In Fall 2010 I taught, for the first time, a new astronomy course called "The Discovery of Galaxies." This is a course intended for non-science majors. The course focuses on the historical development of idea about the place of our solar system within the larger universe of stars, galaxies, etc. We begin with the two sphere model of the Ancient Greeks in which the Earth was thought to sit at the center of a spherical surface, while the stars sat on this surface and rotated around the Earth once each day. We discussed ancient theories about the Milky Way and nebulae, then made our way through history examining important arguments as we went. We looked at various methods that were used to estimate the distances to stars, how the Copernican Revolution ultimately led to the conception that the Sun was one of an infinite number of stars in an endless universe, and how the invention of the telescope revealed the nature of the Milky Way and the nebulae.
Much of this first part of the course deals with very speculative attempts to understand the universe and our place in it. The middle section of the course introduces important new techniques that made stellar astronomy much more quantitative and reliable. The advent of photography, spectroscopy, and photometry radically changed the nature of astronomy and put the study of stars and nebulae in the forefront of the field. The creation of well-equipped and well-located new observatories led to tremendous advances, especially in the US.
The final part of the class dealt with the discoveries of the 20th century. These include Shapley's Big Galaxy, Hubble's discovery of Cepheid variables in the Andromeda Nebula (now the Andromeda Galaxy), the discovery of the expansion of the universe, and the eventual triumph of Big Bang cosmology.
Throughout the course the focus is on understanding the arguments used by astronomers to reach conclusions about the nature of the universe and our place within it. In many cases these arguments are faulty, or they were based on bad data, or they include hidden assumptions that turn out to be incorrect. This is part of the way science works - we slowly sift out the errors and try to keep the good stuff. My goal is to bring the excitement of real science to my students while at the same time giving them an honest view of what science is and how it works.
In order to best show my students how scientific theories are evaluated, and how theories and data are used in conjunction to reach conclusions about nature, I have the students spend their class time working through these arguments on their own. They work in small groups to complete worksheets that guide them through important arguments. In many cases they are assisted by working with computer simulations that I have created for this purpose. Anyone interested in my curricular materials can find more here:
Scale of the Universe Page
I have also written my own textbook for this course (the result of a year-long sabbatical), but the book has not yet been published.
I was generally satisfied with how the course went. I have not taught the course twice, and also taught an honors version of the course. Students seem pretty happy with the course, although they find it challenging. The mathematical level seems appropriate for my students (we use logarithms for the stellar magnitude scale, some trig for parallax, a fair bit of basic algebra, etc), but might be a little high for less selective schools (or a bit low if the audience is mostly science majors). I'm very happy with the way I am teaching the course. The activities are, I think, the most effective way for students to learn this material. They have to work through this stuff themselves. Group dynamics aren't always great, but when the groups are working well this teaching method is very effective.
For the future I would like to develop some large scale projects for the course, thus allowing me to move away from relying on exams for evaluating the students. I already have them do extensive essay writing. It makes the class grading-intensive, but I think the students get a lot out of it.
I'm hoping to publish some of the activities in The Physics Teacher in coming years, but anyone interested need not wait for that. Just look at the materials on the web site linked above.
Showing posts with label astronomy. Show all posts
Showing posts with label astronomy. Show all posts
Sunday, March 4, 2012
Monday, June 22, 2009
AST 120: The Copernican Revolution
AST 120 is a course on the Copernican Revolution originally created by Paul Wallace. I took over teaching the course in Fall 2008 and taught it again in Spring 2009. During the Fall 2008 semester I developed a series of active-learning curricular materials for this course, which I will describe here.
The materials I developed consist of 25 activity worksheets designed to be completed by groups of 4 students during a 75 minute class period (with some time left over for lecture/discussion). The worksheets guide the students through an exploration of astronomical phenomena (mostly naked-eye observations of stars and planets) as well a variety of theories that have been proposed to explain these phenomena. Most of the activities require the use of computer simulations for making simulated observations or visualizing theories of planetary motion. I have created 53 open-source computer simulations for use with these activities. I have also adapted 10 laboratory exercises, originally developed by Paul Wallace and designed to be completed in a 120 minute lab period, to include more active-learning through the use of computer simulations. Finally, I have created two major project assignments that are designed to assess student understanding of the course material.
The first sequence of activities focuses on observing the motion of the sun, moon, stars, and planets. Most of this is done using Starry Night, a commercial planetarium program. (Some, but I don't think all, of the activities could be done using open-source software like Celestia and Stellarium.) Students observe the (apparent) daily motion of the sun and stars, the monthly motion of the moon, the annual motion of the sun, the synodic and zodiacal periods of the planets, and the precession of the equinoxes. They discover that "signs" of the zodiac are way off from their standard astrological definitions (which were correct when they were formulated about 200 BC, but precession has changed things). Students also complete labs in which they use a celestial globe, observe a simulated gnomon (sundial), study the phases of the moon and make their own moon observations, and learn about the constellations during a night lab.
