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

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Presentation transcript:

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 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.

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.

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

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.

Eclipse Predictions by Fred Espenak, NASA's GSFC

Ptolemy (2 nd century AD)

Geometry of an eclipse

Go to animation….

Do the experiment!

Mathematical derivation

Discrepancies & improvements