A.) At what height above Earth\'s surface is the gravitational acceleration redu

Question

A.) At what height above Earth's surface is the gravitational acceleration reduced from its sea-level value by 0.30%?

Express your answer to two significant figures and include the appropriate units.

B.)

At what height above Earth's surface is the gravitational acceleration reduced from its sea-level value by 3.0%?

Express your answer to two significant figures and include the appropriate units.

c.)

At what height above Earth's surface is the gravitational acceleration reduced from its sea-level value by 30%?

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Radius of earth, r = 6.371*10^6 m
A)
Let height be h
At sea level,
g = G*M/r^2
At height h,
g' = G*M/(r+h)^2
It is reduced by 0.3 %
SO,
new g = 99.7% of old g
g' = 0.997*g
G*M/(r+h)^2 = 0.997*G*M/r^2
0.997*(r+h)^2 = r^2
0.997*r^2 + 1.994*r*h + h^2 = r^2
0.003r^2 - 1.994*r*h - h^2 = 0
Put the value of r and solve for h
B)
Here
use:
g' = 97% of g
g' = 0.97*g
C)
Here
use:
g' = 70% of g
g' = 0.7*g

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