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A space craft of mass ‘m’ is flying with its engine off in the gravitational field of a star of mass M that is much larger than the mass of the space craft. Speed of the space craft at great distance from the star is V. After passage around the star, when the space craft is again at great distance from star, the space craft moves with speed V, but at an angle $60^{0}$ with initial direction of motion. Choose the correct option(s)

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Maximum speed of space craft during its motion is 2V

Minimum distance of space craft from the star is $\frac{G M}{V^{2}}$

Angular momentum of spacecraft about star is $2 \frac{G M m}{V}$

Angular momentum of spacecraft about star is $\sqrt{3} \frac{G M m}{V}$

answer is B, D.

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Detailed Solution

$r_{\min} = a (e - 1) L = m \sqrt{G M a (e^{2} - 1)}$

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