Post on 22-Feb-2016
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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