Respuesta :
Explanation:
Given that,
A satellite that goes around the earth once every 24 hours is called a geosynchronous satellite, T = 24 hours = 86400 s
We need to find the radius R of the orbit of a geosynchronous satellite that circles the earth. It can be calculated using Kepler's third law of motion as :
[tex]T^2=\dfrac{\pi^2}{GM}R^3[/tex]
R is the distance from the center of the earth.
[tex]T^2=\dfrac{\pi^2}{GM}R^3\\\\R^3=\dfrac{GMT^2}{\pi^2}[/tex]
G is universal gravitational constant
M is mass of earth
[tex]R^3=\dfrac{6.67\times 10^{-11}\times 5.98\times 10^{24}\times (86400)^2}{\pi^2}\\\\R=\left(\frac{6.67\times10^{-11}\times5.98\times10^{24}\times(86400)^{2}}{\pi^{2}}\right)^{\frac{1}{3}}\\\\R=67.06\times 10^6\ m[/tex]
So, the satellite distance from the earth's surface is :
[tex]h=67.01\times 10^6-6.38\times 10^6\\\\h=6.06\times 10^7\ m[/tex]