The second sequence of activities deals with the astronomical theories of the Ancient Greeks (Eudoxus, Aristotle, Apollonius, Hipparchos, Ptolemy). Computer simulations are used to help students visualize the geometrical constructions used in these theories and also to show what these theories predict for the motions of the planets as seen from Earth. The simulations help students see the real power of the Ancient Greek theories (even though we now know these theories are incorrect). For example, the theory of Eudoxus could produce retrograde motion which is the most striking feature of the motion of the planets. The theory of Ptolemy could produce retrograde motion AND properly correlate that motion with changes in the brightness of the planet. Active engagement with these Ancient Greek theories shows how scientific theories evolve and are replaced by theories with greater explanatory power. A lab in this section allows students to recreate the observations and calculations used by Eratosthenes to determine the diameter of Earth.
The next sequence deals with the revolutionary heliostatic theory of Copernicus. Again simulations are used to help students visualize the theories and how the relate to observed motions of the planets. With the aid of the simulations students can determine the orbital periods of the planets and measure the size of the planetary orbits (relative to the size of Earth's orbit). They also discover the the Copernican theory predicts parallax effects that are not observed, and learn that this problem can be resolved if the stars are MUCH farther away from the sun than Earth is.
After Copernicus we briefly study the work of Tycho Brahe. Students learn how to use parallax measurements to determine the distance to astronomical objects. They use this method (along with simulated observations in Starry Night) to find the distance of the moon, sun, and Halley's comet from Earth. They also use a computer simulation to examine the relationship between the astronomical systems of Ptolemy, Copernicus, and Tycho.
Next is a sequence of activities on Kepler. Students use computer simulations to explore Kepler's idea that the planets were confined to spheres nested between Platonic solids. They also examine simulations that illustrate the development of Kepler's theories on planetary motion. They construct an orbit for Earth using a compass, straight edge, and three observations of Mars. Finally, they complete a lab exercise in which they apply Kepler's three laws of planetary motion to a variety of problems.
A sequence of activities on Galileo's telescope observations and physical theories is next. Students use computer simulations to reproduce Galileo's measurement of the height of mountains on the moon and see how Galileo's observation of the phases of Venus refuted the standard Ptolemaic theory. Students use a computer simulation of Galileo's sunspot observations to determine the rotational speed of the sun, and also apply Kepler's laws to the motion of Jupiter's moons to find the mass of Jupiter relative to that of the sun. Simulations and experiments are used to investigate medieval ideas about motion as well as Galileo's ideas about falling bodies and neutral motions (close to the modern concept of inertial motion).
The final sequence of activities deals with the theories in Newton's Principia. Students use simulations and mini-experiments to learn about Newton's laws of motion. More simulations illustrate how the right centripetal acceleration can produce a circular orbit, and how an inverse square centripetal force can reproduce all three of Kepler's laws. Finally, they examine Newton's argument that projectile motion on Earth is qualitatively the same as the motion of the moon, illustrating the universal nature of gravity.
For the first project students are given observational data for a fictional solar system. From this data they must construct both Ptolemaic and Copernican orbits for their home planet/star, as well as for two other planets (one inferior, one superior). After calculating the orbital parameters they must draw diagrams representing the orbits for each of the two systems. This project assesses student conceptual understanding of these two astronomical systems, as well as factual knowledge about astronomical terms and calculation methods. In the second project students must write a paper defending the Copernican system against an attack from a fictional Aristotelian (I wrote the attack myself, but it I used arguments derived from 17th century primary sources, mainly Galileo's Dialogo). This project assesses student understanding of Galilean/Newtonian physics and how these physical concepts led to the overthrow of the old Aristotelian/Ptolemaic system and justified the acceptance of the Copernican/Keplerian system.
Student response to this course has been very good. The students seem to enjoy the activities and they like working with the computer simulations (especially Starry Night, but they like the simulations I created as well). Overall I have been very pleased with the way this course has gone and I plan to continue teaching it this way indefinitely.
Paul Wallace has written a textbook for this course which I have modified. We plan to publish the textbook in a few years (it's not quite publication-ready at this point, although the students have been pretty happy with it).
Anyone interested in this course and the simulations and curricular materials I use should go to http://facultyweb.berry.edu/ttimberlake/copernican/ where the open-source simulations (but not Starry Night) and activity/lab worksheets can be downloaded for free.
The materials I developed consist of 25 activity worksheets designed to be completed by groups of 4 students during a 75 minute class period (with some time left over for lecture/discussion). The worksheets guide the students through an exploration of astronomical phenomena (mostly naked-eye observations of stars and planets) as well a variety of theories that have been proposed to explain these phenomena. Most of the activities require the use of computer simulations for making simulated observations or visualizing theories of planetary motion. I have created 53 open-source computer simulations for use with these activities. I have also adapted 10 laboratory exercises, originally developed by Paul Wallace and designed to be completed in a 120 minute lab period, to include more active-learning through the use of computer simulations. Finally, I have created two major project assignments that are designed to assess student understanding of the course material.
