Question

At a certain height above the earth surface the gravitational acceleration is 4% of its value at the surface of the earth find the height above the earth surface:

Answer 1

Let the force of gravitation on an object of mass m at an altitude h from the

earth's surface distance be equal to f.

Since,

$f=G\frac{M_{e}m}{(R_e+h{)}^2}=m{g}^{\prime }$

So, $g^{\prime }=\frac{G{M}_e}{(R_e+h{)}^2}$

Since $g=\frac{G{M}_e}{R_e^2}$

Therefore,

$\frac{g^{\prime }}{g}=(\frac{R_e}{R_e+h}{)}^2=0.64$

so, $\frac{R_e}{R_e+h}=0.8$

$h=4R_e$

$=4\times 6400km$

$=25600km$