Serway & Jewett — Universal Gravitation: Problem 2

Activity Jupiter has over 60 moons, most of them discovered in the twenty-first century. The table shows astronomically measured data for the first fifteen moons, in order of semimajor axis of the orbit around Jupiter. (a) For these moons, show that Kepler’s third law is satisfied within reasonable observational uncertainty for the data in the table. (b) Evaluate the ratio \( T^2/a^3 \), where \( T \) is the orbital period and \( a \) is the length of the semimajor axis, for these moons and compare the results to the value for the solar system (Table 13.2). Why is the value of this ratio larger for the moons of Jupiter than for the solar system? (c) Before calculating the value of \( T^2/a^3 \) from the data, could you have predicted what it would be?