The Earth has a radius of 6,400 kilometers. A satellite orbits the Earth at a distance of 12,800 kilometers from the center of the Earth. If the weight of the satellite on Earth is 100 kilonewtons, what is the gravitational force on the satellite in orbit?
Answer (2)
By using a universal gravitational force, we can get that F g = r 2 G . m 1 . m 2 .
For note : r is a distance from center of the earth to the object.
Then, if r 1 is 6.400 km, and if r 2 is 12.800 km, we can say that r 2 is 2 r 1
In first equation we can say that : F g = r 1 2 G . m 1 m 2 = 100.000 N
then in second equation we can say that : F g = r 2 2 G . m 1 m 2 , F g = ( 2 r 1 ) 2 G . m 1 m 2 (because r 2 is 2 r 1 ) F g = 4 r 1 2 G . m 1 m 2 , we can say that : F g = 4 1 r 1 2 G . m 1 m 2 so, by plugging first equation into second equation, we can get F g = 4 1 r 1 2 G . m 1 m 2 = 4 1 .100.000 N = 25.000 N
The gravitational force on the satellite in orbit is calculated to be 25,000 N, which is one-fourth of its weight on the surface of the Earth. This reduction is due to the increased distance from the center of the Earth as the satellite orbits. The relationship follows from the formula for gravitational force which shows how it decreases with the square of the distance.
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