Dear Colleague,
Welcome to the Planet Finder lesson. This lesson illustrates how astronomers find extra-solar planets by the observing periodic variations in the Doppler shifts of the spectral lines of the star. The student can adjust the parameters defining the orbit and mass of the planet to fit data points representing observations of actual planetary systems.1
The lesson has three major learning goals for students:
1. to visualize and understand how the planetary orbit manifests itself in the observed Doppler velocity curve;
2. to understand how scientists determine properties of a model system by fitting a representation of the model to observed data; and
3. to understand how uncertainties in measurement determine the level of confidence of conclusions that can be drawn from the data.
Before undertaking this exercise, your students should already understand that one can measure the projected velocity of a star through Doppler shifts of its spectral lines. They also should have had some exposure to the qualitative properties of planetary orbits - in particular, they should understand that stars and planets orbit a common center of mass, so that the presence of a planet can be detected through the reflex motion of a star. They should also know that the speed of an orbiting body increases as the distance between the masses decreases, both among circular orbits and within an eccentric orbit.
This exercise is designed for collaborative learning. We think that students will learn more if they do it in groups of two or three, and we suggest that you encourage them to do so (but a student can do the exercise alone if s/he wishes).
However, some students may start out working in a group of two or three, but then decide that they would prefer to do the exercise on their own. Therefore, when a student returns to the exercise, s/he will have the option to drop out of a group and start over, in which case the remaining students in the group will be notified automatically.
Each group will analyze the data for 2 or 3 extra-solar planetary systems. There are 14 different sets of data (three stars each) altogether. The exercise can support an unlimited number of groups in a session. If more than 14 groups of students sign up to do the exercise, the software will simply assign students to successive cycles of 14 groups. E.g., group 17 will analyze almost2 the same set of data as group 3. In part 3 of this exercise, each group of students will compare the results of their analysis with results from a pre-set database of 13 other stars that have already been analyzed.3
The exercise consists of seven parts, as follows:
1. *The students are introduced to the applet, and learn how the Doppler velocity of the star depends on the orbital radius and planet mass. The systems displayed correspond to planets in nearly circular orbits, and the data have fairly good S/N and orbital phase coverage. They are also introduced to the concept of fitting a model to data, and to the measurement of uncertainty in the model fit. Students should be able to fit the data well enough that they can identify the planetary system they have analyzed from a list of actual extra-solar planets.
2. *As in part 1, the students will analyze the data from another, different, planetary system. Compared to the data in part 1, the data they analyze will have poorer S/N and/or poorer phase coverage. But they should still be able to identify the planetary system they have analyzed.
3. *Each group of students will be asked to compare the results of their analysis with the results of the analysis of 13 other systems. The students will see several instances where a second set of data representing the identical planetary system has substantially lower quality (S/N and/or phase coverage) than the first set. They will be asked a set of questions intended to lead them to an understanding of how the confidence level of their conclusions depends on the quality of the data.
4. In this brief section, students will learn that the mass of the planet inferred from the Doppler velocity curve of the star depends on the inclination of the orbit (which is usually not known).
5. In this brief section, students will learn that the inferred mass of the planet depends on the mass of the star (which may be inferred from the spectral type of the star).
6. This substantial section introduces the students to the properties of eccentric orbits and gives them the opportunity to analyze and compare data from stars with planets having highly eccentric orbits. It also introduces some actual planetary systems with multiple planets.
7. *The students are asked to reflect on what they have learned and to provide some feedback on the exercise. Every student must complete this section individually.
Parts 1, 2, 3, and 7 (the ones marked with *) are essential. In our experience, students should be able to complete these parts in 2 - 4 hours. Parts 4, 5, and 6 introduce additional concepts. They are independent and optional (you may wish to assign any or all of these in addition to parts 1 - 3). The navigation buttons at the bottom of each page will take students sequentially through parts 1 - 3. Then it will give them the option of jumping directly to part 7 to complete the exercise, or proceeding to parts 4, 5, or 6.
