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logan3
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Homework Statement
A large telescope of mass 8410 kg is in a circular orbit around the earth, making one revolution every 927 minutes. What is the magnitude of the gravitational force exerted on the satellite by the earth?
[itex]M_E = 6.0x10^{24} kg[/itex]
[itex]m_s = 8410 kg[/itex]
[itex]T_s = 927 min = 55,620 s[/itex]
[itex]G = 6.67x10^{-11} Nm^2/kg^2[/itex]
Homework Equations
[itex]T^2 = \frac {4{\pi}^2 r^3}{GM_E} \Rightarrow r = \sqrt[3]{\frac {T^2 GM_E}{4\pi^2}}[/itex]
[itex]F_G = \frac {GM_E m_s}{r^2}[/itex]
The Attempt at a Solution
[itex]r = \sqrt[3]{\frac {T^2 GM_E}{4\pi^2}} = \sqrt[3]{\frac {(55,620 s)^2 (6.67x10^{-11} Nm^2/kg^2)(6.0x10^{24} kg)}{4\pi^2}} = 3.1532x10^7 m[/itex]
[itex]F_G = \frac {GM_E m_s}{r^2} = \frac {(6.67x10^{-11} Nm^2/kg^2)(6.0x10^{24} kg)(8410 kg)}{(3.1532x10^7 m)^2} = 3385 N[/itex]
Is there a simpler equation to get the radius? Am I doing it right?
Thank-you
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