Waves and Wave Motions:
Light and other forms of radiation can be defined in terms of waves. Understand these terms and how they relate.
- wavelength - distance between peaks (crests) of a wave
- amplitude - intensity or height of a wave
- frequency - number of waves per second
- period - time between successive wave crests.
- Know the definition of the electromagnetic spectrum.
- Know the components of the spectrum and how they are ordered: gamma rays, X-rays, visible light, ultraviolet light, infrared light, radio waves, in order of increasing wavelength.
- High energy radiation means: small wavelengths, high frequency, and "blue" color.
- Low energy radiation means: large wavelengths, low frequency, and "red" color.
- Know the definition of the electromagnetic spectrum.
- Know the components of the spectrum and how they are ordered: gamma rays, X-rays, visible light, ultraviolet light, infrared light, radio waves, in order of increasing wavelength.
- High energy radiation means: small wavelengths, high frequency, and "blue" color.
- Low energy radiation means: large wavelengths, low frequency, and "red" color.
- Understand what is meant by a blackbody radiation curve.
- Temperatures in astrophysics are measured on the Kelvin scale. Kelvin temperature scale = degrees Celsius + 273.
- Wien's law - relates the peak of a blackbody spectrum to an object's temperature.
- Stefan's law - relates the total energy emitted by an object to its temperature.
- Doppler effect - relates the shift in the wavelength of spectral features to the line-of-sight velocity of an extraterretrial object. Know what a "spectral feature" is. Review how the amount of any shift is related to that velocity. What's the difference between a blueshift and a redshift ?
- 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
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 ?
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.
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
Earth's daily rotation :
- is responsible for the day/night cycle.
- is in the direction from WEST to EAST, which causes objects to rise in the EAST and set in the WEST.
- be able to visualize/describe the daily motions of the stars, sun, and moon across the sky, as seen at different latitudes on earth.
- Q? Where on earth do the stars travel parallel to the horizon during the day/night? Perpendicular to the horizon? How do stars move across the sky in Denton ?
- causes us to see different parts of the sky during the year. (e.g., the "Summer triangle" is not overhead at night during the winter months).
- the sun to appear to travel on the imaginary circle called the ecliptic.
- Q? If the earth did not rotate, would the sun still travel along the ecliptic?
- Q? If the Earth rotated once per revolution about the Sun, what would an observer see ?
- Be able to visualize the celestial equator and ecliptic on the sky.
- the seasons
- the sun's rising/setting position to "move" along the horizon during the year.
- Be able to describe how the sun appears in the sky during the year, at any particular place on the earth.
- causes the monthly lunar phase cycle.
- results in an angular speed against the background stars of 0.5° per hour, or about 13° per day.
- occurs in an eastward direction around the Earth (counterclockwise when viewed from "above").
- Understand exactly why and how the different phases occur (understand how to draw a diagram to explain it).
- Develop a rough idea of the rising/setting times of various lunar phases.
- Q? Does a waxing crescent moon rise earlier or later than the new moon? When does the new moon rise? When is the full moon on the meridian?
- The Moon rotates once per orbit about the Earth.
- causes Earth-bound observers to always see same side of the Moon.
- Understand their basic cause.
- Be able to sketch or label a diagram of an eclipse.
- Understand why everybody on the night side of the Earth can witness a lunar eclipse, but only a very small fraction of Earth's surface can see a solar eclipse.
- Why are total solar eclipses rare for any given location on Earth ?
- Q? Why doesn't a solar eclipse occur every time there is a new moon (in other words, every month) ?
- Q? What types of eclipses would occur if the Moon was located a few times further from the Earth than its current distance ? A few times closer ?
- All planets orbit eastward around the Sun, as viewed from above.
- The further from the sun, the slower each planet's angular speed across the sky.
- Using a solar system diagram, review the difference between inferior and superior planets, and how their position with respect to Earth, defines where and when each is visible to an Earth-bound observer.
- Understand what causes the retrograde motion of a planet against the background stars.
- Understand the basic differences between the geocentric and heliocentric models for the solar system, especially how retrograde motion is explained in each model.
- Be able to explain how/why some models predicted stellar parallax, and others didn't. In general, if the earth moves, then parallax is predicted; if the earth is stationary, no parallax.
- Understand why Venus goes through phases when viewed through a telescope.
- Q? Does Mercury go through phases also, as seen from the Earth? ANSWER -- yes! (understand why).
- Aristotle
- Erathosenes
- Ptolemy
- Copernicus
- Galileo
- Brahe
- Kepler
- Newton
- Q? What was wrong with Copernicus' basic model ?
- Q? What were the elements of the Copernican Principle ?
- Q? How did technological advances abet the Copernican Revolution ?
- Q? What specific discoveries of Galileo provided support for the heliocentric model ?
- Q? Why was Kepler's work relevant ?
- Understand what is meant by each of Newton's laws of motion.
- Understand what would happen to a moving object if an applied gravitational force is magically turned-off.
