Virial Theorem LessonOverviewWith spiral galaxies, it is easy to see that the spinning of the galaxy causes it to stretch out, while the force due to gravity pulls it in. What, then, is the reason for elliptical galaxies to maintain there shape? This lesson will allow students to model the stability of elliptical galaxies based on how fast stars within the galaxy are moving.Preparation and MaterialsThe teacher should be familiar with the GalaxSee application (for those unfamiliar with this software, there is an online tutorial), have it loaded on a PowerMac or PC, and have some means of displaying the monitor to the class.If the teacher is going to use the helper spreadsheet that comes with this lesson, he/she should have Excel installed on the display computer and all student computers. ObjectivesStudents will
StandardsThis lesson fulfills portions of the following standards and curriculum guidelines:
Activities
Note: Be careful of computer error here. As the stars clump to the center, their speeds will increase rapidly, and error may to accumulate in the model. If the time step is too large, or the shield radius too small, the model will become unrealistic, and could, for example, throw all of the stars out beyond the original boundaries. This is an inaccurate result. Keep an eye on the total energy, and if the energy is not conserved in the model, consider running it with either a smaller time step or a larger shield radius. For more information about detecting and controlling error, see the section about the info window in the GalaxSee tutorial.
NOTE: The students can use the values of kinetic and potential energy from the spreadsheet. Windows users will have potential and kinetic energy displayed in the information window. Discussion of the SimulationAsk the students to discuss why the galaxies just didn't collapse due to gravity. Have them write out a description of the models they ran.Have the students look at a model with the same amount of potential and kinetic energy. Notice that the galaxy expands. As the galaxy expands, the potential energy decreases in magnitude, but the kinetic energy stays roughly the same. Would you expect the galaxy to become more stable or less stable over time (i.e. does it just keep going, or does it eventually stabilize)? Discussion of ObservationAsk the students to compare their models to images of elliptical galaxies. Do the results of a "stable" galaxy look more like the images of an elliptical galaxy? less? the same?Assign them to write a clear and accurate report of what they observed. Emphasize that it is important that they know what software was used, and what parameters were set. Be sure to go through the setup procedure again so that they can record this information. CollaborationAfter they have polished their reports, instruct them to prepare and post a note to WebCaMILE for another group of students to see. If possible, have the other group of students attempt to repeat the experiment as described in the note, verify the findings of the first group, and provide feedback about their methods and conclusions. Encourage both groups to ask questions of each other's procedure and observations. If another group of students is not available, you could split one class into two large groups and require them to communicate only through writing.ExtensionsFurther ExperimentationHave the students create a rotating disk with 256 stars, 200 solar masses each, and with a rotation factor of 1 in GalaxSee. Save the file and open it in Excel. Cut and paste the data into a copy of the helper spreadsheet, to calculate the kinetic and potential energy of the rotating galaxy. Does the same relation between energy of motion and energy of position hold for the spinning disk? Why might this be different?Thinking HarderAsk the students how they would further test the hypothesis that elliptical galaxies do not collapse because of random motion of stars. What observations could be made of elliptical galaxies to test this theory? (what is the range of redshift measurements of stars in the galaxy?) Can this information be determined from the model? (yes, compare to typical velocity.)Go to GalaxSee Curriculum Resources Please direct questions and comments about this page to WebMaster@shodor.org © Copyright 1996 The Shodor Education Foundation, Inc. |