Question

How much less is g 1 km up in the air compared to its value at the surface? Show all work. Values below in mGal.

Answer 1

Value of gravitational acceleration can be determined using the following formula:
Gravitational acceleration=GM/(r^2)
Where,
G=universal gravitational constant=6.673X10^-11 Nm^2/kg^2
r=Distance from Earth's center
M=mass of the Earth=5.98x10^24 kg
For any object situated at the surface of the earth, the distance of that object from the core of the planet = 6.38x10^6 m
Using this value in the provided equation, we get the value of gravitational acceleration=
(6.673X10^-11)X(5.98x10^24)/(6.38x10^6)^2=9.7990 m/s^2=(9.7990X10^5) mgal
=979900 mgal

For a location situated at 1 km into the atmosphere, the distance of the location from the center of the earth increases.
So,r=Distance from Earth's center=(6.38x10^6 m)+10^3 m=6381X10^3 m
So, the value of “g” in this case will be;
g=(6.673X10^-11)X(5.98x10^24)/(6381X10^3)^2=979601 mgal
So, the difference in gravitational acceleration=(979900-979601) mgal=299 mgal
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