Following Kepler's Footsteps
Topic/Concept: Mapping the Martian Orbit
Type of Activity: small group + a little discussion at the end
Prerequisite knowledge required: Kepler’s and Newton’s Laws
Resources required: worksheet, blank cartoon of earth’s orbit (links below), compasses, rulers, protractors
Learning Objectives: apply Kepler’s and Newton’s laws to find martian orbit, use ratios and practice basic math concepts
Common misconceptions: difficulty setting up ratios
Detailed description of activity: I have the students get into groups of three or four and give each group a worksheet, a cartoon of earth’s orbit, a protractor, compass and ruler. I give a short explanation of how Kepler used Tycho Brahe’s observations to determine the orbit of Mars by trial and error, picking sets of dates and triangulating the position of Mars one martian year apart.
I explain the coordinate system (0 degrees is to the right, along a line parallel to the edge of the paper for all observations). I then let them get to work finding the location of Mars with dates that are ~687 earth days apart (one Martian sidereal year). While they’re working, I wander the room, making sure they’re using the correct coordinate system and helping when they get to the math portion of the worksheet.
If any of the groups are finishing quickly, I provide additional questions to think about (i.e. How could you detect planets around other stars? after they’ve found the ratio of the forces on the sun)
I leave about 5-10 minutes at the end of the period to talk about how using a circle to approximate the Martian orbit isn’t really correct, but it’s close enough to work for this, and to go over any lingering math questions.
Assessment: I collected the worksheets and looked over them. I addressed any major misconceptions in the next section. Most of the assessment was done through interaction with the students during the section.
Associated files and images:worksheet .doc file
kepler diagram.jpg
Comments: this has been done for both introductory “not-for-major” students and for first year science-oriented astonomy students. This worksheet is for the not-for-majors class, but additional questions could be added (such as calculating the eccentricity of the martian orbit, or anything else you could think of) for more advanced students. It seemed to provide a good review of Kepler and Newton for the intro class. Thanks to Andrea Dobson of Whitman College for the initial idea for this activity!