Question 377: Gravitation

Question

What is the minimum energy required to launch a satellite of mass ' $m$ ' from the surface of the earth of mass ' $M$ ' and radius ' $R$ ' at an altitude $2 R$ ?

Accepted Answer

The minimum energy required to launch a satellite from surface of earth is equal to the amount of work done against gravity to move it from the surface of earth to a height $h$ and is given by
$$\begin{aligned}
U & =W=G M m\left(\frac{1}{r_1}-\frac{1}{r_2}ight) \
& =G M m\left(\frac{1}{R}-\frac{1}{R+h}ight)
\end{aligned}$$
Here, $h=2 R$
$$\Rightarrow \quad U=G M m\left(\frac{1}{R}-\frac{1}{3 R}ight)=\frac{2 G M m}{3 R}$$

Answer

$\frac{G M m}{2 R}$

Answer

$\frac{2 G M m}{3 R}$

Answer

$\frac{G M m}{3 R}$

Answer

$\frac{5 G M m}{6 R}$

Gravitation

What is the minimum energy required to launch a satellite of mass ' m ' from the surface of the earth of mass ' M ' and radius ' R ' at an altitude 2 R ?

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