Question

A satellite is in a circular orbit of radius $r$. At some point it is given an impulse along its direction of motion causing its velocity to increase $n$ times. It now goes into an elliptical orbit with the planet at the centre of the ellipse. The maximum possible value of $n$ could be

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

Answer 1

Answer: (A)

$\sqrt{2}$

As long as the orbital velocity $v_o$ of the satellite is less than its escape velocity $v_e$, it will revolve around the planet but $v_o=\sqrt{2}{v}_e$, so maximum possible value of $n$ is $\sqrt{2}$, so that it will revolve around the planet