# earth

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a space traveller determines the radius of a planet to be half of earth . After landing on its surface , he finds the acceleration due to gravity to be twice of that of surface of earth. Find the ratio of mass of planet to the earth

• earth -

acceleration on earth: GM/r^2
acceleration on planet X: GM'/(r/2)^2

GM'/(r/2)^2 = 2GM/r^2
4M'/r^2 = 2M/r^2
M' = M/2

makes sense, since with the same mass and half the radius, the force would be 4 times as much.

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