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(III) The orbital periods Τ and mean orbital distances r for Jupiter’s four largest moons are given in Table 6–3, on the previous page. (a) Starting with Kepler’s third law in the form
where mJ is the mass of Jupiter, show that this relation implies that a plot of log(T) vs. log(r) will yield a straight line. Explain what Kepler’s third law predicts about the slope and y-intercept of this straight-line plot. (b) Using the data for Jupiter’s four moons, plot log(T) vs. log(r) and show that you get a straight line. Determine the slope of this plot and compare it to the value you expect if the data are consistent with Kepler’s third law. Determine, the y-intercept of the plot and use it to compute the mass of Jupiter.
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