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 !
 

As in any discipline, there are many terms and expressions whose definitions are vital for an understanding of astronomy. Make use of the end-of-chapter reviews in the text, where many terms are highlighted. Also be aware of those terms specifically described in your class notes.

Distance Measures:     Be aware of how distances are defined, and the actual values of the most important distance, e.g., the Earth-Sun distance.

• An Astronomical Unit (AU) = the Earth-Sun distance.
• 1 AU = 150 x 10⁶ kilometers.
• Light (and radio waves) travels at 300,000 kilometers per second.
• A light year (LY) = the distance light travels in a year
• 1 LY = 6 x 10¹² miles = 3 x 10¹³ kilometers.
• The Moon is 1.3 light seconds from Earth.
• Light takes about 8 minutes to travel from the Sun to the Earth.
• The Solar System is about 11 light hours in diameter.
• The nearest star is 4.3 light years distant.

• Constellations mark specific locations on the sky, all parts of the sky are located in one of 88 constallations.
• Polaris is the "North Star", and marks the position on the sky of the Earth's rotation axis. Polaris is located in the constellation Ursa Minor, the "Little Dipper".
• There is no "South Star".
• The Big Dipper is located in the constellation Ursa Major.
• The "Summer Triangle" is made up of the stars Vega, Deneb and Altair.
• Orion is a prominent constellation in the winter sky.
• Sirius is the brightest star in the sky (excluding the Sun).

• North Celestial Pole, celestial equator, the meridian
• Altitude, azimuth, horizon, zenith
• Ecliptic, zodiac, zodical constellations, equinox and solstice points
• Right ascension and declination

• Q?   What are circumpolar constellations ?
• Q?   How does your latitude determine the "amount" of the celestial sphere visible from any specified location on Earth ?
• Q?   How does the celestial sphere change during the course of a night ?

• Define new and full Moon, first quarter and last quarter phases, waxing and waning gibbous phases.
• Know where the Moon is located in its orbit around the Earth at each lunar phase.
• Be aware of the location of the Moon on the sky at each phase (new, full, 1st quarter, 3rd quarter) with respect to sunset and sunrise. When does a full Moon rise ?   A new Moon ?
• What is the length of the lunar sidereal and synodic month ?   What is the difference between these two "months" ?

• Understand the differences between total, annular and partial solar eclipses.
• Visualize the shadow cast by the Earth & Moon, both the dark inner umbra and the brighter, outer penumbra.
• Understand what is meant by a total and partial lunar eclipse.
• Review when solar and lunar eclipses occur. What is the appropriate lunar phases during which a solar or lunar eclipse occurs ?

• Retrograde motion
• Epicycles and deferents
• The geocentric universe model
• The heliocentric universe model
• Orbits of the inferior planets (name them)
• Orbits of the superior planets (name them)
• Opposition
• Superior and inferior conjunction

• #1 - Law of ellipses: Orbits are in general shaped like ellipses.
• #2 - Law of equal areas
• #3 - The "harmonic" law - P² ~ a³, or in words, the square of the period of a planet's orbit around its Sun, is related to the cube of its average distance from the Sun.

• #1 - the inertial law
• #2 - the force law:   F = m x a
• #3 - the reaction law
• The Law of Gravity - the gravitational force between 2 objects is related to the product of the masses of the objects divided by the square of the distance between the objects. The law of gravity is an example of an inverse square law.

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   =   the distance between peaks (crests) of a wave
• amplitude   =   the intensity or height of a wave
• frequency   =   the number of waves per second
• period   =   the 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.
• Understand what is meant by a blackbody radiation curve.
• Temperatures in astrophysics are measured on the Kelvin scale. The Kelvin temperature scale = degrees Celsius + 273. Be aware of the temperature in Kelvins of important phenomena: for example, water freezes at 273 K.
• 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. How are emission or absorption lines produced ?
  • A continuous spectrum
  • Am emission line spectrum
  • An absorption line spectrum
  • A continuous spectrum with absorption lines

• 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 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.

• 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 during the course of a night as seen from Denton ?

• causes us to see different parts of the sky during the year. (for example, 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 we experience ?
• 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's daily appears in the sky during course of a year, at any particular place on the Earth.

• causes the monthly lunar phase cycle.
• results in an angular speed of the Moon against the background stars of about 0.5° per hour, or about 13° per day.
• occurs in an eastward direction around the Earth (counterclockwise when viewed from "above").

• Understand why and how the different phases occur (be able to draw a diagram to explain it).
• Be aware of the rising and 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 sees 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 (counterclockwise) 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
• Aristarchus
• Ptolemy
• Copernicus
• Galileo
• Brahe
• Kepler
• Newton

• Q?   What was wrong with Copernicus' basic model ?
• Q?   What are the elements of the Copernican Principle ?
• Review how advances in technology help foment the Copernican Revolution in the 1600s ?
• Q?   What specific discoveries of Galileo provided support for the heliocentric model ?
• Q?   Why was Kepler's work relevant to the adoption of the heliocentric model ?

• 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 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.

• 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.
• The 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 red shift and those which produce a blue shift.
• 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 ?

• 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.

• Q?   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", 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.

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:
(3)	Gravitational Force:			(4)	Newton's 2nd Law:

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 .

Be cognizant of the angular sizes of typical astronomical objects, and how to estimate the angular size of an object in the sky.

• 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 ?

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.

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 = the mass of that object, and a = the acceleration of the 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 ?

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 mass of an o bject is increased ?
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

Speed of light (or any radiation): is designatd "c"   =   wavelength x frequency of that light.
Note that the wavelength and frequency of EM radiation can vary but their product must equal 300,000 km/sec.

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) is proportional to 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 the photon's frequency. E   =   h   x   n

---