Halliday, Resnick & Walker — Gravitation: Problem 31

31 In 1610, Galileo used his telescope to discover four moons around Jupiter, with these mean orbital radii \(a\) and periods \(T\): Name \(a\) (\(10^8\) m) \(T\) (days) Io 4.22 1.77 Europa 6.71 3.55 Ganymede 10.7 7.16 Callisto 18.8 16.7 (a) Plot \(\log a\) (\(y\) axis) against \(\log T\) (\(x\) axis) and show that you get a straight line. (b) Measure the slope of the line and compare it with the value that you expect from Kepler’s third law. (c) Find the mass of Jupiter from the intercept of this line with the \(y\) axis.