Lesson Plan - Three D Constellations

Suggestions for Instructors

A major misconception with students of astronomy deals with the student's understanding of scale. Even the ancient astronomers considered the stars to be all at the same fixed distance in the heavens.

This lesson is designed to introduce students to both celestial coordinates and to the first rung on the distance determination ladder, parallax. Students will convert spherical coordinates, together with parallax, to cartesian coordinates to construct a three dimensional model of a constellation which can be viewed from any angle.

The following points should be made with students:

• The stars are all at different distances from us.
• Parallax only works on the nearest stars to us.
• The stars only appear to move across the sky throughout the night because of the Earth's motion. With small exceptions, they appear to be fixed relative to each other.
• The pattern made by different constellations is purely due to our perspective.

Standards

The exploration meets the following National Standards:  Science Content Standards: 9-12

• CONTENT STANDARD A:
• Abilities necessary to do scientific inquiry
• Understandings about scientific inquiry
• Fundamental abilities and concepts that underlie this standard include:
  • Use technology and mathematics to improve investigations and communications.
  • Formulate and revise scientific explanations and models using logic and evidence.
  • Recognize and analyze alternative explanations and models.
  • Communicate and defend a scientific argument.
• CONTENT STANDARD B:
• Physical Science Standards
  • Structure and properties of matter
  • interactions of energy and matter
• Earth and Space Science Standards
  • Origin and evolution of the universe
  • Origin and evolution of the earth system
• History of Science Standards
  • Nature of scientific knowledge

Solutions

1. Suppose you could take the stars that make up the big dipper, and rotate the whole thing by 90 degrees. Draw a picture of what you think the Big Dipper might look like from this perspective.
   This is a leading question meant to allow students to face their misconceptions. Many students will think that from the side, a constellation would look "flat".
2. How many arc-minutes as used for Dec are in one minute of angle as used for RA?
   Declination is expressed in hours, arc-minutes, and arc-seconds. If 24 hours of arc is 360 degrees, then 1 hour of arc is 15 degrees, and 1 arc-minute (1/60th of an arc-hour) is 0.25 degrees. A minute of angle measured in degrees, minutes, and seconds is 1/60th of a degree, or 0.0167 degrees. An arc-minute of angle is larger than a minute of angle.
3. As you look at stars that are further and further away, what happens to the parallax of those stars?
   Parallax effects get smaller as the objects being observed are further away.
4. Why can parallax only be used for nearby stars?
   Since parallax effects get smaller for stars that are further away, they become more difficult to measure.
5. Look up the data for the Big Dipper. Convert RA, Dec, and parallax to X, Y, and Z coordinates for each star, and make a 3-D model. You can do this either with materials such as paper mache or styrofoam balls and sticks, or you can use a computer program.
   Click on the big dipper model to open a window with a solution.