(Ill) The orbital periods T and mean orbital distances
Chapter 6, Problem 6.47(choose chapter or problem)
(Ill) The orbital periods T and mean orbital distances rfor Jupiters four largest moons are given in Table 6-3, on theprevious page, (a) Starting with Keplers third law in the form\Gntj Jwhere mj is the mass of Jupiter, show that this relationimplies that a plot of log(T) vs. log(r) will yield a straightline. Explain what Keplers third law predicts about theslope and ^-intercept of this straight-line plot. (b) Using thedata for Jupiters four moons, plot log(T) vs. log(r) andshow that you get a straight line. Determine the slope ofthis plot and compare it to the value you expect if the data areconsistent with Keplers third law. Determine the ^-interceptof the plot and use it to compute the mass of Jupiter.
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