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.
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:
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.
Gravity is proportional to mass and inversely proportional to the square of distance. Two moons of the same mass but of different densities would have different surface gravities because their radii were different. If one moon were made of ice and one of iron the density of the second moon would be about eight times the first; the radius about half and the surface gravity about four times as great.
So how to make the moons smaller? Two sci-fi ways that spring to mind are:
Both these methods have the disadvantage that compression releases a lot of heat so your squashed moon would have to deal with that somehow. Also you loose a lot of surface area - if you halve the radius to increase the surface gravity by a factor of four then you will also reduce the surface area by a factor of four.
As others have already said, the only 2 ways are to decrease the radius or increase the mass of the moon.
Both of them come with problems. Increasing the mass of the moon in an extent that brings the gravity closer to earthlike, means that you would also change it's orbit and or orbital velocity. Decreasing the radius means less surface to live on.
So why change the moon when you can change the people living there way more easy?
Have people be genetically engineered to keep their muscle and bone structure the same way they would be on earth and you have some nice advantages. Those people could easily lift heavy stuff, they could propell flying machines with only their muscles and so on.
All it takes is some treatment that makes sure bones and muscles stay healthy + a bit of engineering newborns to keep genetical drift at bay.
Have you considered (electro-)magnetic forces?
My first thought was that if the colonists had something magnetic on them, they could be pulled toward the surface by electromagnets, for which I have three working ideas:
A non-toxic compound that can be magnetically attracted is spread through their body, much like some elements that are used forensically to identify where someone grew up and get in our system through the food chain but aren't there for any specific purpose. This might even already exist, though we probably don't like putting weird stuff inside us and wasting a lot of energy to create artificial forces for such purposes. This has the great advantage that by spreading evenly through the body we'd perceive gravity perfectly fine (as it would also be in the instruments near our ears that tell us which way is up, a set of three canals per ear filled with a liquid if I'm not mistaken)
Metallic implants, spread across the body, this would probably not give us the complete feeling of gravity unless we also tampered with the canals in the ears. Should be doable, though maybe not very comfortable
Suits with metal woven into them. This would give us a much more even distribution of the forces than implants at regular intervals, and we could again modify the ear canals. These also have the advantage of being adjustable to different conditions, either by just swapping them for another suite in a different environment, or by even being powered and creating small electromagnetic fields themselves. This would also allow them to respond to the following issue:
Other than losing power to the electric field, which would essentially bring you back to microgravity, a far more powerful electric field would equate to bone-crushing gravity, and that would, in fact, be a very interesting hack I'd like to see in a story some day.
An other point is that if you make the implants smaller and compensate by increasing the number, if you keep going you'll end up with the first solution.
Then I remembered a passage from a book I started reading (or rather, hearing, as an audiobook) a while ago, here's what I remember, maybe someone else can correct anything I got wrong. I think I came across this one in Michio Kaku's Physics of the Impossible, where he theorizes on ways to implement some sci-fi ideas in the (not particularly) near future, based on what we know.
The author was saying that sufficiently large electrical fields would manage to magnetize (not sure it's the right term) a lot more than the usual metals, and this would allow artificial gravity. More specifically I believe he was referring to levitation, actually lifting us off the ground. This would require enormous amounts of energy, and would possibly affect us in other ways, but maybe fusion reactors would permit it.
On a side note, I should note that you can get electronics to work under extreme magnetic forces, and it would be conceivable that they are all manufactured so (fluctuations would be more of a problem but they'd be a problem for humans too with my solutions so presumably there won't be any). So this should not stand in the way of the rest of your tech.
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.
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.
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.
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.
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.
If the gravity on the surface of the moon is only 5% of Earth's gravity, it's an airless moon so outside you need (probably heavy) pressurized suites. This will help with the perceived weight (but not with improving movement rates, which are mostly due to ground friction.
On the other side, inside you could have undergound shelters/bases with metal floors and magnetic harnesses worn on the body (this has a lot of drawbacks though).
Criss-cross your planetoid with gigantic underground particle accelerators, whose purpose is to generate collisions in the 126.0 ± 0.6 GeV/c² range, and thus artificially generate short-lived Higgs Bosons to temporarily increase the interaction between nearby matter and the Higgs field.
This means that the rock inside your planetoid will be providing a gravitational effect consistent with a higher level of mass than actually exists in situ.
If you can shrink and arrange these artificial Higgs generators into some sort of Halbach array, then you have artificial gravity deck-plating for your ships too.
How about the idea that humans remain as power hungry as ever. So they found a way to harness the power of a contained black hole that can be created in the core of a moon. Depending on the size of the black hole you can different power outputs thus different gravities can be created?
Since we are talking about moon colonization, I assume humanity has some advanced technology. Introduce black hole generator technology/device which can generate, contain and grow black holes under very well controlled conditions. Then install such a device at the center of the moon and at this point you have two courses of action: a) if you want to keep the moon size, feed off-moon materials to thegenerator, e.g. space junk or nearby asteroids. This, however, would required a lot of mass to be brought to the moon. b) if you dont need the surface area, strip away outer moon layers and feed them to the generator until the size is small enough to gave the desired gravity. This would required considerably less mass to be fed to the generator.
Creating artificial gravity on the surface of a planet or moon is possible without resorting to pseudo-magic. Ever been in a Gravitron? It's a carnival ride where, as the donut-shaped capsule spins, you're plastered to the wall by a centrifugal force of three Gs or so.
As Ben pointed out, this force combined with the natural gravity of the moon makes the floor, if perpendicular to the axis of rotation, feel tilted. Luckily there's a simple solution: tilt the floor. To oversimplify, if you tilt the floor at 45 degrees, and calibrate the centrifugal force to equal the moon's natural gravity, you will have doubled that gravity and the floor will feel flat. For any given ratio of natural to centrifugal gravity, you can tilt the floor such that it's perpendicular to the apparent combined force. (Technically, it should be a slightly concave shape, because the centrifugal component diminishes relative to the natural along the down/in direction, but maybe don't worry about that.) Keep in mind that the bigger the wheel, the better/less nauseating it is.
This results in a long, narrow, circular space with any desired g-force, which would probably make a better running track than full-time habitation. Make the colonists run daily laps to keep their bodies in shape, and let them hop around in low-g the rest of the time... That will keep their Earth muscles in shape, while keeping costs down and avoiding the need for imaginary technology.
In this case in order to increase the gravity of the moon it is technically by increasing the mass by doing so you have increased it's gravity another method is also by decreasing the speed of it's rotation
Rotational Gravity is your best bet. I'm working on a sci-fi universe similar to yours. I have what amounts to ring stations and O'neil cylinder buried into the ground of the either the asteroid or planetoid in question if the gravity is that low. Another solution I have is to use a crater and a wide maglev train like platform that runs the perimeter of the crater. Use the natural slope of the crater/ slope the platforms and the constant acceleration to induce another version of spin gravity.