- Understand why the acceleration of a pebble and a boulder falling from the same height above the Earth are identical, yet the gravitational force that the Earth exerts on each of them is different.
- Understand why the force exerted on the above pebble BY the earth is exactly equal (but opposite in direction) to the force exerted ON the earth BY the pebble.
- Understand why the Moon does not collide with Earth, even though the Earth's gravitational force tends to pull the moon directly in towards the Earth.
- Understand why the Moon orbits the Earth, rather than the Earth orbiting the Moon. (But WHY is this the case, if the Moon pulls just as hard on the Earth as the earth pulls on the moon?)
- Understand why planets have longer orbital periods, the further they are from the Sun. (This fact is expressed by Kepler's 3rd law, and explained by the law of gravity.)
- Electromagnetic radiation is the means by which energy (and information) is transmitted through space.
- Radiation travels in the form of waves.
- Understand the concept of a wave and how waves are described in terms of their length, frequency, period, and height.
- Understand the difference between electromagnetic waves which do not require a medium in which to propagate, and sound waves, which do.
- The electromagnetic spectrum runs from high-frequency, short wavelength, high energy gamma rays to low-frequency, long-wavelength, low energy radio waves.
- Understand why only specific types of radiation can pass through the Earth's atmosphere and be detected at the earth's surface. Also review which forms of radiation can reach the Earth's surface.
- Remember that ALL forms of electromagnetic radiation travel at the exact same speed, 3 x 108 meters per second. This means that a long-wavelength signal such as radio waves travel at the same speed as a short-wavelength signal, such as X-rays.
- Understand what is meant by the spectrum emitted by an object.
- Be able to label a sketch of a spectrum, and understand what is displayed in such a sketch. What is plotted along the X-axis and along the Y-axis ?
- Review the concept of temperature. The temperature of an object measures the amount of microscopic motion within the object.
- What is blackbody radiation ? Know that the radiation emitted by a blackbody is described by a blackbody curve. Be able to plot a blackbody curve. What is another name for this curve ?
- Understand how the temperature of an object is related to its blackbody emission curve. Objects at at given temperature emit radiation at a range of wavelengths.
These "laws" are statements of physical principles which aid in the interpretation of extraterrestrial objects. Be cognizant of what each law tells us about objects in space.
- Stefan's law: hotter objects emit more energy. The rate of energy emission depends on temperature to the 4th power.
- Wien's law: the wavelength of peak emission is inversely proportional to temperature-- cooler objects have peak wavelengths that are smaller. Think about how this concept relates to the appearance of an object as its temperature is altered.
- Doppler effect: Motion along the line-of-sight to an object alters the wavelength or frequency of its emitted radiation. Understand the conditions which produce a redshift and those which produce a blueshift.
- Visualize how each of these "laws" affects the spectrum of a object. What happens when (a) the temperature is increased or decreased, (b) the energy output increases or decreases, (c) the object's velocity changes ?
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.
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.
- 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", i.e., 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.
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) | Centripedal force: |  |
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| (3) | Gravitational Force: |  |
(4) | Newton's 2nd Law: |  |
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| (5) | Kepler's 3rd Law: |  |
(6) | Wave equation: | wavelength × frequency = wave speed |
Scientific Notation & Orders-of-Magnitude:
Scientific notation is a set of rules for expressing very large and very small numbers. Use the handout on this webpage to review this notation and be able to translate a number into its "English" eqivalent. Example: 1 billion = 109. An "order-of-magnitude" refers to one unit in the exponent.
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 .
- The Moon and Sun extend about 0.5°.
- A typical constellation is several degrees across
- Planets typically are observed to extend a few arcseconds up to about 50 arcseconds on the sky. Q? Can you see this with your eye ?
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.
Ellipses: Ellipses are geometric figures which can be described as
"flattened" circles. Planetary orbits trace ellipses. Know what the eccentricity of
an ellipse measures (for a circle, e = 0). Be able to draw an ellipse with a planet
and the Sun properly oriented.
Q?: The more "squashed" (flattened) an ellipse, the closer
the value of eccentricity is to _______ ?
Understand how to describe forces:
- Any and all forces can be described by Newton's Second Law:
F = m × a
where F = the force exterted ON an object, m = mass of an object, a = acceleration of an object, due to application of a force. - The force due to gravity is expressed:
Know what the symbols "m" and "r" mean in different situations.
Q? How does the force of gravity change if your distance from a massive object doubles ? triples ? - A force that causes an object to execute circular motion (i.e., force
of gravity, which causes a planet to move within a circular orbit):
where F = the force causing the circular motion, m = the mass of the object that is in circular motion, r = the radius of circular motion, v = the speed of an object along its circular path.
Escape velocity: Defined as the velocity needed to escape the gravitational pull of a planet or other massive object.
Q? How does the escape velocity change if the radius of an object is increased while the mass remains constant ?
Properties of Waves:
- wavelength ( l ) X frequency ( n ) = wave speed
- frequency = 1 / wave period
Note that the wavelength and frequency can vary but must = 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 |