Kepler’s Second Law Using Integration by Weighing (Journal Article)

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Abstract-

Kepler’s second law, also known as the law of equal areas, can be difficult for introductory students to explore using actual data given the complexity of the formula for finding the area of a sector of an ellipse. It is also possible to demonstrate Kepler’s second law with simplified math using video analysis of objects in a gravitation funnel1 if students have access to the necessary materials. In this activity, students discover Kepler’s second law using minimal equipment and mathematics using the technique of integration by weighing,2 where students cut out sections of an ellipse and use the mass of the sections to compare their areas.

Given Kepler’s use of Mars’s orbital data, it provides a natural starting point for this activity. Students will need a scaled plot of Mars’s orbit with known time intervals, which students can produce themselves or can be provided to students. To have...