It seems to me that this setup is equivalent to “skim air from the top of Earth’s atmosphere, drop it back to Earth, extract gravitational energy”, with some more details that don’t change much. This fails for density reasons, unless I’m missing something.
You’re right that it superficially resembles the Earth atmosphere example, but there’s a crucial difference that makes it more interesting.
In the Earth case, you’re fighting against atmospheric buoyancy. The air you’re trying to drop is surrounded by denser air, so no net energy gain.
In my setup, the helium that accumulates near the shell has escaped the asteroid’s atmosphere entirely and is drifting in near-vacuum. When you capture it at the shell (e.g. 31 radii out, gravity ~0.1%), you can lower it through essentially empty space (no buoyancy to fight against).
The key insight: atoms that barely escape arrive at the shell with near-zero kinetic energy, creating a density enhancement. Most will arrive radially and scatter in all directions as they hit a microscopically jagged 5 K surface. Some will bounce multiple times at different parts of the shell before returning to the asteroid.
You will get an ever so slight density increase close to the shell compared to the near-vaccum between the atmosphere and the shell. You’re not “skimming atmosphere”—you’re collecting atoms that have already paid their full gravitational escape cost.
I’ve laid out a bit more of the mechanism in my response to AnthonyC if you’re interested in more details. Happy to address specific objections!
The interior surface of the shell is larger than the surface of the asteroid, reducing the density. I don’t know if this completely compensates for that effect or if there’s also something else involved, but you didn’t even consider it. (And if you try to fix this by making the asteroid so big that it’s more like a flat sheet, the flat sheet’s escape velocity, at the scale where it behaves like a flat sheet, is infinite.)
It seems to me that this setup is equivalent to “skim air from the top of Earth’s atmosphere, drop it back to Earth, extract gravitational energy”, with some more details that don’t change much. This fails for density reasons, unless I’m missing something.
You’re right that it superficially resembles the Earth atmosphere example, but there’s a crucial difference that makes it more interesting.
In the Earth case, you’re fighting against atmospheric buoyancy. The air you’re trying to drop is surrounded by denser air, so no net energy gain.
In my setup, the helium that accumulates near the shell has escaped the asteroid’s atmosphere entirely and is drifting in near-vacuum. When you capture it at the shell (e.g. 31 radii out, gravity ~0.1%), you can lower it through essentially empty space (no buoyancy to fight against).
The key insight: atoms that barely escape arrive at the shell with near-zero kinetic energy, creating a density enhancement. Most will arrive radially and scatter in all directions as they hit a microscopically jagged 5 K surface. Some will bounce multiple times at different parts of the shell before returning to the asteroid.
You will get an ever so slight density increase close to the shell compared to the near-vaccum between the atmosphere and the shell. You’re not “skimming atmosphere”—you’re collecting atoms that have already paid their full gravitational escape cost.
I’ve laid out a bit more of the mechanism in my response to AnthonyC if you’re interested in more details. Happy to address specific objections!
The interior surface of the shell is larger than the surface of the asteroid, reducing the density. I don’t know if this completely compensates for that effect or if there’s also something else involved, but you didn’t even consider it. (And if you try to fix this by making the asteroid so big that it’s more like a flat sheet, the flat sheet’s escape velocity, at the scale where it behaves like a flat sheet, is infinite.)