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Please help with Physics Practice question. The moon is about 3.8 x 10^5km from Earth. Show that its average orbital speed about Earth is 1026 m/s

Physics
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This is what I come up with, am I right/close? mv^2 R = GMm/R^2 v = √ GM/R v= √ 6.673e-11*5.977e24/3.8e8 v=1025 m/s
GMm/R^2 gives you Force (grams*distance/seconds^2). However, m*v^2*R will not give you force, you get (grams*distance^3/seconds^2). You have one little mistake in that, I think...but your answer is so close, which is super weird.
weird

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R is in division. Rest of the procedure is fine. Also R should be the distance from the center of the earth and not from the surface. But nonetheless ,radius of the earth is negligibly small(6400km) compared to the distance given. So we can take R to be distance from surface without much inaccuracy.

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