Question 387: Gravitation

Question

The minimum energy required to launch a satellite of mass $$m$$ from the surface of earth of mass $$M$$ and radius $$R$$ in a circular orbit at an altitude of $$2 R$$ from the surface of the earth is:

Accepted Answer

Apply energy conservation,
$$\begin{aligned}
& U_i+K_i=U_f+K_f \
& \Rightarrow \quad-\frac{G M m}{R}+K_i=-\frac{G M m}{3 R}+\frac{1}{2} m v^2 \
& \Rightarrow \quad-\frac{G M m}{R}+K_i=-\frac{G M m}{3 R}+\frac{1}{2} 	imes m 	imes \frac{G M}{3 R} \
& \Rightarrow \quad K_i=-\frac{1}{6} \frac{G M m}{R}+\frac{G M m}{R} \
& K_i=\frac{5}{6} \frac{G M m}{R}
\end{aligned}$$

Answer

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

Answer

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

Answer

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

Answer

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

Gravitation

The minimum energy required to launch a satellite of mass $m from the surface of earth of mass M and radius R in a circular orbit at an altitude of 2 R$ from the surface of the earth is:

Choose the correct answer: