A satellite is moving on a circular orbit around a planet. A sharp impulse is given to the satellite such that it just escapes from the gravitational field of the planet. The impulse can be given in two different ways as shown. The ratio of the impulse given in the two different cases $(\frac{P _{1}}{P _{2}})$ is :-

Question

TestHub · Accepted Answer

Let orbital speed be v; escape speed from that orbit is $2 v$

Case 1 (impulse along motion): $P_{1} = m (2 - 1) v$

Case 2 (impulse perpendicular): $v^{2} + u^{2} = 2 v \Rightarrow u = v$ , so $P_{2} = m v$

$\frac{P _{1}}{P _{2}} = 2 - 1 = 0.414 \approx 0.41$

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