Question

As you go above the Earth's surface, the acceleration due to gravity will decrease. Find the height, in meters, above the Earth's surface where this value will be 1/310 g.

m

Answer 1

using equation

g = G M / ( R + h )²

then the ratio can be written as

g₂ / g₁ = R² / ( R + h )²

( 1 / 310 ) g / g = ( R / R + h )²

1 / 310 = ( R / R + h )²

( R + h / R )² = 310

R + h / R = 17.606

R + h = 17.606 R

h = 17.606 R - R

= 16.606 R

above says that the height is 16.606 times radius of the earth

so the height is

H = 16.606 x 6371 x 1000

H = 105796826 m