Question: Using Newtons Law of gravitation determine the height from thesurface

Question

Question: Using Newtons Law of gravitation determine the height from thesurface of the Earth one should go in order for that person'sweight to be reduce to 1/5 of the weight at the surface of theEarth. The only other information you are given is that the radius ofthe Earth is equal to 6.4 x 106 m. What will be the acceleration due to gravity(g) at thedistance you detemined in first part? Question: Using Newtons Law of gravitation determine the height from thesurface of the Earth one should go in order for that person'sweight to be reduce to 1/5 of the weight at the surface of theEarth. The only other information you are given is that the radius ofthe Earth is equal to 6.4 x 106 m. What will be the acceleration due to gravity(g) at thedistance you detemined in first part?

Explanation / Answer

F = m g F2 / F1 = m g2 / (mg1) =   g2 / g1 F2 / F1 = [(G M m /R22 ) / (G M m /R12 )] = R12 /R22 = 1 / 5 R2 = 5 R1 = 5 * 6.4* 10E6 = 14.3 * 10E6 h = R2 - R1 = (14.3 - 6.4) * 10E6 = 7.9* 10E6 m F2 / F1 = [(G M m /R22 ) / (G M m /R12 )] = R12 /R22 = 1 / 5 R2 = 5 R1 = 5 * 6.4* 10E6 = 14.3 * 10E6 h = R2 - R1 = (14.3 - 6.4) * 10E6 = 7.9* 10E6 m

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