A small asteroid is orbiting around the sun in a circular orbit of radius \( r_{0} \) with speed...

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A small asteroid is orbiting around the sun in a circular orbit of radius \( r_{0} \) with speed \( V_{0} \). A rocket is launched from the asteroid with speed \( V=\alpha V_{0} \) 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 effect of other planets)
[KVPY 2012]
(a) \( \sqrt{2} \)
(b) 2
(c) \( \sqrt{3} \)
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