Question

At what altitude above the Earth's surface would your weight be two-thirds of what it is at the Earth's surface? (Assume Re = 6.371 103 km.)

Answer 1

For any one body, the gravitational constant, GM , and your reference mass, m, remain constant. Therefore, you can derive your apparant weight at high altitudes from W = Wo(Ro/R)^2 where Wo = your refernce weight on the body surface, R = the altitude at which the new weight is desired and Ro = the radius of the body surface. Thus, on earth, W = Wo(3963/(3963 + h)^2 where Ro = the earth's radius and h = the height above the earth's surface, in either feet or miles.

I'll let you do the math.