Explanation:
What could be the value of g on the surface of Earth if its mass were twice as large, and the radius also twice what it is now?
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Andreas Xi
Updated 1 year ago
G would be half of what it is now, since it is proportional to mass and inversely proportional to distance squared. Such a planet would be only a little more dense than water, quite similar to Neptune, but smaller.
See below for the answer to the (completely different) original question:
What would be the value of g on the surface of the earth if its mass was twice as large and its radius half of what it is now?
G would be eight times larger, since it is proportional to mass and inversely proportional to distance squared. [Thanks to Niels for pointing out an earlier mistake]
The Earth would need to be 16 times as dense, though, which is quite impossible. The density of rock is around 3 g/cm^3, of iron around 8 and the Earth overall (consisting mostly of those two materials, including compression) around 6. The densest known material is around 22 g/cm^3 (Osmium), which is only roughly 4 times as much. Even when you consider increased compression, no planet could possibly satisfy your conditions, even if it were made of pure Osmium.
