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 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 the satellite is given by:

T = 2π√(r^3/GM)

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

We are given that T = 9.92 hours, or 35,712 seconds.

Substituting the given values, we get:

35,712 = 2π√(r^3/(6.67 × 10^-11 * 1.898 × 10^27))

Simplifying:

r^3 = (6.67 × 10^-11 * 1.898 × 10^27 * (35,712/(2π))^2)

r^3 = 1.74 × 10^26

Taking the cube root:

r = 1.60 × 10^18 meters

Therefore, the best answer choice is C: 1.60 × 10^18 meters.

Jupiter Completes One Revolution About Its Own Axis Every 9