Question

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.

Answer 1

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.

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