The first sequence of activities focuses on observing the motion of the sun, moon, stars, and planets. Most of this is done using Starry Night, a commercial planetarium program. (Some, but I don't think all, of the activities could be done using open-source software like Celestia and Stellarium.) Students observe the (apparent) daily motion of the sun and stars, the monthly motion of the moon, the annual motion of the sun, the synodic and zodiacal periods of the planets, and the precession of the equinoxes. They discover that "signs" of the zodiac are way off from their standard astrological definitions (which were correct when they were formulated about 200 BC, but precession has changed things). Students also complete labs in which they use a celestial globe, observe a simulated gnomon (sundial), study the phases of the moon and make their own moon observations, and learn about the constellations during a night lab.
The second sequence of activities deals with the astronomical theories of the Ancient Greeks (Eudoxus, Aristotle, Apollonius, Hipparchos, Ptolemy). Computer simulations are used to help students visualize the geometrical constructions used in these theories and also to show what these theories predict for the motions of the planets as seen from Earth. The simulations help students see the real power of the Ancient Greek theories (even though we now know these theories are incorrect). For example, the theory of Eudoxus could produce retrograde motion which is the most striking feature of the motion of the planets. The theory of Ptolemy could produce retrograde motion AND properly correlate that motion with changes in the brightness of the planet. Active engagement with these Ancient Greek theories shows how scientific theories evolve and are replaced by theories with greater explanatory power. A lab in this section allows students to recreate the observations and calculations used by Eratosthenes to determine the diameter of Earth.
The next sequence deals with the revolutionary heliostatic theory of Copernicus. Again simulations are used to help students visualize the theories and how the relate to observed motions of the planets. With the aid of the simulations students can determine the orbital periods of the planets and measure the size of the planetary orbits (relative to the size of Earth's orbit). They also discover the the Copernican theory predicts parallax effects that are not observed, and learn that this problem can be resolved if the stars are MUCH farther away from the sun than Earth is.
After Copernicus we briefly study the work of Tycho Brahe. Students learn how to use parallax measurements to determine the distance to astronomical objects. They use this method (along with simulated observations in Starry Night) to find the distance of the moon, sun, and Halley's comet from Earth. They also use a computer simulation to examine the relationship between the astronomical systems of Ptolemy, Copernicus, and Tycho.
Next is a sequence of activities on Kepler. Students use computer simulations to explore Kepler's idea that the planets were confined to spheres nested between Platonic solids. They also examine simulations that illustrate the development of Kepler's theories on planetary motion. They construct an orbit for Earth using a compass, straight edge, and three observations of Mars. Finally, they complete a lab exercise in which they apply Kepler's three laws of planetary motion to a variety of problems.
A sequence of activities on Galileo's telescope observations and physical theories is next. Students use computer simulations to reproduce Galileo's measurement of the height of mountains on the moon and see how Galileo's observation of the phases of Venus refuted the standard Ptolemaic theory. Students use a computer simulation of Galileo's sunspot observations to determine the rotational speed of the sun, and also apply Kepler's laws to the motion of Jupiter's moons to find the mass of Jupiter relative to that of the sun. Simulations and experiments are used to investigate medieval ideas about motion as well as Galileo's ideas about falling bodies and neutral motions (close to the modern concept of inertial motion).
The final sequence of activities deals with the theories in Newton's Principia. Students use simulations and mini-experiments to learn about Newton's laws of motion. More simulations illustrate how the right centripetal acceleration can produce a circular orbit, and how an inverse square centripetal force can reproduce all three of Kepler's laws. Finally, they examine Newton's argument that projectile motion on Earth is qualitatively the same as the motion of the moon, illustrating the universal nature of gravity.
For the first project students are given observational data for a fictional solar system. From this data they must construct both Ptolemaic and Copernican orbits for their home planet/star, as well as for two other planets (one inferior, one superior). After calculating the orbital parameters they must draw diagrams representing the orbits for each of the two systems. This project assesses student conceptual understanding of these two astronomical systems, as well as factual knowledge about astronomical terms and calculation methods. In the second project students must write a paper defending the Copernican system against an attack from a fictional Aristotelian (I wrote the attack myself, but it I used arguments derived from 17th century primary sources, mainly Galileo's Dialogo). This project assesses student understanding of Galilean/Newtonian physics and how these physical concepts led to the overthrow of the old Aristotelian/Ptolemaic system and justified the acceptance of the Copernican/Keplerian system.
Student response to this course has been very good. The students seem to enjoy the activities and they like working with the computer simulations (especially Starry Night, but they like the simulations I created as well). Overall I have been very pleased with the way this course has gone and I plan to continue teaching it this way indefinitely.
Paul Wallace has written a textbook for this course which I have modified. We plan to publish the textbook in a few years (it's not quite publication-ready at this point, although the students have been pretty happy with it).
Anyone interested in this course and the simulations and curricular materials I use should go to http://facultyweb.berry.edu/ttimberlake/copernican/ where the open-source simulations (but not Starry Night) and activity/lab worksheets can be downloaded for free.
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