# How much mining can we get out of Pasiphae?

Pasiphae is an irregular moon of Jupiter in a retrograde orbit. It's probably an asteroid capture and is only about 60 kilometers across (compare to Europa's 3121.6 km diameter).

Suppose that I set up a mining colony on Pasiphae with virtually-unlimited access to oxygen, food, etc. so that it can run pretty much indefinitely (this is justified by having consistent access to shipments of food, water, etc. from farms on Earth). The mining colony is on the surface, so once they mine Pasiphae to the point that it starts to collapse in on itself, they have to evacuate to orbit.

Here's the question: how long/much can the miners mine until Pasiphae is no longer stable and collapses, destroying the colony, assuming that the colony runs indefinitely until it's destroyed and that metal and useful ore drilled from the moon is lifted off the surface and away from the gravity well?

• Why does it collapse? Minimal g forces there… Commented Jan 25 at 3:30
• I calculate approximately 2 mm/s^2, but even then we're talking about a hundred trillion tons of asteroid. If the collapse of the asteroid isn't possible, I'd love to know in an answer! Commented Jan 25 at 3:36
• @controlgroup TL;DR it isn't possible unless you mine it apart from the very inside (like, starting right at the core) and even then the collapse probably won't do much other than kill miners. Commented Jan 25 at 5:17
• How do you plan to anchor the mining colony to the surface of Pasiphae? Commented Jan 25 at 9:04
• Strip mining? No reason to dig into the thing at all really. I guess if you're going for an enclosed mining habitat, dig a few meters down, honeycomb the terrain, then collapse, clean, and repeat. Commented Jan 25 at 11:48

I'd say only a few percent of its mass could be mined, but only because of the amount of material actually worth mining -- there's not really a risk of a potential collapse.

The key point is that I'm not convinced that Pasiphae would collapse in on itself at any point. It's significantly smaller and lower-mass than any known object in hydrostatic equilibrium, and well smaller than even some of the more conservative estimates of the minimum mass needed to round itself through its own gravity. What this means is that mining away much of it wouldn't necessarily trigger a collapse; it might well maintain an irregular shape.

I think the better question is how much material on Pasiphae is even worth mining. Wikipedia says that imaging indicates it has much in common with C-type asteroids, and may well be a fragment of one. In that case, its most valuable resources would be water ice, rather than metals (so you might not even need shipments of water!). Water might then take up somewhere in the vicinity of 4-5% of Pasiphae's mass (Beck et al. 2021). If it's indeed the remains of a C-type asteroid, it's not an attractive mining target at all, but could function as a pit stop of sorts for miners en route to mines on other moons of Jupiter.

So realistically, only a small fraction of Pasiphae might be worth extracting, and even that wouldn't be anywhere near enough to cause a collapse.

• Agree the risk of collapse is low. The fact that it's irregularly shaped means it's held together by cohesive forces in the rock, not by gravity - you'd need to physically fracture large chunks of rock before they could fall. Commented Jan 25 at 13:59
• And I would suppose that with careful mining techniques, you could strip the moon down without fracturing the asteroid too much? Commented Jan 25 at 15:22

## Mining station vs. mining colony

Minor frame challenge: why a mining colony on the surface? To my knowledge, the approximately $$\frac{1}{445}$$ of a G of gravity on Pasiphaë's surface does essentially nothing useful or detrimental, whereas if you place a mining space station in a quasi-satellite orbit of Pasiphaë — that is, with the same semi-major axis, inclination, and ascending and descending nodes, ahead of or behind Pasiphaë on its orbital track — it also stays in a constant position and is less prone to solar eclipses. It will still be very easy to get to Pasiphaë's surface from such a colony, given Pasiphaë's escape velocity of approximately 36 m/s (which will fall as it gets mined away), and it won't fall inwards at any point. 36 m/s is almost always (like, 99.999% of the time, exceptions exist) too high a speed for a human to survive uninjured but not too hard to get around with jetpacks or very light rockets, likely low-impulse monopropellant ones — like, Lunar Escape System-level barebones. Hell, maybe a couple of really powerful fire extinguishers strapped together if it's an emergency.

Provided the mining colony must be on Pasiphaë's surface, however, the answer to this question can be one of two things.

