Final answer:
The mass of Jupiter can be calculated using Kepler's Third Law of Planetary Motion, resulting in an approximate mass of 1.9 × 10^27 kg.
Step-by-step explanation:
The mass of Jupiter can be calculated using Kepler's Third Law of Planetary Motion, which states that the square of the orbital period of a planet is directly proportional to the cube of its average orbital radius. Based on the given data for Ganymede's orbit, we can use the following formula:
Mass of Jupiter = (4π² × (Orbital Radius of Ganymede)³) / (Gravitational Constant × (Orbital Period of Ganymede)²)
Substituting the values given, we get:
Mass of Jupiter = (4π² × (421,700 km)³) / (Gravitational Constant × (1.77 days)²)
Calculating the numerical value gives us an approximate mass of Jupiter as 1.9 × 10^27 kg.