A satellite moves in a circular earth orbit that has a radius of 7.49 x 106...

A satellite moves in a circular earth orbit that has a radius of 7.49 x 106 m. A model airplane is flying on a 24.1-m guideline in a horizontal circle. The guideline is nearly parallel to the ground. Find the speed of the plane such that the plane and the satellite have the same centripetal acceleration.

Solutions

Expert Solution

If M is the mass of earth and m the mass of satellite the gravitational force at the satellite altitude H is

, assuming R is measured from the center of the Earth

By writing also we observe that the gravitational acceleration at altitude R is

which need to be equal to the satellite centripetal acceleration.

For the aircraft that is moving in a horizontal circle of radius r just above the earth, the centripetal acceleration is

Both accelerations are equal means that

The numerical values are

R=7.49.10⁶m

Therefore

V=√(6.67×10^-11×5.97×10²⁴×24.1)/(7.49×10⁶)²)

The speed of the plane need to be 13.07 m/s to have the same centripetal acceleration as the satellite has.

Please give your feedback it counts a lot and sorry for any mistake

genius_generous answered 1 year ago

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