1. Paper Moon: Simulating a Total Solar Eclipse Juniata College June 18, 2013 John Bukowski & Jerry Kruse

2. Mathematical Modeling We use models to represent something in the “real world”. - equations, graphs, computer programs, …

3. Mathematical Modeling We use models to represent something in the “real world”. - equations, graphs, computer programs, … The real world is complicated, so we make assumptions to simplify our models.

4. Mathematical Modeling We use models to represent something in the “real world”. - equations, graphs, computer programs, … The real world is complicated, so we make assumptions to simplify our models. An important step in math modeling: ask if the solution is reasonable – if not, go back and adjust the model.

5. What is a solar eclipse? The moon passes in front of the sun, from our point of view.

6. What is a solar eclipse? The moon passes in front of the sun, from our point of view. A total solar eclipse is when the moon completely obscures the sun.

7. Eclipse Predictions by Fred Espenak, NASA's GSFC

8. Ptolemy (2 nd century AD) http://sunearthday.nasa.gov/2006/locations/ptolemy.php

9. Geometry of an eclipse

10. Go to animation….

11. Do the experiment!

12. Mathematical derivation

17. Discrepancies & improvements

18. bukowski@juniata.edu kruse@juniata.edu