Question

What is the orbital radius and the speed of o sycronous satellite which orbits the earth once evry 24h? Take G=6.67x10^11Nm^2/kg^2, Mass of the earth is 5.98x10^24kg

Answer 1

\[T ^{2} = (4\pi ^{2}/GM) \times R ^{3}\]\[(24)^{2} = (4\times3,14^{2}\div(6,67\times10^{-11}\times5,98\times10^{24})) \times R ^{3}\]\[R \approx 17,9\times10^{4}m\]\[mV ^{2}/R = GMm/R ^{2}\]\[V = \sqrt{6,67\times10^{-11}\times5,98\times10^{24}/ 17,9\times10^{4}}\]\[V \approx 6,95\times10^{4}m/s\]
;)

Answer 2

T should be 86400

Answer 3

yeah T is "86400", i'm sorry for that, just plug in 86400 where i put "24"