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April 17, 2013
This activity explores models for the elliptical orbit of Jupiter.
In Problem 1, students use information about Jupiter’s orbit to draw a picture of it. Students study the picture. They should see that the orbit is elliptical, with the sun at one focus of the ellipse. They form two equations and graph them.
Students animate a point on the graph to represent Jupiter. They will realize that they do not have a very good model. Students will notice that Jupiter is at a certain place relative to the sun at a certain time.
Students then move on to Problem 2, where they are introduced to parametric equations. This is necessary since this ellipse cannot be expressed as a single equation in terms of only x and y. Instead, x and y are defined in terms of t as follows x = f(t) and y = g(t).
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