Answer to Question #150297 in Astronomy | Astrophysics for Rejaul

Question

Calculate the value of the g at a hight h = 4R from surface earth ( take g = 10m/s) at the earth

Answer 1

The acceleration due to gravity on the surface of Earth can be found as follows:

$$g=\dfrac{GM}{R^2}.$$

The acceleration due to gravity at a height $h$ from surface Earth can be found as follows:

$$g_{h}=\dfrac{GM}{(R+h)^2}.$$

Since, $h=4R$ we get:

$$g_{h}=\dfrac{GM}{(R+4R)^2}=\dfrac{GM}{(5R)^2}=\dfrac{1}{25}\dfrac{GM}{R^2}=\dfrac{g}{25},$$ $$g_{h}=\dfrac{10\ \dfrac{m}{s^2}}{25}=0.4\ \dfrac{m}{s^2}.$$

Answer:

$g_{h}=0.4\ \dfrac{m}{s^2}.$