PHYSICS 1060       Dr Mike Fanelli
Spring   2005
EXAM 2     REVIEW SHEET
This review covers these topics:
Atoms & Molecules, Spectra of Celestial
Objects, Telescopes, Light Detectors, Space Astronomy,
Experimental Astronomy, The Sun, Solar Activity & Solar Power,
Distances and Motions of Stars, Properties of Stars,
The HR Diagram
Use these pages as a study guide - in other words,
as a list of terms, facts, concepts, and relationships that you
will want to understand for the exams. This review is NOT
intended as a synopis of the class notes or textbook. Rather,
it mixes some factual information with lists of items that students
should review. Sample questions, some given with answers, some
without, are included. These are indicated with a preceding
"Q?" symbol.
I have attempted to include just about every topic and concept
that might show up in an exam questions, but this review sheet is
not guaranteed to be comprehensive - exams cover the text and
notes !
 
A.    
DEFINITIONS & FACTS
Spectra:
- Be able to visualize the spectrum of an object; use the figures in the text.
- Relate the patterns within an observed spectrum to the object producing
the spectra.
- Define and understand how each of the following types of spectra are produced.
Also, how are emission or absorption lines produced ?
- continuous spectrum
- emission line spectrum
- absorption line spectrum
Atoms and Atomic Structure:
Understand the internal structure of atoms. Each chemical element is defined by
the number of protons in the nucleus of an atom of that element.
- Identify protons, neutrons and electrons. Q? Which are electrically
charges, which are not ?
- Know the difference between protons, neutrons and electrons in terms of
their relative masses.
- Where are these various particles located within an atom ?
- Be aware of the "atomic number", i.e., the number of protons in some common
elements. Hydrogen atoms have 1 proton, uranium atoms 92. All other
naturally occuring elements possess between 1 and 92 protons. Look at
the Periodic Table of the Elements given in the Appendix of the text.
- Know the definition of an isotope and the periodic table.
- Electrons "orbit" an atomic nucleus in various energy levels. Understand
the meaning of the term "energy level".
- Know what "ground state" implies with respect to electron energy levels
within atoms.
- Understand what "ionized" implies-- the removal of 1 or more electrons
from an atom.
- Atoms can combine to form molecules. What are some common, simple molecules ?
Molecules & Beyond
Contrast atoms with molecules.
- Molecules are composed of 2+ atoms linked via the sharing of electrons.
- Know the chemical composition of some simple molecules, e.g., water,
carbon dioxide
- Be aware of the added complexity concerning energy levels in molecules.
In addition to their electron levels, molecules also rotate and
vibrate.
Information from Spectra:
Review the types of information that can be gleaned from spectra of
astronomical objects, the physical principles involved, and how that information
is extracted from the spectra.
- continuous spectra - temperature, energy rate
- emission line spectra - composition, velocity, rotation, temperature
- absorption line spectra - composition, velocity, rotation
- spectral measurements - wavelength, strength, width & wavelength shift of spectral lines
Telescopes:
- Review the operating principles of both major types of telescope:
- Reflectors use curved mirrors to collect & focus light
and can be manufactured large. If the mirror is constructed incorrectly, it can suffer from spherical abberation.
- Refractors use curves lenses to focus light, and are
limited to sizes less than about 1 meter. Lenses, made of glass, suffer
chromatic abberation -- the focal point of the lens is
different for different wavelengths of light.
- Know the advantages and disadvantages to each basic telescope type.
- Telescope "size" is defined by the diameter of the objective:
either a lens or a mirror.
- Know the meaning of light-gathering power and resolving power.
- All major research telescopes are of the reflecting type. Be aware of the different designs for these telescopes. How do astronomers get the
light "out" of the telescope to study and make a record of it ?
Light Detectors:
- Know the basic methods astronomers employ to make astronomical
observations.
- Images of the sky are constructed using a variety of technologies.
Photographs are chemical recorders of information, CCD camers
record light digitally in electronic form. Which is used more
commonly today ?
- Astronomers use spectrographs to split the light of an object up
into its component colors.
- Spectrograms provide information on a celestial object's temperature,
composition, line-of-sight velocity, density, and luminosity. How ?
Experimental Astronomy
- Space-based telescopes are required to observe in many parts
of the spectrum. Understand how the Earth's atmosphere interferes with astronomical observations from the Earth's surface.
- Understand the advantages and disadvantages of space-based telescopes vs those on the ground.
- Radio telescopes use large dish antennae to record radio waves from
astronomical sources.
- X-rays and gamma-rays are much harder to collect and focus than optical
light. Astronomers have constructed special devices to capture this type of radiation.
Structure of the Sun (& Stars):
- What is a star ?   Review the basic definition of a star.
- Be aware of the the values of important parameters which
describe the Sun.
