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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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
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.
Answered by
7
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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