A planet with radius 128 km: ocean

The planet has a radius of 128 kilometres and the surface gravity is the same as Earth's. My calculations have discovered that the planet would have a density of about 50 times the Earth's: $$g_P=g_E$$ $$\frac{GM_P}{(r_P)^2}=\frac{GM_E}{(r_E)^2}$$ $$\frac{\rho_PV_P}{(r_P)^2}=\frac{\rho_EV_E}{(r_E)^2}$$ $$\frac{\rho_P\frac43\pi(r_P)^3}{(r_P)^2}=\frac{\rho_E\frac43\pi(r_E)^3}{(r_E)^2}$$ $$\frac{\rho_P(r_P)^3}{(r_P)^2}=\frac{\rho_E(r_E)^3}{(r_E)^2}$$ $$\rho_Pr_P=\rho_Er_E$$ $$\rho_P\times128\ km\approx\rho_E\times6371\ km$$ $$\rho_P\approx\frac{6371}{128}\rho_E$$ $$\approx49.78\ \rho_E$$ $$\approx49.78\times5.51\ g/cm^3$$ $$\approx274.29\ g/cm^3$$ $$=274290\ kg/m^3$$ I am aware that such a planet would be denser than the core of the sun. However, I am handwaving the problems, such as what the planet would be made of, etc. The density of the core is at around $320000\ kg/m^3$.

My question:

This planet has an ocean taking up roughly the same portion of surface area as the Earth's. How deep can it be? (The bottom must be liquid water) What else can be said about it?

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posted about 7 years ago

user_194421‭

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