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The force between two objects due to gravity is proportional to the product of the two masses. That part doesn't change compared to his weight on earth.

The force is also inversely proportional to the square of the distance between their centers. On the planet with a diameter equal to twice the earth's diameter, the distance is changed by a factor of 2, so the force is changed by a factor of (1/22) = 1/4. His weight on the alien planet is 25% of his weight on earth. Naturally we're assuming that the planet's mass is symmetrically distributed. It doesn't have to be homogeneous with constant density throughout, but it has to be evenly spread around the center. The geometric center of the sphere also has to be its center of mass, with no big off-center lumps.

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