## From the inside out

Let's assume miners dig all the way to the core, or close to the core, then hollow it out from there. If they're doing a network of criss-crossing tunnels across the insides I can't really model that.

This excellent Astronomy Stack Exchange answer provides the total downward pressure applied by gravity to a hollow shell, because, like you, many people are apparently interested in hollowing out astronomical bodies:

$$\frac{11\pi G \rho}{8}R^2$$

wherein $$G$$ is the gravitational constant, $$\rho$$ is the density of the shell, and $$R$$ is the radius of the shell. Plugging in 2.9$$\frac{g}{cm^{3}}$$ for density (sources conflict between 2.6 and 2.9$$\frac{g}{cm^{3}}$$) and 30 kilometers for radius gets about 752 pascals of downwards pressure (as opposed to the 2.9 megapascals of the hypothetical hollow moon in the linked example). This represents a net pressure of $$(\pi/8) R^2 P dr$$ wherein $$R$$ is the radius of the overall thing, $$P$$ is the pressure figure, and $$dr$$ is the derivative of the shell's thickness (i.e. a dimensionless number equal to the shell's thickness in km). This is then divided over an area of $$A = \pi W dr$$, wherein $$W$$ is the radius of the hollow section and $$dr$$ is another derivative of the thickness of the shell, to find the downwards pressure across the inside of the shell.

Plugging in values of $$R$$ = 30 km, $$P$$ = 752 pascals, $$dr$$ = 29.9 (representing a shell thickness of 29.9 kilometers), and $$W$$ = 0.1 (representing a hollow area 200 meters across) gets me a pressure figure of about 8.46 megapascals, which is not an unreasonable level of pressure for rock to withstand. This math breaks down the closer you get to the center, with the pressure asymptotically approaching infinity, but provides a roughly accurate indicator of roughly how small a hollow sphere around the core can be without causing a collapse.

In other words, this means the hollow area in the middle can be as small as 200 meters across, and potentially somewhat smaller depending on rock compressive strength, without the outer layers collapsing onto it. The larger that radius gets, the greater the ratio of rock strength to downwards force; if Pasiphaë is reduced to a shell 100 meters thick with a hollow sphere 29.9 kilometers in radius within, the downwards pressure on that sphere is only ~95 pascals, although at that point imperfections in the rock likely mean it'll crack and break up into a debris field. The image of a thin little Pasiphaë-shaped balloon of rock where a moon once stood, pretending to be it while actually being hollow, is amusing but unfortunately impossible.

To sum this up: if you want to mine it from the inside out, mine down to about half a kilometer from the center, for safety's sake, and then mine out a hollow shell between the outer shell and an inner sphere surrounding the core. The shell will be too strong for gravity to collapse it (and it will get stronger the further out you mine) while the sphere around the core can be mined out once the shell has been disconnected from it.

Note that all these values depend on what you plug into the equations, but the general concepts should remain the same. For instance, if it turns out Pasiphaë is a little less dense, that reduces downwards pressure somewhat but implies some of it might be made of water ice, meaning lower compressive strength, meaning maybe you want to mine down to two kilometers away from the core instead of half a kilometer or somesuch.

If you're wondering why this can't be done with larger objects: they have hot cores that kill your miners and drills. I'm pretty sure a body has to be about the size of 4 Vesta to do that kind of thing with rock and metal; Vesta is internally differentiated which means that there's enough heat to melt its guts and rearrange them. Pasiphaë is nowhere close to large enough for that, as far as I'm aware, although it might be warm enough on the inside for volatiles to do something similar.

## From the outside in

If you mine from the outside in (strip mining, so to speak), things become significantly easier, simpler, and less mathematical. In this case, think of Pasiphaë as a dog with a tick (the mining colony) attached to it, rather than thinking of the mining colony as sitting on Pasiphaë.

In this case you simply mine Pasiphaë from the outside down/in, layer by layer, until you have the mining colony sitting atop a 30-kilometer deep wedge of rock. Then you just mine the wedge of rock, starting from the side opposite the mining colony and ending at it.

## In all cases, the answer is the same: the entire thing. You can mine the entire moon into nonexistence.

However long that takes you depends on the rate at which you mine it.