- Radius:   ~700,000 km   =   ~ 110 Earth radii
- Mass:   2 x 1030 kilograms   = ~ 332,000
Earth masses.
- Surface temperature:   ~ 5800 K.
- Rotation rate:   25-30 days, depending on latitude.
- Review the overall structure of the Sun, both the interior
zones, and the regions which define the solar atmosphere.
Be able to label a diagram with these zones.
- Be cognizant of the differences between the solar interior
zones: the core, the radiation zone,
convective zone, and photosphere. What defines each
zone ?
- What is granulation ?
- Understand the basic attributes and physical properties of the solar
atmosphere. What are the differences between the photosphere,
chromosphere, and corona ?
- Understand the temperature and pressure profiles of the solar
interior-- from 15 million K at the center, to ~6000 K at the surface.
- Be aware of the Sun's composition - the chemical makeup of the
solar photosphere.
Solar Activity:
- Understand what is meant by solar activity. Solar activity
manifests itself through a variety of phenomena: sunspots, prominences,
flares, coronal mass ejections. Describe and understand the difference
between these phenomena.
- Sunspots   How are they observed ?
- Prominences   Where are these seen on the Sun ?
- Flares  
- Coronal holes
- Active regions
- Know the basic phenomena associated with the solar activity
cycle. Sunspot counts (the number of spots recorded each day),
sunspot locations, the frequency and intensities of solar flares, etc
all increase and decrease during the 11-year cycle.
- What is the solar wind ? & How might this wind affect the Earth ?
Solar Power:
- The Sun produces energy (light) through the process of nuclear
fusion. Be aware of which substance(s) are being "fused", and
be familiar with the steps in the fusion process.
- Define the proton-proton chain
- Q:   Where does fusion occur within the Sun ?
- Understand the difference between atomic particles important to the
fusion process:   protons, neutrons, positrons, electrons, neutrinos,
gamma rays
- Neutrinos, subatomic particles produced in fusion reactions, radiate
from the Sun and pass right through the Earth. Understand how the
technically difficult problem of counting solar neutrinos resulted
in an "undercount" compared to the standard solar model .
Distances and Motions of Stars:
- Know the meaning of the term stellar parallax. How is this
particular "motion" of stars in the sky used to find the distances to
stars ?
- Understand the term proper motion.
- Proper motion is the motion of stars across the sky.
- This motion is measured in units of arcseconds per year, i.e., a rate
expressed in angular units, not linear units.
- Nearby stars and fast-moving stars will exhibit larger proper motions.
- Understand what a star's space velocity measures.
Properties of Stars:
- Review the defintion and use of the magnitude scale (see also Part
C in this review).
Magnitudes measure the brightnesses of stars, both their apparent
brightness AND their true brightness.
The true energy output of a star is known as its absolute
magntiude and also its luminosity.
- Review the stellar spectral classification system devised by
astronomers.
- Spectral classes are assigned letters:
O,B,A,F,G,K,M
- How are spectral types assigned ?   What information is used for
this purpose ?
- What property of a star defines its spectral type ?
- How is spectral type related to the surface temperature of stars ?
- How is a star's color related to surface temperature ?
- Luminosity class is a second type of stellar classification -
defining the range in stellar brightnesses. Know the difference
between a dwarf, giant and supergiant star. Which is brighter ? Why ?
- Be familiar with the range of stellar properties:
- Masses: from 0.08 M(sun), which are the faintest M dwarfs,
to 100 M(sun), which are very luminous O stars.
- Surface Temperature: from 50,000 K (O stars) to 3000 K
(M dwarfs).
- Size (radii): from ~500 times the Sun's radius (supergiant
stars) to 0.1 R(sun) (M dwarfs).
- Luminosities: 105 times L(sun) for O stars, to
10-4 L(sun) for M dwarfs.
- What is the composition of typical stars ?   Does this vary among
stars ?
Herzsprung - Russell Diagrams:
- Understand the appearance and purpose of an HR diagram. What
stellar properties are plotted on the HR diagram ?   What units
are used ?
- Know the principal regions within the HR diagram: the main sequence,
giants, supergiant region, white dwarfs.
- Know which regions of the HR diagram are heavily populated with stars,
and which appear sparse.
- Know that the Sun is a dwarf star, spectral type G2, "located" on the
main sequence.
B.     CONCEPTS
Atomic Structure:
Be cognizant of the basic structure of an atom-- nucleus, electron "cloud",
energy levels. Be able to sketch and label the standard picture of an atom.
Review the basic process of how EM radiation interacts with atoms, how photons (particles of light) can be absorbed or emitted.
- Atoms have varying numbers of protons, electrons, and neutrons. Understand how the properties of an atom are defined by those
varying numbers
- The number of protons in an atomic nucleus determines the
type of element.
