for the phenomenon of A Nova star.
28) Describe the phenomenon of different types of Supernovae stars.
29) Provide possible explanations for the phenomenon of different types of
Supernovae.
30) Describe the phenomenon of Cepheid variables and explain how they are
used to determine the distance to stars.
Missing links:
Models in Physics
The word “model” is used for many purposes. It usually stands for “simple
version” of something. In physics one can say that this something can be:
a) an object;
b) a change;
c) a phenomenon;
d) a technical device.
Also there is a completely different set of models, I would call them the
conditions of geometry and symmetry. For example, on our world we are using
the model of Euclidean space, and the ideas of symmetry (homogeneity of space
and time, isotropy of space, barion symmetry, left-right symmetry, etc). For each
type of symmetry there is a law of conservation (time - energy, space- momenta).
For any model (from a, b, c list) one should separate the definition of it (what are
the main features of the model) and the criteria of application of this model
(when can we apply this model explaining the behavior of real systems).
Models of objects
The first group can be called models with localized properties
1. A particle (dimensionless object) - an object that has no size or volume but
can be located in space, possesses mass, has velocity and acceleration and can
be acted upon by forces. A real object can be described as a particle when its
size is much smaller than the distances in the problem or all its points follow
the same path with the same velocity.
2. Ideal gas - an object that is made up of particles that do not interact with each
other than in elastic collisions and obey Newton’s laws. Real gas can be
described as ideal when the distances between the particles are much greater
than their dimensions and the temperatures are high.
3. Point-like charge - a charges particle. Can be a small charged object, or a
spherical dielectric object, or a spherical metal object if we are very far away
from it.
4. Electron gas - an object that is made up of the ideal gas of electrons in metals
which collide with ions and move with constant velocity from a collision to a
collision. Real electrons can be described as ideal at temperatures above
superconductivity. This model explains Ohm’s and Joule’s law but does not
explain linear dependence of metals’ resistivity on the temperature.
The second group can be called models with continuously distributed properties
1. Model of a regular wave - all particles of the medium or space participate in
wave motion. Real wave can be described by this model when the size of the
container is much larger that the wavelength.
2. Model of a field (gravitational, electric, magnetic, electromagnetic).
3. Model of a uniform field.
Models of change
1. Linear change (motion with constant speed, Ohm’s law, thermal expansion).
2. Quadratic change (motion with constant acceleration).
3. Sinusoidal change (circular motion with constant speed, simple harmonic
motion, sinusoidal wave).
4. Exponential change (amplitude for damped motion, radioactive decay).
Models of phenomena
Here I include models of phenomena we study in the physics course and models
of scientific phenomena (the first person to do this was Galileo, the same way he
was the first to start thinking about the model of change for position of a falling
object).
1. Free fall (phenomenon in which we neglect all forces acting on an object
except the force f gravity). Can be used when the force of friction is much
smaller that the force of gravity.
2. Existence of an inertial reference frame. Can be used when the acceleration of
the reference frame is much smaller than the acceleration of gravity.
3. Phenomenon of an isolated system.
4. The motion of a particle attached to a massless spring which obeys Hooke’s
law (mass on a spring). Can be used when the size of the mass is much
smaller that the spring and the spring stretches much less that its own size.
5. Motion of a simple pendulum (particle on a string). Can be used when the
length of the string is much greater than the size of the bob.
6. Carnot cycle.
7. Phenomenon of wiring with no resistance.
8. Phenomenon of resistivity (scattering of phonons).
9. Phenomenon of superconductivity (interaction of electron pairs - Cuper
pairs).
10. Phenomenon of a white dwarf.
11. Phenomenon of a neutron star.
12. Phenomenon of a black hole.
13. Phenomenon of a Solar corona.
…………………………………………………..
Models of technical devices
1. Internal combustion engine.
2. Model of a bridge.
…………………………………………………..
The Doppler Effect for Light
Doppler Effect situations for light involve the relative motion of the source, S, and
the detector, D. In other words, “source moving toward detector” and “detector
moving toward source” are physically identical situations. This is based on the
relativistic fact that the speed of light is constant for any observer. (With sound
waves, these are 2 different physical situations, which lead to different equations
for the Doppler Effect for sound.)
Suppose that there is a source of light, S, that moves at a speed u relative to the
detector, D. The source, for our purposes, may be a galaxy, a quasar, a star, or
even (for one of the questions that follow) our sun. The detector is an
observatory here on earth that receives the light.
Case A)
Source Recedes from Detector at Relative Speed u
Suppose that the source S is moving away from the detector (earth observatory)
at a relative speed u. What effect does this have on the wavelength(s) of light
received here on earth?
If S emits a light wave, it will travel a distance in a time T. This is based on the
fact that the speed of light, c, is found by
c = /T
(1)
Now suppose that at the instant S emits wave 1, it begins receding from D at a
relative speed u:
By the time T that S emits wave 2, there is a separation  uT between wave 1 and
wave 2. This separation represents the Doppler-shifted wavelength ’ of the waves
reaching the detector D :





