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.
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.
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.