The planet Jupiter is the largest in the solar system, both in volume and mass. Jupiter has 79 known moons, the four largest having been discovered by Galileo in 1610. Two of these moons, Io and Europa, are shown in Figure 7.22. Given that Io is an average distance of \(4.22 \times 10^{5} \mathrm{~km}\) from the enter of Jupiter and has an orbital period of 1.77 days, compute the mass of Jupiter.
THINKING IT THROUGH. Given the values for Io's distance from the planet \((r)\) and period \((T)\), this would appear to be an application of Kepler's third law, and it is. However, keep in mind that the \(M_{\mathrm{S}}\) in Equation 7.22 is the mass of the Sun, which the planets orbit. The third law can be applied to any satellite, as long as the \(M\) is that of the body being orbited by the satellite. In this case, it will be \(M_{\mathrm{J}}\), the mass of Jupiter.
Equation 7.22: