A spherical uniform planet is rotating about its axis. The velocity of a point on its equator is V. Due to the rotation of planet about its axis the acceleration due to gravity g at equator is 1/2 of

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A spherical uniform planet is rotating about its axis. The velocity of a point on its equator is V. Due to the rotation of planet about its axis the acceleration due to gravity g at equator is 1/2 of g at poles. The escape velocity of a particle on the pole of planet in terms of V.

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At the pole there is no rotational effect: $g_{p o l e} = \frac{GM}{R ^{2}}$ . At the equator: $g_{e q} = \frac{GM}{R ^{2}} - \frac{V ^{2}}{R} = \frac{1}{2} g_{p o l e}$ , so $\frac{V ^{2}}{R} = \frac{GM}{2 R ^{2}} \Rightarrow \frac{GM}{R} = 2 V^{2}$ . Escape velocity from the pole: $V_{e} = \frac{2 GM}{R} = 4 V^{2} = 2 V$ .

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