’ =  + uT
(2)
Clearly, ’ > , resulting in the detected wavelengths being “shifted” toward the
red end of the spectrum, where the longer wavelengths of visible light are found.
By solving equation (2) for the relative velocity u we get
u = (’ - )/T
(3)
The term 1/T represents the frequency of the source, fs. And, the frequency of
the source can be represented by the fundamental wave equation
fs = c/


(4)

As a result, the expression for the recessional velocity (which we’ll be using in
our lab exercise) is given by
u = (’ - (c/)
or
u/c
(5)
The value for ’ -  is referred to as the Doppler shift of the wavelength
received by the detector.
Case B)
Source Approaches Detector at Relative Speed u
The mathematical reasoning here is similar to Case A), with the exception that
the waves reaching the detector have a Doppler-shifted wavelength ’ found by
’ =  - uT
Here, the wavelength reaching the detector is less than the wavelength emitted
from the source, resulting in a “blue shift”, or a shifting of wavelengths to the
shorter end of the spectrum.
This leads to
u = (’)/T
u = (’)(c/)
- / = u/c
General Result :
If  is (+), then a red shift has occurred and the source
moves at a relative speed u away from the detector.
If  is (-), then a blue shift has occurred and the source
moves at a relative speed u towards the detector.
Gravitational Potential Energy
The formal expression for gravitational potential energy is :
Ug = -GMm/R.
Where does this expression come from? It does not look like the more familiar
mgh. The truth is, you need to be able to perform a calculus operation known as
integration to fully understand how this expression is determined. Any calculusbased college level physics text will include a derivation of this expression.
In the absence of calculus, we are going to offer some arguments for the validity
of this expression (sometimes this is called hand-waving). Hopefully these
arguments will persuade you to accept the expression. Here goes:
(1) When you lift something, you are doing work because you are applying a
force (which we measure in Newtons) through a distance (which we measure in
meters). This work results in that something gaining gravitational potential
energy. The unit for work is the Joule.
1 Joule = 1(Newton) x (1 meter)
If you check the unit associated with (-GMm/R), you will see that it is
(Newtons) x (meters). So this expression does represent energy.
(2) The force one applies in lifting something (at a nice steady rate) must equal
the force of gravity, which we know is GMm/R2. And, we are going to separate
m and M until they are some distance R apart. So, we can see that the product of
this force and this distance “sort of” yields our gravitational energy expression.
(Beware! It is not as simple as just multiplying the two terms. Why not? Because
as the R value changes, so does the force of gravity! This is why calculus is
needed.)
(3) On a universal level, physicists have agreed to set gravitational potential
energy equal to 0 when M and m are infinitely far apart. The further apart two
masses are, the greater the gravitational potential energy (remember, the higher
you lift something, the further it is from the center of the earth, and the more
gravitational energy it acquires). So, the most gravitational energy a mass m can
have is 0 Joules, which happens when it is infinitely far away from M. Therefore,
any lesser separation means that the gravitational potential energy must be
negative, which it is in our expression!!!
(4) You are probably familiar with the expression of gravitational potential
energy as mgh, where h is the height above the surface of the earth that a mass m
has been lifted. This expression does represent force (mg) times distance (h). It
also represents the change in the gravitational potential energy, because m has
been moved from one position to another. So,





Ug = mgh
(1)
According to our expression,


Ug = Ufinal - Uinitial = [-GMm/(R+h)] - [-GMm/R]
(2)
As an exercise, you can show that if h << R, then the right side of equation (2),
when simplified, will equal the right side of equation (1).
Note 1 : g = GM/R2
Note 2 : The denominator in the expression for Ug represents the distance
between the centers of m and M. At the surface of the earth, this distance equals
the radius of the earth.
Note 3 : If you substitute k for G, and q1 and q2 for M and m, the same handwaving argument as above (particularly steps 1, 2, and 3) should help you to
accept, by way of mathematical similarity, that electric potential energy is given
by (-kq1q2/R).