



 
Hi Rohan. The formula for gravitational force F is given by F = GMm/R^{2} where G is the gravitational constant (good for the whole universe), M is the mass of one object (say the Earth), m is the mass of the other object (say, you) and R is the distance between the centers of the two objects. So for your question, G, m and M don't change, just F and R. If we say R is the radius of the earth and h is the height about the surface of the earth at which the force is half the original, then we have this: (1/2)GMm/R^{2} = GMm/(h+R)^{2} And we try to solve this now: This is a quadratic. So we can use the quadratic formula to calculate it: h = [ b ± √(b^{2}  4ac) ] / (2a) where a, b and c are the coefficients in ah^2 + bh + c = 0, so in our case a = 1, b = 2R, c = R^2 h = [2R ± √(4R^{2} + 4R^{2}) ] / 2 Now clearly of these two answers, the negative value of h is not all that useful; we want the height above ground, not the height below ground. So the answer is h = [1 + √(2) ] R According to Wikipedia, the mean radius R of the earth is 6,371 km. Thus h = [1 + 1.41421] 6371 = 2639 km. So if you are 2639 km above earth's surface, the gravitation force that the planet exerts on you is half what you experience on the surface. Cheers,  


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