Question

A satellite is in a circular orbit close to the surface of a planet. At some point it is given an impulse along the direction of motion, causing its velocity to lncrease $n$ times. It now goes into an elliptical orbit. The maximum possible value of $n$ for this to occur is

• A. $2$
• B. $\sqrt{2}$
• C. $\sqrt{2}+1$
• D. $\frac{1}{\sqrt{2}-1}$

Answer 1

Answer: (B)

$\sqrt{2}$

Initial velocity of satellite$v=\sqrt{\frac{GM}{R}}$
The satellite will remain in elliptical orbit as long as $v<v_e$ escape velocity.
Also$v_e=\sqrt{\frac{2GM}{R}}$
$\therefore \eta v\le \le v_e$ or $\eta \sqrt{\frac{GM}{R}}\le \sqrt{\frac{2GM}{R}}$
$\eta \le \sqrt{2}$ or ${\eta }_{max}=\sqrt{2}$