# Atmosphere of a terraformed 10 km planetoid with Earth gravity

Bernal spheres and other O'Neill cylinders are complicated, maintenance-high and fragile beasts. Someone started to make micro-black-holes and put them in asteroids, in order to have 1 to 10+km rock spheres with ~1g of surface gravity, and started terraforming those.

The micro-black-hole is in a state of equilibrium: too small an event horizon to efficiently feed, the pressure from its Hawking radiation keeps matter from falling into it. Let's assume the entire thing is stable on a geological scale. (How would this work is the subject for another question elsewhere, let's assume here that it does.)

What would the atmosphere of such a planetoid look like? The goal is to make it as adapted to unmodified human life as possible. So the right amount of nitrogen and oxygen, water vapour, ability to retain some hydrosphere, shielding from radiation, stable temperature... Distance to the Sun, rotation period, exact radius and surface gravity that can be tweaked as necessary, and a molten core can rotate at a different speed if it helps generating a magnetic field. What would the ideal (or as best as possible) atmosphere look like, and how stable would it be over a long time period?

This question was originally inspired by the book Revenger by Alistair Reynolds, where most of the Solar system seems to have been converted to those, though most don't seem to have much of an atmosphere.

This question asks for hard science. All answers to this question should be backed up by equations, empirical evidence, scientific papers, other citations, etc. Answers that do not satisfy this requirement might be removed. See the tag description for more information.

• You're probably going to run into issues with how much atmosphere you need for one atmosphere of pressure. The steeper gravity gradient's going to require a much taller atmosphere for the same surface pressure. – notovny Apr 15 at 13:30
• It wouldn't be stable. The problem is the very steep gravity gradient; the 1G at the surface is going to fall off very quickly with altitude, which will result in significant bleed off and accompanying loss of atmospheric pressure. The fact that you would need a taller atmosphere to produce the same amount of surface pressure as @notovny notes would further exacerbate the problem. – Gene Apr 15 at 14:54
• My approach to this problem wouldn't be terraforming but paraterraforming. Meaning that putting a global dome around the place seems to be the best option. A few kilometers hight and some towers for habitation and structural support. That said, active support solutions might be more elegant. Would this suffice for you proposes? – TheDyingOfLight Apr 15 at 20:48

# Calculating GM

If we desire surface gravity to be $$1g = 10 \text{ m}\text{ s}^{-2}$$ (close enough!) at a radius of 10 km, then surface gravity is

$$10 = \frac{GM}{r^2} = \frac{GM}{10000^2}$$ $$GM = 1\times10^{9} \text{ m}^3\text{ s}^{-2}$$

Given the value of the constant $$G$$, this puts the mass of the object at around $$1\times10^{19} \text{ kg}$$; in the range of objects like Mimas, moon of Saturn, belt asteroid Metis, and Hektor, the largest Jupiter Trojan.

# Escape Velocity

$$\sqrt{\frac{2GM}{r}} = \sqrt{\frac{2\times10^{9}}{10000}} = 447 \text{ m}\text{ s}^{-1}$$

Escape velocity is usually expressed in terms of km/s; Earth is about 11 km/s for example. At 0.45 km/s, this planetoid has a very low escape velocity.

Because I have a deep and abiding love of spreadsheets, I have one with the escape velocity of all places of interest in the Solar System. 447 m/s fits in right between Ceres (~500 m/s) and Tethys (~400 m/s), among reasonably well investigated objects.

# Problem

As shown below, with that escape velocity no atmosphere will stay on the planet; certainly not the Oxygen-Nitrogen kind, and certainly not at human-tolerable temperatures.

You will need another solution beyond gravity alone for keeping an atmosphere stable on your planetoid.

• Well, here go hard-SF no-maintenance Baby Planets... – Eth Apr 16 at 13:51

The tag is merciless

And that means I have to say no to your premise. This is a frame challenge.

To add to Kingledion's excellent answer, I believe you have a problem with the Roche limit of the micro black hole in your scenario. In short, the micro black hole might not suck in the planetoid surface, but there's no way to keep the surface predictably solid and stable at a 10 km distance. It appears the planetoid would be torn apart and form a ring around the micro black hole.

• @kingledion absolutely! Let me know when you're ready and I'll even delete my answer so it doesn't compete with what you're doing. – JBH Apr 15 at 20:52
• Turns out the Roche limit doesn't apply for an object inside of another object. But, differential gravity from the black hole tearing apart the asteroid would be an issue. Too complex to get a good math handle on, so I'll just leave my answer as is. – kingledion Apr 15 at 21:16
• @kingledion, All that mass had to form somehow. The micro black hole couldn't have started inside the planetoid (I don't think). Once the planetoid is pulverized, does it apply then? You've piqued my curiosity. – JBH Apr 16 at 0:11
• The question here assumes that the 10km planetoid already exists is stable, so this is outside of the scope of the question. However, both "would it be stable" and "could it be built" make for good questions. Not sure whether to ask them here, in Physics or in Astronomy, though. – Eth Apr 16 at 10:07
• Asked what it would look like and whether it would exist in the first place on Physics – Eth Apr 19 at 16:30