A spacecraft travelling with speed V approaches a planet of mass M along a straight line whose perpendicular distance from the centre of the planet is p. When the spacecraft is at a distance c from the planet, it fires its engines so as to multiply its current speed by a factor k (0 <k <1), its direction of motion being unaffected. [You may neglect the time taken for this operation.]

Find the condition that the spacecraft should go into orbit around the planet.

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