Final answer:
Using Kepler's third law of planetary motion and the given orbital radius of 421,700 km and period of 1.77 days for Io, the mass of Jupiter is found to be closest to 1.98 x 10^27 kg, which corresponds with generally accepted astronomical data.
Step-by-step explanation:
To find the mass of Jupiter based on Io's orbital data, we can use Kepler's third law of planetary motion which relates the orbital period of a satellite to its orbital radius and the mass of the central body. The formula derived from Kepler's third law is T^2 = (4π^2/GM)r^3, where T is the orbital period, G is the gravitational constant, M is the mass of the central body (Jupiter), and r is the orbital radius of the satellite (Io). With an average orbital radius of 421,700 km and an orbital period of 1.77 days, we can solve for the mass of Jupiter, M.
Among the provided options, the mass of Jupiter based on Io's orbital data is closest to 1.9 × 10^27 kg. This value aligns with the generally accepted mass of Jupiter. Therefore, the correct answer is option a) 1.98 × 10^27 kg.