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Paper Moon: Simulating a Total Solar Eclipse

Paper Moon: Simulating a Total Solar Eclipse. Juniata College June 18, 2013 John Bukowski & Jerry Kruse. Mathematical Modeling. We use models to represent something in the “real world”. - equations, graphs, computer programs, …. Mathematical Modeling.

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Paper Moon: Simulating a Total Solar Eclipse

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  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 (2nd 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

  13. Mathematical derivation

  14. Mathematical derivation

  15. Mathematical derivation

  16. Discrepancies & improvements

  17. bukowski@juniata.edukruse@juniata.edu

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