- The number of electrons determines the ionization state of an atom. How ?
- The number of neutrons determines the particular isotope
of that element.
- Understand and be able to describe the Bohr atomic model for hydrogen.
How does Bohr's initial idea differ from our modern view of atomic
structure ?
- Understand the energy level concept for how EM radiation (light, radio waves, X-rays) is emitted and absorbed by atoms & molecules.
- An electron "jumps" to an excited state when it absorbs a photon with exactly the right amount of energy. Understand physically what happens
in the atom when a photon is absorbed.
- An electron can be "de-excited" (drop down a level) by emitting a photon, releasing energy.
- Understand how the energy of an emitted or absorbed photon is defined by the difference in energy between two levels.
- Understand why each different element (hydrogen, helium, carbon, etc) has its own unique emission/absorption spectrum, and how that spectrum is related to its pattern of energy levels.
Molecules & The States of Matter
Understand the heirarchy of matter from atoms to molecules to solids, liquids and gases.
- How is matter constituted as the temperature changes ? What causes the
change in state as temperature changes ?
- Cold - atoms form molecules, molecules link up into solids & liquids
- Warm - some solids melt or evaporate into gases
- Hot - molecules split into their constitute atoms, solids melt, liquids evaporate
- Really hot - all molecules split apart, atoms begin to lose their electrons, matter becomes a plasma.
- Consider what states of matter might your find in different astronomical environments.
Information from Spectra:
- Understand how astronomers use the information in spectra to explore the properties of objects in space-- their temperature, radial motions,
rotation, chemical composition, etc.
- Many physical processes can cause spectral lines to be "broadened",
in other words, appear to the observer to be wider than normal. Be
cognizant of these processes, and how they affect the line width, via
the Doppler effect.
Telescopes & Detectors:
- Understand how light is collected and focused by telescopes.
Sketch the light "path", based on textbook illustrations.
- Understand why astronomical images are "blurred" by the atmosphere, and review some of the techniques used by astronomers
to compensate for this blurring.
- Q?   What is a digital image and
how does it differ from a photographic image ?
Experimental Astronomy
- Review the technique of interferometry. How does it help
improve astronomical observations ?
- Why are computers essential to modern astronomical research ?
- Understand the fundamental importance of observations over the entire
elecromagnetic spectrum. In the past 40 years, astronomers have moved from optical, then radio observations to the ability to explore the whole
spectrum.
Q?   How does radio and x-ray astronomy
complement optical observations ?
- Understand why radio telescopes are substantially larger
than telescopes which work in the optical part of the spectrum.
Structure of the Sun:
- Why is the Sun stable ?   What physical processes keep the Sun from collapsing under gravity or exploding due to its high temperature
and pressure interior ?
- Understand the physical concept of convection. How does it
apply to the Sun ?
- Understand why the corona of the Sun is hotter than the surface;
6000 K vs about 3,000,000 K. Astronomers believe that release of
magnetic energy at the base of the solar atmosphere accounts for the
heating of the corona.
- Review the reasons that solar eclipses provide unusual and scientifically useful observations of the solar atmosphere.
- How do astrophysicists explore the Sun ?   How is information gleaned about the solar interior and the solar atmosphere ?
- Helioseismology, a branch of solar physics, is the study of
surface patterns on the Sun. Review the basis for and the usefullness
of this subject. What exactly are the "patterns" visible on the Sun's
surface ?   How does helioseismology permit us a view into the
solar interior ?
- What is meant by the "Standard Solar Model" ?
Solar Activity:
- Why are sunspots dark compared to the surrounding solar disk ?
- Describe the source of the solar wind. How does material manage to
escape the powerful gravitational field of the Sun ?
- Review ideas for the origin of solar activity-- what drives these
phenomena ?   Most solar activity is powered by the tangling and
untangling of lines of magnetic force.
Solar Power
- Q?: Why does the fusion process require
high temperatures and pressures ?
- Q?: How does the fusion process produce
energy ?
ANS: The sum of the masses of 4
protons is greater than the mass of the helium nucleus into which those
4 protons fused. The excess mass is converted to energy, and emitted
in the form of gamma rays.
- Energy is produced in the Sun's core via nuclear fusion. How does that
energy "get out" to the surface and to us ?
- How do observations of solar neutrinos provide information about
reactions deep in the Sun ?
- Solar neutrinos are measured at "observatories" that are very different
than the traditional "telescope in a dome". Describe a solar neutrino
observatory and detail why they are differently-enabled.
- In the last few years, an explanation for the solar neutrino problem
appears to have been discovered. Define this "problem" and
describe the explanation ?
Distances and Motions of Stars:
- Understand why the pattern of stars in the night sky does not
change appreciably during human lifetimes, despite the fact that
most stars are moving through space at scores to hundreds of kilometers
per second.
