Applying Newton's Universal Law of Gravitation

1. Mar 31, 2016

science_rules

1. The problem statement, all variables and given/known data
This problem only requires to find h, but I want to make sure that I also found Me and g correctly.
Starting with Newton's Law of Gravitation, determine the height h one person has to go from the surface of the earth in order for that person's weight to be reduced to one-third of his/her weight at the surface of the earth. The only information you have is that the radius of the earth is 6.4X106m. Knowing that the acceleration due to gravity at the surface of the earth is 9.8m/s2, determine the acceleration due to gravity at the point were the weight of the person is reduced to 1/3rd.

2. Relevant equations
GMem/r2 = 1/3GMem/Re2
r2 = 3Re2
r = √3(6,400,000)
h = r - Re = 11,085,125.17m - 6,400,000m = 4,685,125.17m
Me = gRe2/G
g = G9.0 X 10-9/6.4 X 106

3. The attempt at a solution
GMem/r2 = 1/3GMem/Re2 Cross out the GMem, leaving: r2 = 3Re2
r = √3(6,400,000) = 11,085,125.17m
h = r - Re = 11,085,125.17m - 6,400,000m = 4,685,125.17m
6400km X 1000m/1km = 6.4 X 106m
h = 4,685,125.17m,
Me = gRe2/G = 9.8m/s2 X (6.4 X 106)2/6.67 X 10-11 = 9.0 X 10-9
Acceleration due to gravity at the point were the weight of the person is reduced to 1/3rd = g = G9.0 X 10-9/6.4 X 106 = 9.37 X 10-3m/s2

Last edited: Mar 31, 2016
2. Mar 31, 2016

science_rules

Last edited: Mar 31, 2016