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No, the gravity of this planet will not be greater than that of earth. If the new planet has a mass equal to that of earth, its total gravity will be the same. There is a little ambiguity regarding 4 times earth density and half the earth's diameter if the idea is to keep the mass of this proposed planet the same as the earth. But setting that aside and assuming that the mass of the new planet is the same as earth's, the gravimetric field will be the same. Gravity is proportional to mass, and identical mass yields identical gravity. Now to the good part! The surface gravity of the new planet will be considerably higher than the surface gravity of earth. Both planets have the same mass and the same gravity, but a person standing on the surface of the new planet will be experiencing a whole lot more force pulling on him. All the mass of the new planet is beneath this person, but he's a lot closer to the center of gravityand will weigh a whole lot more.

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Q: If a planet has 4 times the density but half the diameter of earth is it's gravity stronger or less?
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