Perhaps there's a ceremony for when the last chunk of Pasiphaë is hauled into the mining station and processed. Maybe the last couple hundred tons are broken up and sold as souvenirs: "look, Ma, I have a piece of a long-dead moon!"

• But what do you do with the spoil? Only a few percent of what you dig up is likely to be useful and worth shipping away, so the rest will hang around and gravitate. Commented Jan 25 at 6:26
• @MikeScott Put it in bubbles with attached laser sails, then push the bubbles elsewhere in Jupiter's gravity well via big laser. Alternatively, use solar sails if you don't have the materials science, laser physics, or power supply for laser sails, but solar irradiance is weak out at Jupiter so that'll take longer. If pulverized it'll make good radiation shielding for things where mass efficiency isn't an issue, and if mixed with certain biologically essential elements it'll make good fertilizer, meaning you can just ship said elements out to Jupiter without shipping heavy substrate with them. Commented Jan 25 at 6:35
• @MikeScott In space nearly everything is valuable. Commented Jan 25 at 11:50
• @MikeScott With an escape velocity of 36 m/s, decent pitchers could throw fist-sized chunks of rocks out of the gravity well. Maybe encourage the miners to play golf or baseball with the tailings (or have snowball fights) during their off hours. As the remaining mass shrinks, it'll become harder to keep the chunks from floating away on their own. Only downside is the novelty will probably wear away long before the moon does. Commented Jan 26 at 19:43

You can mine it all.

once they mine Pasiphae to the point that it starts to collapse in on itself, they have to evacuate to orbit

60 kilometers across is just a big lump of loosely connected material, it is far from being under any form of hydrostatic equilibrium, meaning that mining will have not to much to worry about lifting whatever ore is being extracted and also that there is not so much collapsing happening.

If any, they need to worry that fragments produced by mining do not get escape velocity and fly away.

The mining term that you want is "Recovery Ratio" in mining this is how much of the minable material can be removed. For terrestrial underground mining the ratios vary greatly but average around 50-60%. Assuming lower gravity would lead to less support structure required you might get slightly higher, but real world numbers would be the most likely basis for a realistic estimate.

### Frame Challenge: Space mining will not be done in site.

There's no reason to mine asteroids or even small moons where they are. It is cheaper to move them.

Why go through the trouble of taking the mining setup to the moon when you can just tow it to you? By mining in-site, you need to make THREE trips. One to send the mining equipment, another to bring the ore back, and a third to retrieve the equipment.

Save two of those. Just strap some rockets onto the rock you want to mine, and bring it home. Right next to where the orbital manufacture will use said ores.

Time is not an issue. Yes, moving an asteroid from the belt to High Earth Orbit might take a few years, but you can even program them to arrive as they are needed, saving fuel if the demand is low. And if ore prices go up, burn more fuel and bring it back earlier.

Small moons can be accelerated out of orbit and then towed by the rockets.

But what if the asteroid has a low ore content? Assuming it is still economically viable to mine. Break it down, and bring home the chunks you want.

This way, the mining companies do not need to pay a premium to have people or expensive robots go all the way to Jupiter's orbit and do stuff there.

Even if the ores are needed in Jupiter, towing the moon to a better place is easier than moving an entire mining colony there.

• The vast, vast, majority of material from a mining site is waste. The amount of energy to "tow a moon" is literally astronomical. The amount to ship the output of a refinery/smelter is orders of magnitude less. You do have to take into account setting up the refinery/smelter, but it is still going to be very heavily weighted towards onsite mining, even more so if Nostromo-type ships are viable. Commented Jan 25 at 17:22
• The moon in question weighs 300 trillion metric tons. If one has access to enough energy to move that much mass any significant amount — especially out of Jupiter's gravity well, the second-deepest in the Solar System besides that of the Sun itself — it's probably incredibly easy to simply ship everything out there as well. Commented Jan 25 at 20:07
• The mass of the mining equipment is utterly dwarfed by the mass of the material it will be used to process, and by the unwanted waste materials. You will not be going all the way out to Pasiphae for silicon and oxygen and it would be a waste of resources to haul them back. Mining on-site and processing the mined material to extract what you actually want vastly reduces the amount of mass you have to transport. There's also little reason to retrieve the equipment...there's nothing for it to do back home. Send it to the next asteroid or moon. Commented Jan 26 at 19:30