Answer:
According to Kepler's 3rd law.
It states that the orbital period, T is related to the distance, r as:
T² = 4 π²r³ /G M
where G is the universal gravitational constant = 6.673 × 10⁻¹¹ Nm²/kg²
Rearranging for M should give Jupiter's mass.
M = 4 π²r³/GT²
T= 1.77 days × 24 h/day × 60 min/h × 60 s/min = 1.53 × 10⁵ s
r = 4.22x10⁸ m
M = 4π² ((4.22 × 10⁸ m)³/(6.673 × 10⁻¹¹ Nm²/kg² x (1.53 × 10⁵ s)²)
M = 1.90 × 10²⁷kg
The mass of Jupiter is 1.90 × 10²⁷kg.
1.90 × 10²⁷kg
T= 7.16 days × 24 h/day × 60 min/h × 60 s/min = 6.19 × 10⁵s
r = 1.07x10⁹ m
M = 4π² ((1.07 × 10⁹ m)³/(6.673 × 10⁻¹¹ Nm²/kg² x (6.19 × 10⁵ s)²)
M = 1.90 × 10¹⁷kg
The mass of Jupiter is 1.90 × 10¹⁷kg.
THE RESULTS TO PART A and B ARE NOT CONSISTENT. The reason is because of the difference in radius of each satellites from Jupiter. i.e the farther away the moons, the smaller they become in space and the more the number of days to complete an orbit.
