calculate the value of acceleration due to gravity using equation g=gm/r^2
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Explanation:
g = GM/r^2
a) Δg ≅ dg/dr Δr
dg/dr = -2GM/r^3 = -2g/r
Δg ≅ -2g/r Δr = -2g(Δr/r)
b) r is measured from the center of Earth. As r increases, g decreases; hence, the minus sign shows the change in g with a change in r.
c) Rearrange the result in part a to get Δg/g ≅ -2(Δr/r) =
-2(4.315 / 6400) = -0.00135 or -0.135% change in g.
Pike's Peak is 4.315 km above sea level.
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