Applying Newton's Universal Law of Gravitation

[science_rules]

Homework Statement

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.

Homework 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

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

 

[science_rules]

Homework Statement

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.

Homework 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

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
g = G9.0 X 10^-9/6.4 X 10⁶ = 9.37 X 10^-3m/s²