Question

A satellite is orbiting around the earth at a distance 5 times the radius of the earth from its centre. Of the acceleration due to gravity on the earth is 9.8 m/s^2 , calculate the acceleration due to gravity acting of spaceship. ​

Answer 1

Given:

A satellite is orbiting around the earth at a distance 5 times the radius of the earth from its centre.

To find:

Gravitational acceleration on the spaceship?

Calculation:

General expression for gravitational acceleration at a height h from earth surface:

$\therefore \: g' = \dfrac{g}{ {(1 + \frac{h}{r} )}^{2} }$

Now, height from centre of earth = 5r, so height from earth surface is :

$\therefore \: h = 5r - r = 4r$

Now, continuing with the calculations:

$\implies \: g' = \dfrac{g}{ {(1 + \frac{4r}{r} )}^{2} }$

$\implies \: g' = \dfrac{g}{ {(1 + 4)}^{2} }$

$\implies \: g' = \dfrac{g}{ {(5)}^{2} }$

$\implies \: g' = \dfrac{g}{25}$

$\implies \: g' = \dfrac{9.8}{25}$

$\implies \: g' = 0.392 \: m/ {s}^{2}$

So, gravitational acceleration on spaceship is 0.392 m/s².