A Geosync TV satellite of mass 2000 kg is in a circular orbit around the earth,

Question

A Geosync TV satellite of mass 2000 kg is in a circular orbit around the earth, making one revolution or orbit every 24 hrs [86,400 seconds ].
(1) What is the radius of the orbit? (2)What is the magnitude of the centripetal acceleration ?
(3) What must be the magnitude of the gravitational force exerted on the satellite by the earth? Note, You cannot assume it is close to the Earth's surface! ( mass of the earth is6.0×10^24kg.) A Geosync TV satellite of mass 2000 kg is in a circular orbit around the earth, making one revolution or orbit every 24 hrs [86,400 seconds ].
(1) What is the radius of the orbit? (2)What is the magnitude of the centripetal acceleration ?
(3) What must be the magnitude of the gravitational force exerted on the satellite by the earth? Note, You cannot assume it is close to the Earth's surface! ( mass of the earth is6.0×10^24kg.)

Explanation / Answer

a)T=86400,m=2000kg, M=6x10^24kg from T^2=4pi^2R^3/GM solving for we get R=4.231x10^7m b)centripetal acceleration a =4pi^2R/T^2 = 0.2235 m/s^2 c)the magnitude of the gravitational force exerted on the satellite by the Earth=GMm/R^2 = 447.1N

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