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I'm trying to do calculations for a planet around the size of Mercury with the gravity of Earth. Would the gravity be too high for a planet this size? Do I have to change some numbers, or is this plausible? Right now, the mass of the planet is around 3.3 x 10^23 kg, and its gravity is 9.7 m/s^2.

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marked as duplicate by Mołot, Don Qualm, Alex2006, Trish, Frostfyre Feb 6 at 13:44

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  • $\begingroup$ Potentially, you could have a "planet" which was really one of a binary star system, where the secondary star was a sub-brown-dwarf. I think a cooled sub-brown-dwarf could be dense enough, but I think the smallest we know of is a little larger than Jupiter, so it potentially matches the density, but not the size requirement. $\endgroup$ – Baldrickk Feb 6 at 13:22
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Radius of mercury: 2440km Mass: 3.3*10^23 Surface gravity: 3.7 m/s

It's a simplification but to get 3 times the gravity you need 3 times the mass.

The current density of Mercury is around the same as Earth at 5.43 g/cm3 (Earth is 5.51).

So you would need it 3 times as dense which is hard as all the rocky planets are around that same density. (Gas giants are less dense than rocky). - you need the material of the planet to have a density of around 16.5 g/cm3.

Solid Iron comes in at 7.8g/cm3 but that's not getting there.

http://www.ambrsoft.com/CalcPhysics/Density/Table_2.htm

Gold gets up to 19.3g/cm3 and Platinum to 21.4g/cm3. Tungsten and Uranium are also up in that range (but a planet made of Uranium would have .... issues). Even Lead is not dense enough.

So realistically speaking in a natural planet the answer is no. The only way it could happen is if the planet is made almost entirely of materials like Gold, Platinum, Tungsten and Uranium. All of which are rare.

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  • $\begingroup$ Planet of gold or platinum would looks stunning, though. Not really livable, but stunning. $\endgroup$ – Nyakouai Feb 6 at 10:12
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    $\begingroup$ (+1) Note that this is by increasing your proposed mass three times. if you want to stick with your specified measures of 3,3E23 kg of mass and surface gravity of 9.7 m/s2 your planet would be only around 1500km of radius (far smaller than Mercury), and thus a density of about 23 g/cm3. This is above the densities of any stable element. $\endgroup$ – Rekesoft Feb 6 at 10:19
  • $\begingroup$ @Rekesoft Was that comment meant to be on the Q? I took the question to mean "radius of mercury but surface gravity of earth" not "mass of mercury and gravity of earth". I've not done the math but it sounds right that it would be even more impossible the other way around. $\endgroup$ – Tim B Feb 6 at 10:28
  • $\begingroup$ @TimB In the question the OP says "about the size of Mercury" and provides numbers for both mass and surface gravity. I cannot do math with "abouts" so I used the only numbers given to estimate the radius. $\endgroup$ – Rekesoft Feb 6 at 10:31
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    $\begingroup$ +1. Btw, surface gravity would be Earth-like, but low orbits would require faster speeds due to the different gravity gradients. $\endgroup$ – Renan Feb 6 at 11:02

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