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A GPS satellite moves around Earth in a circular orbit with period 11 h 58 min....

A GPS satellite moves around Earth in a circular orbit with period 11 h 58 min. Determine the radius of its orbit. Hint: use the Newton’s 2nd law of motion relating the gravitational force and the centripetal acceleration of the satellite. Assume the following is given: Earth’s mass MEarth = 6x10^24 kg, Earth’s radius REarth = 6.378x10^6 m, and the gravitational constant G = 6.67x10^-11 Nm2/kg2.

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Answer #1

Gravitational constant = G = 6.67 x 10^-11 N.m2/kg2

Mass of Earth = M = 6 x 10^24 kg

Mass of the satellite = m

Radius of orbit of the satellite = R

Orbital speed of the satellite = V

Orbital period of the satellite = T = 11 hr 58 min = 11 x (3600) + 58 x (60) sec = 43080 sec

The gravitational force of Earth on the satellite is the required centripetal force for the circular motion of the satellite.

R = 2.66 x 10^7 m

Radius of the orbit of the satellite = 2.66 x 10^7 m

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