Jupiter completes one revolution about its own axis every 9.92 hours. What is the radius of the orbit required for a satellite to revolve about Jupiter with the same period? Jupiter has a mass of 1.90 × 10²⁷ kg and G = 6.67 × 10^-11 N ∙ m²/kg². A) 1.04 × 10⁷ m B) 2.26 × 10⁹ m C) 1.60 × 10⁸ m D) 3.41 × 10⁸ m E) 7.45 × 10⁸ m

Question

Quizplus · Accepted Answer

The period of revolution of a satellite around a planet can be found using Kepler's third law:

T² = (4π²a³)/(GM)

where T is the period of revolution, a is the radius of the orbit, G is the gravitational constant, and M is the mass of the planet.

In this case, we want to find the radius of the orbit (a) for a satellite to revolve around Jupiter with a period of 9.92 hours. We can rearrange Kepler's third law to solve for a:

a = [(GMT²)/(4π²)]^(1/3)

Plugging in the values:

a = [((6.67 × 10^-11) * (1.90 × 10^27) * (9.92*3600)^2)/(4π²)]^(1/3)

a ≈ 1.60 × 10^18 meters

Therefore, the best answer is (C).

Jupiter Completes One Revolution About Its Own Axis Every 9