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Can a planet two, three, or even ten times the size of earth have the same gravity?

For example, I heard that a planet that is two or three times the size of earth but equal or close to the density earth has can have the same gravitational pull. Would that mean that if we were to find a planet with these characteristics would we be able to walk on its surface an experience little to no change in our weight?

Answer 1

A planet with up to around twice the radius or eight the volume of the Earth could have the same gravity.

A planet's or any other body's gravity is directly related to its mass.

The density of the Earth is about 5.51 g/#cm^3#. A planet with double the volume of the Earth would have to have half the density to have the same mass and hence the same gravity. Now 2.75 g/#cm^3# is about the density of some of the lighter rocks.

A planet with eight times the volume of the Earth would require a density of about 0.7 g/#cm^3#. This is about the density of the gas giant Saturn which is the least dense of all of the planets in our solar system.

Keep in mind that a planet's volume increases by the cube of its radius, or a factor of 8, when it is said to be twice the radius of Earth.

Thus, a planet could have Earth's gravity even if it had twice the radius or eight times the volume of Earth.

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Answer 2

Nova Adams

No, gravity depends on both radius and mass, meaning that the gravitational pull of a larger planet is generally stronger.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.