Activity: Graphing the Orbits of Planetary Objects

Materials:

metric ruler, graphing calculator, graph paper

About this Activity:

Students will be given information about planetary objects. Based on the characteristics described in the background information, students will sketch the elliptical orbit of the planetary objects, name the x- and y-intercepts, and write an equation for these ellipses.

Procedure:

  1. First review sketching ellipses and writing equations using examples from your own books and materials or the worksheet provided.

    *As an extension, you may want to use a graphing calculator or a computer graphing program to graph the equations of the ellipses from the worksheet. Students may have to convert equations into "y=" form.

  2. Hand out the worksheet with information on the planetary objects.
  3. Students will need to do the calculating first and then graph the ellipses.

    *Example: Write an equation for Saturn's orbit. Saturn has an eccentricity of 0.06 and the average distance to the Sun is 9.5 AU.

    Since a = 9.5, the vertices (x-intercepts) are (9.5,0) and (-9.5,0). e= c/a, so .06 = c/ 9.5 making c= 0.57. The foci are at (0.57,0) and (-0.57,0). Use the Pythagorean Theorem to get that b=9.48, the y-intercept. The equation for this ellipse is (x^2)/(9.5)^2 +(y^2)/(9.48)^2 = 1

    [Graph of Saturn's Orbit Ellipse]

  4. You may want the students to just sketch the graphs of the ellipses or to use the method for drawing ellipses described in the lesson on Kepler's Laws using cardboard and thumbtacks.

    *As another extension, use the students' equations for the planets' orbits to graph on a graphing calculator or a graphing computer program.

  5. Discuss in class the students' observations about the planets' orbits, Eros' orbit, and how they relate to each other.
Review Worksheet on Ellipses

Handout: Graph the Elliptical Orbits of Planetary Objects

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[LMGFP home page] Contact Karen Krupinsky (kgurley@gsfc.nasa.gov) or
Tammy Seergae (tseergae@umd.edu) for further information.