The students will enter all their work on-line, and their entries will be captured in a database. Moreover, the exercise is self-checking: if students enter answers that are not in the correct range, the exercise will identify the faulty answer and will require them to try again before proceeding to the next page.4
To see how the exercise works, open this page: http://scatter.colorado.edu/PlanetFinder/, and enter the session name sample. Then enter your email address and name, choose a password, and follow the instructions as if you were a student. The session sample. This session differs from the usual session in that it is not self-checking. The user can browse through this session at will without correctly answering all the questions on the page.
New vocabulary words that may be unfamiliar to students (e.g., semi-major axis), are "live" -- i.e., upon placing the mouse pointer on such words, a balloon containing a definition will pop up.
The little scuba divers that say "go deeper" upon mouse-over will take the students to deeper explanations of the physics and mathematics underlying the exercise. We recommend that you advise your students to skip most or all of these sections, at least on the first pass. We want the students first to observe and explore the phenomena illustrated by the applets before becoming concerned with formulas and algebra. In our view, actual scientific research typically follows this sequence: (1) observation; (2) data analysis; and (3) theoretical interpretation. So, after the students have explored and analyzed the phenomenon, they might want to follow the scuba divers. But not during the first time through.
To help your students get started, you may wish to log into the session sample and demonstrate how to fit the data. We also suggest that you identify a location and times where students can begin the exercise with a trained assistant (any bright undergraduate can fulfill this function). After the students get started, they should be able to resume working at their convenience on any PC.
The exercise requires the Java 1.4 Webstart environment, which should be available on both PCs and Macs. You should ensure that this environment is available on any facilities you recommend to your students. A help button on the bottom of each page in the exercise provides the necessary information to install this environment on PCs or Macs.
If you wish to try this exercise with your students (and we very much hope that you will), go to the instructor home page and hit the link BROKEN LINK: Planetfinder: Create Session. That will permit you to create a session for your class and a password by which you can retrieve your students' work from the database. Then instruct your students to go to the website http://scatter.colorado.edu/PlanetFinder/ and enter the name of the session that you have created.
We have tried to make this exercise as "instructor-friendly" as possible. Accordingly, we have developed software that will enable you (or your TA) to view and grade your students' work and to download the scores. Since the students must enter correct numerical and multiple-choice answers to proceed, the only answers that need to be graded are those in the text boxes.
To retrieve and grade your students' work, hit the link BROKEN LINK: Planet Finder: Retrieve Data and enter the session name and password that you have created for the session. There you can find your students' answers, listed either by each group of students or by each question. After doing so, you can retrieve your students' cumulative scores with the BROKEN LINK: Download Scores page. To see how this works, just enter the session name sample and password sample in the link BROKEN LINK: Planet Finder: Retrieve Data.
This exercise is definitely a work in progress, and we will greatly value your feedback. So please don't fail to complete the on-line questionnaire that you will be reminded of when you retrieve your students' work.
After you have tried this out with your students and have provided us with your advice, we'll be happy to arrange for you to import the necessary software to your own server.
This exercise has been designed by Dick McCray (richard.mccray@colorado.edu), Drew Koelemay, and Scott Gettman, with the support of grants to the University of Colorado from the National Science Foundation and NASA.
1 The data that the students fit are actually pseudo-data, produced by a random number generator. But the students will see that the data they analyze are very similar to actual data from real planetary systems.
2Almost, because the data displayed in the applet are generated by a random number generator. Therefore, the student will see a different set of data every time s/he pulls up the applet -- having the same statistical properties, but quantitatively different.
3In creating a session, you have the option of choosing a pre-set database of stars that have been analyzed, or letting the students compare their analysis with the actual analysis of other students.
4The self-checking is the default option control in creating a session. If you choose not to include self-checking, you, or your students, can browse through the exercise without answering any questions, as is the case in the session sample. There is no self-checking in the optional parts 4, 6.
Last Updated: 1/11/06