- Visualize the motions of stars. Contrast motion across the sky with
motion along the line-of-sight to a star. How are these measured ?
How would these motions change if a star was moved closer/further from
Earth, all else being equal ?
Properties of Stars:
- Stars appear as unresolved points of light even in the largest
telescopes. How are stellar dimensions (sizes) determined ?
- The intensity of light from a source becomes fainter according to the
inverse-square rule. What does this mean, and why does light
fade in this manner ?
- The observed brightness of stars depends on their (a) true
brightness (luminosity) and (b) their distance to us. Observed brightnesses
of stars are measured using telescopes and CCD detectors. How are
a star's true brightness and distance determined ?
- What information can be obtained from stellar spectra, that can be
used in the classification process ?
Herzsprung - Russell Diagrams:
- Understand what is meant by a star's "location" in the HR diagram.
- Be cognizant of the significance of the main sequence.
- Understand why the HR diagram of nearby (to the Sun) stars is
populated with stars along the lower main sequence, while an
HR diagram of bright stars in the sky contains many giant and
supergiant stars.
- Classification of stars allows us to estimate their distance via the
concept of spectroscopic parallax. How does this work ?
- Interpretation of the HR diagram has resulted in major discoveries
related to stars.
- Which stars are most common in the nearby universe ?
- Which stars are the least common ?
- Which stars the hottest ?   coolest ?   most massive ?  
least massive ?
- Which properties of a star defines its location on the HR diagram ?
C.    
QUANTITATIVE RELATIONSHIPS
This section reviews specific quantitative (meaning mathematical) relations,
and how to interpret those relationships.
Some formulae:
(1) |
Small Angle formula:   |
true size = distance x angular size |
    |
(2) |
Wave equation: |
wavelength × frequency = wave speed |
    |
Angular size:   Understand the meaning of angular size and the
system of units used to express these quantities.
- Angular measure is used to define a distance along an arc.
- There are 360°, or 2 p radians, in the
circumference of a circle.
- 1° = 60 arcminutes; 1 arcminute = 60 arcseconds.
- The circumference of a circle = p x diameter or 2 x p x radius.
- The area of a circle is: p x radius 2
- The volume of a sphere is: 4/3 x p x radius 3 .
Angular Size and True Size:   Know that the true or physical size
of an object (Moon, Sun, building, tree, etc) is directly proportional to its angular size and the distance to the object.
  true size   ~   distance × (angular size in degrees /
57.3).
This relation is known as the small angle formula, and
allows the direct calculation of the size of an object if the distance is
known, or conversely, one can determine the distance to an object if its
true size is known. The small angle formula implies that the further
away that an object is located, the smaller its angular size
will be. If distance increases, then the angular size must
decrease.
Properties of Waves:
- wavelength ( l )   X   frequency
( n )   =   wave speed
- frequency   =   1 / wave period
Speed of light (or any radiation): is designatd "c"   =  
wavelength x frequency of that light.
Note that the wavelength and frequency can vary but their product must equal
300,000 km/sec, when multiplied together.
Radiation:
(1) |
wavelength × frequency = speed of the wave |
  -   the "wave" equation |
(2) |
wavelength of peak emission is ~ 1 / temperature |
  -   Wien's Law |
(3) |
E(total) ~ T4 |
  -   Stefan's Law |
(4) |
(shift in wavelength) ÷ wavelength   =   velocity
÷ speed of light |
  -   Doppler effect |
(5) |
Energy of a photon, E, equals Planck's constant times frequency.
E   =   h   x   n |
  |
Properties of Telescopes:
(1)   Light Gathering Power (LGP) of a telescope is proportional
to the area of the mirror.
       
LGP ~ D2, where D is the diameter of the mirror.
(2)   Resolving power of a telescope is proportional to the
diameter of the mirror and the
   
    wavelength of light being imaged.
The resolution (expressed in arcseconds) = 0.25 × wavelength (in microns)
÷ diameter (in meters).
Parallax & Distance
The distance to a star     =     1 ÷
its parallax,
with distance expressed in parsecs,
and parallax expressed in arcseconds.
Radius - Luminosity - Temperature relation.
These fundamental properties of a star are interrelated -
L   =   R2   ×   T4,
    expressed in solar units.
The Magnitude Scale
- Magnitudes measure the brightness or luminosity of celestial
objects.
- The magnitude scale is logarithmic, for example a
difference of 5 magnitudes represents a brightness (luminosity)
difference of 100, not 5.
- Brighter magnitudes are expressed with
smaller values, which is not a common-sense method.
For example, a star with m = 3, is brighter than one with
m = 6.
The difference between the observed (apparent) magitude of a star and
its true (absolute) magnitude depends on its distance:
(m - M)   =   5 × LOG ( distance ÷ 10 pc)