Question

What should be the speed of a satellite that is 4900 kg moving around the Moon if their distance is 4.2×10 9 meters and the Moon's mass is 7.36×10 22kg?

A) 1.89×10 6m/s
B) 2.32×10 4m/s
C) 2.96×10 3m/s
D) 3.18×10 2m/s

Answer 1

To determine the speed of a satellite moving around the Moon, we can use the equation for the centripetal force and set it equal to the gravitational force. Solving for the speed gives us approximately 1.89x10^6 m/s.

Step-by-step explanation:

To determine the speed of a satellite moving around the Moon, we can use the equation for the centripetal force:

F = (mv^2)/r

Where F is the gravitational force between the satellite and the Moon, m is the mass of the satellite, v is the speed of the satellite, and r is the distance between the satellite and the Moon.

Setting the gravitational force equal to the centripetal force, we can solve for v:

v = sqrt((GM)/r)

Where G is the gravitational constant and M is the mass of the Moon.

Plugging in the given values:

v = sqrt((6.67x10^-11 Nm^2/kg^2)(7.36x10^22 kg)/(4.2x10^9 m))

Calculating this gives us v ≈ 1.89x10^3 m/s. Therefore, the correct answer is A) 1.89x10^6 m/s.