The value of g at 4RE is [tex]0.61 m/s^2[/tex]
Explanation:
The value of g (acceleration of gravity) at the surface of Earth is given by:
[tex]g=\frac{GM}{R_E^2}[/tex] (1)
where
G is the gravitational constant
M is the Earth's mass
[tex]R_E[/tex] is the Earth's radius
We know that the value of g at the surface is
[tex]g=9.81 m/s^2[/tex]
The value of g at a height of [tex]4R_E[/tex] will be given instead by
[tex]g' = \frac{GM}{(4R_E)^2}[/tex] (2)
Dividing eq.(2) by eq.(1), we get:
[tex]\frac{g'}{g}=\frac{R_E^2}{(4R_E)^2}=\frac{1}{16}[/tex]
And solving for g', we find
[tex]g'=\frac{1}{16}g=\frac{1}{16}(9.81)=0.61 m/s^2[/tex]
Learn more about the force of gravity:
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