Space/Science — HabitableZone

Space/Science » in reply to re: Smallest exoplanet!

Big Earths = Waterworlds

This body would have a surface gravity around 2g if it were predominantly rocky, as the reference suggests.

To see this, consider an Earth-like world with 8 times the mass, but otherwise identical.

It would have twice the radius, so gravity at its surface would be 8x that on Earth (due to the mass) but lessened by 1/4 due to the inverse square law, so only 2g

For a rocky planet, gravity and radius scale as the 1/3 power of Mass (neglecting any additional compaction due to higher pressure at the core - worth around 5%)

For this 14 Me body, the scaling would be 2.4

Now, this is where things get interesting. If that planet had the same ratio of water as Earth does, its oceans would be 2.4 times deeper (trust me, the scaling works the same because the water is spread over the surface, which scales as the square of radius). At the same time, mountains would be 2.4 times smaller, since g is higher but rock strength is similar.

On Earth, Everest is 8 km above sea level, or 12 km above the mean level of the ocean floor. So on this planet, the highest mountains would be ~12/2.4 km high (5 km).

The oceans on Earth average 3 km deep. One can get into confusing arguments about how much water is used up soaking the pore spaces in the rocks, but neglecting that, the oceans on the hypothetical mega-Earth would be 2.4 times this = 7 Km deep.

Therefore, we would have a giant waterworld with global oceans and no land, unless it was much poorer in volatiles than our Earth

(BTW, atmospheric volatiles probably scale, too. 2.4 times the atmospheric column density, and 2.4 times the g gives a similar thickness of atmosphere, but 2.4^2 times the pressure = 5.8 bars.

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