Question

Jupiter's four large moons – Io, Europa, Ganymede, and Castillo – were discovered by Galileo in 1610. Jupiter also has dozens of smaller moons. Jupiter's rocky, volcanically-active moon Io is about the size of Earth's moon (7.22 x 1022 kg). Io has a radius of about 1.82 x 106 m, and the mean distance between Io and Jupiter is 4.22 x 108. If Io's orbit were circular, how many earth days would it take for Io to complete one full revolution around Jupiter? If Io's orbit were circular, what would its orbital speed be?

Answer 1

Answer:

The orbital speed is approximately 17,325.57 m/s

The number of Earth days it would take lo to complete its orbit is approximately 1.77 days

Explanation:

The given parameters are;

The mass of lo, m ≈ 7.22 × 10²² kg

The radius of lo, R ≈ 1.82 × 10⁶ m

The mean distance between Jupiter and lo = 4.22 × 10⁸ m

The orbital equation is given as follows;

$\dfrac{m \cdot v^2}{R} = \dfrac{G \times M \times m}{R^2}$

$\therefore v = \sqrt{\dfrac{G \cdot M}{R} } = \sqrt{\dfrac{ 6.67408 \times 10^{-11} \times 1.898 \times 10^{27}}{4.22 \times 10^8} } = 17,325.57 \ m/s$

The orbital speed ≈ 17,325.57 m/s

The time to complete one orbit = (2 × π × 4.22 × 10⁸)/(17325.57) ≈ 153039.94 s

The time to complete one orbit ≈ 153039.94 s ≈ 1.77 days

The number of Earth days it would take lo to complete its orbit ≈ 1.77 days.