At a height equal to earth's radius, above the earth surface, the acceleration due to gravity is-

Concept:

• Acceleration due to gravity: The acceleration achieved by any object due to the gravitational force of attraction by the earth is called acceleration due to gravity by the earth.
  • As each planet has a different mass and radius so the acceleration due to gravity will be different for a different planet.

Acceleration due to gravity of the earth having mass (M) and radius (R) on earth surface is given by:

\(g = \frac{{GM}}{{{R^2}}}\)

Here G is the universal gravitational constant.

Acceleration due to gravity at any depth (h) of the earth’s surface whose distance from the centre of the earth is r is given by:

\(Acceleration\;due\;to\;gravity\;at\;depth\;\left( {g'} \right) = \frac{{g\;r}}{R}\)

Acceleration due to gravity at height (h’) whose distance from the centre of the earth is r is given by:

\(Acceleration\;due\;to\;gravity\;at\;height\;\left( {g''} \right) = \frac{{g\;{R^2}}}{{r{'^2}}}\)

Where G is Universal gravitational constant, r = (R - h) and r’ = (R + h).

Calculation:

New Gravity above the surface of earth g' :

\(g' = g{\left( {1 + \frac{h}{{{R_e}}}} \right)^{ - 2}}\)

\(g' = \frac{g}{{{{\left( {1 + \frac{h}{{{R_e}}}} \right)}^2}}}\)

When h = R_e

\(g' = \frac{g}{{{{\left( {1 + \frac{{{R_2}}}{{{R_e}}}} \right)}^2}}}\)

\(g' = \frac{g}{{{2^2}}}\)

\(g' = \frac{g}{4}\)

Alternate Method Acceleration due to gravity = \(g = \frac{{GM}}{{{R^2}}}\)

R = distance from the centre of the earth.

At a height = R above the earth's surface \(g = \frac{{GM}}{{{(R+R)^2}}}\)

\(g' = \frac{{GM}}{{{4(R)^2}}} = \frac {g} {4}\)