Paper Moon:Simulating a Total

Solar Eclipse

Juniata CollegeJune 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 (2nd century AD)

• http://sunearthday.nasa.gov/2006/locations/ptolemy.php

Geometry of an eclipse

Go to animation….

Do the experiment!

Mathematical derivation

Mathematical derivation

Mathematical derivation

Mathematical derivation

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Discrepancies & improvements

bukowski@juniata.edu

kruse@juniata.edu