What are the Shapes of the Planets' Orbits?

PURPOSE

In this investigation, you will learn about the shapes of the planets' orbits by experimenting with ellipses of different proportions.

MATERIALS

PROCEDURE

  1. Form a loop by tying the ends of a piece of string 25 cm long. When the loop is held taut, it should be 11 cm long; that is, the circumference of the loop should be 22 cm.
  2. The planetarium teacher will provide you with a sheet of unlined paper upon which six points are marked (Points A, B, C, D, E, F). Place the unlined paper on a piece of corrugated cardboard. Partially push the two thumbtacks into points A and B. Place the loop of string around the the two thumbtacks. Put the pencil point inside the loop of string; pull the slack out of the string. While keeping the loop of string taut, run the pencil around inside the loop while drawing on the paper. Be careful that the string is always looped around both thumbtacks (otherwise, what shape will be drawn?). Label the figure drawn "Ellipse AB." Repeat the procedure for Points CD and EF.

ACTIVITY QUESTIONS

  1. As the distance between the two thumbtacks (called foci) increases, how does the shape (not size) of the ellipse change?


  2. Mathematicians call the measure of the shape of an ellipse "eccentricity" -- ellipse AB is the least eccentric (roundest); ellipse EF is the most eccentric (flattest). If we assign dollar values to the eccentricity of the three ellipses that you drew, then AB would equal $0.10 (ten cents), CD equals $0.60 (sixty cents), and EF equals $0.90 (ninety cents). If you know that the shape of the Earth's orbit equals $0.02 (two cents!), then which of the three ellipses that you drew resembles the shape of Earth's orbit most closely: AB, CD, or EF?


  3. Examine a typical diagram of the Solar System (such as the diagram included in the booklet, The Sun and Its Neighbors). Many diagrams of the Solar System inaccurately depict the shape of the planets' orbits. Based upon what you have learned in this investigation, explain how the shape of the planets orbits should appear.


ACTIVITY EXTENSION

After learning how to draw/measure/calculate the eccentricity of ellipses offline (prerequisite math skills: students should be familiar with the metric system; be able to divide a smaller number by a larger number; and be comfortable working with decimal numbers), students will use NIH Image (freeware image processing software) and an online interactive aerial photograph of Washington, DC to locate/measure/calculate the eccentricity of the "Ellipse" (in front of the White House -- refer to a street map of Washington, DC). Students will then compare/contrast the eccentricity of the "Ellipse" with the eccentricity of the planets' orbits.