Answer:
A gravitational force of 6841.905 newtons is exerted on the satellite by the Earth.
Explanation:
At first we assume that Earth is represented by an uniform sphere, such that the man-made satellite rotates in a circular orbit around the planet. Hence, the following condition must be satisfied:
(1)
Where:
- Period of rotation of the satellite, measured in seconds.
- Distance of the satellite with respect to the center of the planet, measured in meters.
- Gravitational constant, measured in newton-square meters per square kilogram.
- Mass of the Earth, measured in kilograms.
Now we clear the distance of the satellite with respect to the center of the planet:
![r = \sqrt[3]{\frac{G\cdot M\cdot T^{2}}{4\pi^{2}} }](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7BG%5Ccdot%20M%5Ccdot%20T%5E%7B2%7D%7D%7B4%5Cpi%5E%7B2%7D%7D%20%7D)
(2)
If we know that 
, 
and 
, then the distance of the satellite is:
![r = \sqrt[3]{\frac{\left(6.67\times 10^{-11}\,\frac{N\cdot m^{2}}{kg^{2}} \right)\cdot (6.0\times 10^{24}\,kg)\cdot (25800\,s)^{2}}{4\pi^{2}} }](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7B%5Cleft%286.67%5Ctimes%2010%5E%7B-11%7D%5C%2C%5Cfrac%7BN%5Ccdot%20m%5E%7B2%7D%7D%7Bkg%5E%7B2%7D%7D%20%5Cright%29%5Ccdot%20%286.0%5Ctimes%2010%5E%7B24%7D%5C%2Ckg%29%5Ccdot%20%2825800%5C%2Cs%29%5E%7B2%7D%7D%7B4%5Cpi%5E%7B2%7D%7D%20%7D)
The gravitational force exerted on the satellite by the Earth is determined by the Newton's Law of Gravitation:
(3)
Where:
- Mass of the satellite, measured in kilograms.
- Force exerted on the satellite by the Earth, measured in newtons.
If we know that , , 
and , then the gravitational force is:
A gravitational force of 6841.905 newtons is exerted on the satellite by the Earth.
