# The acceleration due to gravity at a height(1/20)th the radius of the earth above the earths surface is 9m/sec sq. it's value at a point at an equal distance below the surface of the earth is

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by santhoshkrish0302

2015-10-17T16:45:12+05:30

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Gravity g = G M / R²

gravity above Earth's surface = g'  ,  at altitude h.
g'/g = R² / (R +h)² = 1 - 2 h/R

gravity below Earth's surface = g"   at a depth d and radius R".
M" / M =  R"³ / R³
g" / g = (R² / R"² ) * (R"³ / R³)    =  R" / R
=  (R - d) / R = 1 - d/R

g" / g'  =  (R - d) / (R - 2 h)

if d = h = R/20  then:

g " / g'   =  (19R /20) / (18R/20)  = 19/18

g" = 19/18  * 9 m/sec²  = 76/9 = 9.5 m/sec²
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gravity decreases as much as twice while going above Earth, as compared to going below surface.