I am building a sci fi universe where humans have colonized the moons of Jupiter. They are very small and thus have low gravity. In fact, some of them have gravity equal to less than 5% of Earth.

What would be a believable sci fi way to artificially increase the surface gravity to make the moons more hospitable?

The answer, unfortunately, is "artificial gravity," and don't explain it.

Speaking from a purely scientific perspective there is no known substitute for mass. The only known way to cause gravity is to have mass (or an ungodly amount of energy which is equivalent to said mass). We simply don't know of anything else.

In science fiction landscapes, artificial gravity is simply too useful to not have. We use it all over. Nearly every major science fiction show set on a spaceship has it. Only a handful dare to deal with microgravity in its true form. There's plenty of handwavy reasons for it, but most shows seem to merely assume that artificial gravity works, and move on with the plot. Some will rely on centrifugal force to create the artificial gravity, but that only applies on stations where your people operate on the inside. Since you're on the outside of a planet, that won't work. That being said, if you were operating a mining expedition, you might be able to spin the planet and have "gravity" face the other way (for a short while, before the rocks of the planet break up and fly off).

If you want to add some pseudoscience, feel free to say something about gravitons. That's the hypothetical particle in QM that is supposed to be responsible for gravity. However, nobody has been able to figure out how to work the math for gravitons, so we don't even know how to look for them, much less create them. Still, as far as believability goes, it's at least the name scientists use when exploring gravity.

And besides, microgravity is pretty cool when you really get down to it.

Two Options

Actual Increased Gravity

Gravity is a product of mass and in the case of a human and a moon, to make the gravitational attraction increase one may either increase the mass of the human or the mass of moon.

1. Increasing the mass of the moon would create a situation most similar to "Earth conditions." One could do this by dumping mass on the outside, or by removing parts of the innards and replacing with more dense material. Either of these options are well outside the capabilities of our current civilization, and even for a civilization that was ready to colonize the Jovian system this would almost certainly be prohibitively expensive or impossible. A bigger problem would be that increasing the mass of Jovian moons would change the orbits of said moons. The largest Jovian moons orbit in stable resonance and adding mass to some/all of them would destroy this stable condition, leading to more erratic orbits and possible collisions between moons or with Jupiter.


2. Increasing the mass of the astronaut/settler is less commonly suggested. For instance, if a settler on some moon experiences 1/3g, and that person wears garments that effectively distribute double their weight across their body, they will feel 1g in their normal movement such as walking or moving their arms. This will not help with things like changing in the shape of the eyes or deterioration of the heart, but it would help a lot with muscle atrophy. This would also not help with other aspects of low-g environments such as drinking fluids, moving objects, etc. For more detail see this.

Artificial Gravity

By artificial gravity I mean simulation of gravity via an "apparent" force. This is most commonly done in science fiction by having people live in rotating habitats shaped as a cylinder or wheel. The (centrifugal) force is outward against the outer edge, which essentially become a floor that curves around. You can visualize and learn more about these schemes here and here. This could be done either on the surface or in orbit:

1. On the surface, the only way to keep the artificial gravity constant would be to rotate with a rotational axis perpendicular to the surface. Otherwise when rotating away from the surface one would feel lighter, then heavier as they approached the surface again (ferris wheel configuration). So if rotating with an axis perpendicular to the surface (merry go round configuration), combined with the moon's gravity, this would make the "floors" of your rotating habitat feel tilted. This is because force would be generated outward (parallel to the surface) but the gravity field would act downward (toward the surface). If you're interested I can try and draw a vector diagram to demonstrate this. The point is there's not really a perfect way to do this at the surface.


2. In orbit, a space habitat would be in freefall, thus experiencing what we call zero-g (like on the ISS). In this case, a rotating habitat could provide a constant 1g by spinning at the right speed for its size. If reaching the surface for mining/farming/building is necessary, it can be done by shuttling or using some future tech such as a space elevator.


3. There is a third option that I think is even less likely but possible. Habitats could be built in the interior, with the floor being the outer surface (think like being upside down in a cave). The moon could then be accelerated rotationally, until the spin simulates an outward force of 1g plus whatever the moon's gravity is. This would allow for living in subsurface dwellings at 1g, but there are big issues: First, the energy required to increase the moon's spin this much would be massive, and it's unclear how exactly this would be done besides literally strapping rockets to the moon. Second, the outward force would be most apparent at the equator, and go to zero at the poles. So in a strip at the equator this is workable, but as one moves away in latitude the effect decreases noticeably. Third, anyone on the outer surface would feel an outward force of 1g (think like if gravity on Earth reversed and you had to hang on to keep from flying off). This relates to the former issue in that it would be most drastic at the equator and not apparent at the poles. Fourth, it's up for debate whether a moon would even stay in one piece rotating fast enough to provide 1g outward. The whole thing might fly off in a bunch of chunks. This idea is commonly proposed for colonizing small asteroids, but would not be a great idea for, say, Io. Though maybe for some of the much smaller outer moons this would be more valid.

What's Likely?

It seems that you really want settlers to live in 1g on the surface of these Jovian moons. It is really unlikely that this setting would ever happen without handwaving some material that "magically" increases density/gravity. In all likelihood your settlers would settle (hah) for living in reduced gravity on the surface and deal with the health effects, or live in 1g in a space habitat and transfer to the surface when necessary.

You would have to increase the planet's mass or core; I'm not sure how you could manage to do that though.

The surface gravity of a spherical body is governed by the following equation:

$$
g propto frac {m}{r^2}
$$

Thus, there are two ways to increase the gravity.

1. Add more mass $m$.


2. Decrease the radius $r$.

Adding more mass

If a moon has 5% of the surface gravity of the Earth then you'll have to add many more moons of material in order to increase the gravity to Earth levels. At this point you're no longer modifying the existant moon. You're building a new bigger moon.

Decreasing the radius

You're better off decreasing the radius. If you decrease a moon's radius while keeping the mass constant then the surface gravity increases. You can do this by transmuting the moon's light elements into denser elements. Human beings can already transmute some elements on a small scale. If generalized to the right elements and scaled up, then this process could increase the surface gravity of a planet or moon.

Option 1:

Depleted uranium shell on the moon's surface, of sufficient thickness to add the mass required, but that would add cost to whatever activity needs to break the surface. Plus the increase radiation hazard, but you're on a moon with no atmosphere or magnetic field. Alternately, a better, but more expensive, solution would be to drive shafts down to the core of the moon and dump the depleted uranium there.

Option 2:

Rather than increasing gravity across the entire surface of the moon, do it only in enclosed, inhabited biospheres. Use high pressure pumps to circulate air by drawing in in from the bottom and releasing it at the top of the biosphere dome. The atmospheric pressure plus the downward velocity of the air should act as a suitable simulation of gravity.