In the episode, there were multiple Class-M asteroids around a Class-D Planet. Class-D is a small, rocky, barren planet, and
John W. posted about a Voyager episode (Emanations) where they found a Class-M Asteroid, and the question came up as to whether such a thing would even be possible.
In the episode, there were multiple Class-M asteroids around a Class-D Planet. Class-D is a small, rocky, barren planet, and Class-M means nickel-iron core, water, atmosphere, and overall suitable for human life.
This sent me off into research into what the minimum size might be for a human-habitable planet. Sea Level Pressure on Earth is 101.3 kPa, with 21% Oxygen. Minimum partial pressure of oxygen is 16 kPa, below which we cannot adapt. (15 kPa we lose cognitive functions, peripheral vision, and it gets worse the lower it goes.)
Pure oxygen atmosphere at 16kPa is not feasible either, because of dehydration and fire risks, plus oxygen toxicity. Bump up to 25% nitrogen to mitigate that. We also need a little moisture, at least 30% RH. At room temperature, we're looking at another 1kPa.
Lastly, we need a buffer, because we'll breathe out CO2, and cannot have more than 5%, though Earth normal is 0.04kPa. In a spacecraft, the buffer would depend on air circulation, reaction times, etc..Mir used 34kPa total atmospheric pressure, with 25% Nitrogen, 75% oxygen, and the CO2 and H2O were under 1% absolute.
On a dwarf planet or planet, the buffer would be the difference in pressures across the habitable zones of the planet. Maybe the highest peak would be 14kPa O2, maybe 21kPa total. Maybe the lowest trench would be 36kPa total, and 24kPa O2.
For a third pressure, we're looking at a third of surface gravity. Assuming similar density to Earth, this could be about the size of Mercury. You still want a molten core, so you can have a magnetosphere. Either the rock is young (relatively speaking), or it's a moon for tidal heating. The other options of high radioactivity, or much closer to the star, have issues for survivability.
With a gravity of around 3.3m/s, and a 34 kPa mean surface air pressure, humans would be limited to the bottom 4km of atmosphere. That's totally reasonable. Maybe people get altitude sickness at 2km instead of 6-7km. Fine.
Planet diameter is, again, close to a third, more like 38-39%. So, we're talking about 4900 km in diameter, and about 3.3E23 kg (about 5.5% of Earth). Our largest known asteroid is 1000km, and our largest known dwarf planet is 2600km.
For our solarsystem, a "Class M" asteroid would not be possible. If you get big enough, you move from asteroid to dwarf planet, though this term was not in use during that part of Voyager's production. However, if it were big, they would have just called it a small planet, or even a moon since they're orbiting a Class-D planet. NOTE: We have M-Type asteroids, which a re "metallic". Ceres is a G-Type, which is carbon rich.
If there were a higher density core, you could reduce the size requirements. Remember that asteroids are basically shattered planets, or proto-planets that never could accrete, so you could have one that used to be mostly core material. The earth is 35% iron, 30% oxygen, 15% silicon, 13% magnesium, and 7% other stuff by mass.
Something with higher percentages of other stuff, such as late generation supernovae fragments might be possible. You could get three times the density out of things like Osmium, Platinum, and Gold without being toxic, though at some point, you're looking at terraforming rather than evolved life, and it would be extra extra rare.
You couldn't just do a 2600km 60% iron planetoid, because you wouldn't be able to have enough silicate to protect the surface. The planet would cool too quickly unless it were close to the star (like Mercury). You'd have a very hot side, and a very cold side, or a very narrow window of access on astronomical and geological scales. It would be very magnetic (and conductive), and very reactive with water (part of Class-M is lots of water). The limit is probably somewhere around 40%. Even 43% is only 20-30% increased density. Even Mercury at 65% is too big to be even a Dwarf Planet. The density here is just not enough to bring gravity up to our target on a sub-3000km body.
You might be able to scrape by with 25% gravity, and a breathing apparatus, or if it were a really young planet, or had some other source for keeping the atmosphere relatively thick, but that gets so much more difficult to find AND call "Class-M".
A Chthonian planet that got shattered by impact might work, if it were somehow put into a reasonable orbit. It could have very high density for a small core, 4x that of the Earth. But, they get that size by being a gas giant, then having the atmosphere stripped by being in too close of an orbit to a star. So then, it would have to be shattered, and one of those pieces would have to be ejected into a stable orbit inside of the habitable zone. That really means TWO collisions, one to transfer, and one to remove eccentricity. Not very likely, but maybe even smaller than Ceres might work. You'd need a more radioactive core, otherwise the planet would cool way too quickly. But, a radioactive core, on a shattered planetoid, would have a radioactive surface. Not Class-M.
A planet that had a Platinum inner core, and iron outer core might work. I'm thinking 30% Platinum, 20% iron, 20% oxygen, 12% silicon, 8% magnesium, and 10% other stuff (lots of carbon since it's a smaller planet) could totally work on a 1200km planetoid. Though, this type of body would not really be a "Class-M" body by Trek standards (nickel-iron core), but it might be close enough. "Exotic Class-M" maybe. Might be an issue for heavy metal poisoning, since not all of the increased platinum would be in the core. Excess surface level might mean excess platinum salts... etc.
We still have to be concerned with loss of atmosphere through interaction with other asteroids, solar radiation, maintainingthe magnetic field, etc. The planet would not be habitable for nearly as long, and probably would not evolve life on its own. This asteroid did not. The only life were dead bodies (basically a cemetery planetoid). It's possible even the atmosphere came from the subspace voids, though why the moons had atmospheres, but the central planet did not, does not seem rational to me. The lower pressure means water boils at 60C, which limits our range of surface temperatures (and increases cooking times!)
I did not calculate the scale height, nor any of the stuff to get exact with all of this. I might be off. This is just my mental gymnastics after too much dinner caffeine.
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