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 x 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 formula for the period (T) of a satellite orbiting a planet is:

T = 2π√(r³/GM)

where r is the radius of the orbit, G is the gravitational constant, and M is the mass of the planet.

We can rearrange this formula to solve for r:

r = (GT²M/4π²)^(1/3)

Plugging in the values given:

r = [(6.67 x 10^-11 N·m²/kg²)(9.92 hours x 3600 s/h)^2(1.90 x 10^27 kg)/(4π²)]^(1/3)

r = 1.60 x 10^18 meters

Therefore, the radius of the orbit required for a satellite to revolve about Jupiter with the same period is 1.60 x 10^18 m, which is answer choice C.

Jupiter Completes One Revolution About Its Own Axis Every 9