Satellite 101

physics problem i cannot figure, thanks for any help?

Hello, I have a problem I am unable to discover, I would like if anyone can try. Thanks. Work and please if you can show an artificial satellite around Earth com-plete each orbit in 101 minutes. What is the value of g at the location of this satellite? The mass of the Earth is 5.98 × 10 ^ 24 kg and the gravitational constant is 6.67259 × 10 ^ -11 N • m2/kg2. An-swer in units of m / s ^ 2.

Hello friend, here is what I came up with: G = (G * Mearth) / d ^ 2 We know G and the mass of the earth, but do not know d. Has 101 minutes to complete its rotation around the Earth. I have not done this in a while, but I am assuming that the satellite has a centripetal acceleration, force and speed. (I hope who is familiar with the centripetal concept.) Bis (centripetal) = (v ^ 2) / r we know that the centripetal acceleration is equal to "g" in the first equation. Let r is equal to D in the first equation. Since we do not know d, we will try to eliminate it. 'S replace this: V (centripetal) = 2 * pi * r / t for the V in Eq acceleartion. A = ((2 * pi * r / t) ^ 2) / r = 4 * pi * r ^ 2 / t ^ 2, R canceled If you were wondering. Now, let to solve for r. r = a * t ^ 2 / (4 * pi ^ 2) Now, substitute this for "d" in the first equation g = (G * Mearth) / d ^ 2 … g = G * Mearth / ((A * t ^ 2) / (4 * pi ^ 2)) ^ 2 g = G * Mearth / ((a ^ 2 * t ^ 4) / (16 * pi ^ 4)) since a = g , let's change the name from A to the G. Now, let's collect the g. G ^ 3 = (16 * pi ^ 4 * G * Mearth) / (t ^ 4) g = square root [(16 * pi ^ 4 * G * Mearth) / (t ^ 4)] After conversion of 101 minutes at 6060 s, the final number I get for g after replacing all values is as follows: 7.7 m / s ^ 2. That yes, I may have made a calculation or other minor errors, but you get the idea. I hope I have helped. Good luck!

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