Question #104644

Calculate the height of a satellite from the surface of the earth if its period is 12 h. Compare this height with the radius of the earth.

Expert's answer

"m\\frac{v^2}{r}=m\\frac{GM}{r^2}"

"v=\\frac{2\\pi r}{T}"

So,

"(6.38\\cdot 10^{6}+h)^3=\\frac{(6.67\\cdot 10^{-11})(5.97\\cdot 10^{24})}{4\\pi^2}(12\\cdot 3600)^2"

"h=20.22\\cdot 10^{6}\\ m"

"\\frac{h}{R}=\\frac{20.22\\cdot 10^{6}}{6.38\\cdot 10^{6}}=3.17"

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