Answer
See answer.
Work Step by Step
The relationship between satellite period T, mean satellite distance r, and Jupiter’s mass M is derived in Example 5-14.
$$M=\frac{4 \pi ^2 r^3}{GT^2}$$
a. Substitute the values for Io to get the mass of Jupiter.
$$M=\frac{4 \pi ^2 (4.22\times10^8m)^3}{G(1.77d*86400s/d)^2}=1.90\times10^{27}kg$$
b. Do the same for the other moons.
Europa
$$M=\frac{4 \pi ^2 (6.71\times10^8m)^3}{G(3.55d*86400s/d)^2}=1.90\times10^{27}kg$$
Ganymede
$$M=\frac{4 \pi ^2 (1.07\times10^9m)^3}{G(7.16d*86400s/d)^2}=1.89\times10^{27}kg$$
Callisto
$$M=\frac{4 \pi ^2 (1.883\times10^9m)^3}{G(16.7d*86400s/d)^2}=1.90\times10^{27}kg$$
Yes, the results are consistent.
