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Objective: To identify whether positive, negative, or zero work is being done, to identify the force that is doing the work, and to describe the energy transformation associated with such work.
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Kepler’s Third Law
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To use a variety of graphs and linearization methods to determine a mathematical relationship between two quantities.
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To describe the periodradius relationship using mathematical equations, words, or data that illustrate the relationship.
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To recognize radius and period ratios in both the planetary data and a set of simplified data and to relate the radius ratios to the period ratios.
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Kepler’s Law of Harmonies
In the late 1600s, Johannes Kepler acquired the carefully collected planetary data of Danish astronomer Tycho Brahe. Kepler attempted to analyze the known planetary information of that day. Kepler attempted to identify the mathematical relationship between the period (time for a complete orbit) of each planet and its average distance from the sun. Table 1 shows a more polished form of the data that resulted from his analysis.
Some physics students plotted the values of period (T) and distance (R) raised to various powers. Their goal was to find a linear relationship between the two quantities so that they could use the slopeintercept equation to relate them mathematically. They performed a linear regression analysis for each plot; the slope (m), and correlation coefficient (COR) are reported below.
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PhysicsInteractives/StaticElectricity/
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