Find the altitude above the Earth's surface where Earth's gravitational field strength would be two-thirds of?

Let "r" be the height measured from center of earth. Then (3/5)GM/re^2 = GM/r^2 r = (re)SqRt(5/3) But you want the height "h" above the earth. So let r = re + h h = (re)SqRt(5/3) - re.

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