Question

A semi-major axis of lo's orbit around Jupiter is 4.217 x 10^5 km. what is lo's orbital period if the period of Europa around Jupiter is 3.551 days and its semi-major axis is 6.710 x 10^5 km?

Answer 1

The orbital period of lo around Jupiter is approximately 2.236 days.

Step-by-step explanation:

Kepler's third law states that the square of the orbital period of a planet is directly proportional to the cube of its semi-major axis. In order to calculate the orbital period of lo around Jupiter, we can set up a proportion using the given information:

Europa's Orbital Period / Europa's Semi-Major Axis = Io's Orbital Period / Io's Semi-Major Axis

Using the given values, we can solve for Io's Orbital Period:

3.551 days / 6.710 x 10^5 km = x / 4.217 x 10^5 km

(3.551 days)(4.217 x 10^5 km) = (6.710 x 10^5 km)(x)

x = (3.551 days)(4.217 x 10^5 km) / (6.710 x 10^5 km)

x = 2.236 days

Therefore, lo's orbital period around Jupiter is approximately 2.236 days.