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That being said, if you knew how the gravity field varied throughout all space (including parts internal to the planet), you could determine the distribution of mass (and so, density).

However, if we take a planet to be a spherically symmetric distribution of mass with spherically symmetric layers, then the surface gravity will only depend on the total mass of the planet and the radial distance to the surface. The densities of the different layers will not change the surface gravity (though it will affect how gravity varies within the planet) . This can be seen with Gauss's law for gravity.

So, knowing the surface gravity of Earth, and the radius of the Earth, we could only calculate it's total mass, and from that, the average density of the planet.

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The radius of the moon is about 27 percent the radius of the Earth, but it has a surface gravity of only about 17 percent that of Earth. From this, we can conclude that the average density of the moon is less than that of the Earth (since if it had the same density, it's surface gravity would be 27 percent of Earth's).

If the moon had a surface gravity five times that of the Earth, it would need to have an average density a more than fifteen times that of the Earth's density, which puts its density well above the most dense elements, at least six times as dense as osmium, and more times as gold or lead.

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marcus

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One way to understand all this is notice what Jfizzix says here and make one simple equation out of it with everything (radius density gravity) compared with Earth as a standard:

surface gravity compared with Earth's = G... the surface gravity would be proportional to density times radius...

radius compared with Earth = R

density compared with Earth density = D

So as Jfizz says:

G = D x R

So if you want the planet's surface gravity to be the

If you want the radius to be 1/3 of Earth's you have to make the density D = 3, three times Earth density

1 = 3 x 1/3

Whatever planet you imagine, you always have to have G = D x R (where the numbers are just comparisons with Earth). So if you want the planet's surface gravity to be

6 = D x R

So if you want the planet radius to be 3 times the size of Earth's, you have to make the density TWICE earth density:

6 = 2 x 3

Or if you want the planet to be twice the size of Earth, you have to have the density 3 times Earth's

6 = 3 x 2

Or if you want the planet density to be HALF of Earth's density then you have to make the planet much bigger, 12 times Earth radius:

6 = 1/2 x 12

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