Question

A small asteroid is orbiting around the sun in a circular orbit of radius $r_0$ with speed $V_o$. A rocket is launched from the asteroid with speed $V=\alpha V_o$, where V is the speed relative to the sun. The highest value of $\alpha$ for which the rocket will remain bound to the solar system is (ignoring gravity due to the asteroid and effects of other planets)

• A. $\sqrt{2}$
• B. $2$
• C. $\sqrt{3}$
• D. $1$

Answer 1

The correct option is A $\sqrt{2}$

For rocket to remain bounded the max value of $\alpha$ can be found by using $\frac{m(\alpha V_o{)}^2}{2}=\frac{GMm}{r_o}=m{v}_o^2$

so $\alpha =\sqrt{2}$