This post will be weird. I talk about childbirth. Also, my idea is weird. But enough said. Let's begin.
One major problem on Mars (or, anywhere else, for that matter) is that the gravity will be different. As in, you will weigh just over one third of your Earth weight on Mars. This....could create some problems.
The largest problem, at first glance, is the same problem experienced by astronauts in the microgravity of space: loss of muscle and bone mass. A person who lives on Mars for too long, and anyone born on Mars, will probably not be able to return to Earth gravity without extreme discomfort and danger, because our bodies only grow strong enough for our environments. If my muscles think I weigh 52 lbs. and suddenly I go back to earth and weigh 140, my muscles won't be able to cope.
A related problem is bone growth. I might be born on Mars, but my genes are still designed for Earth gravity. Most of you will know that bones grow faster at night, because they are not being pressed by gravity and activity as much. As a result, the lower pressure from Mars gravity poses a major problem. Our bodies, normally programmed to grow only when we rest, may be convinced that we are always resting, and therefore that we should always be growing. Giantism could thus become epidemic, along with all of its related health problems. The effects of low or micro gravity on children have not been studied thoroughly, since all the people who have spent substantial time in space were fully grown adults. So, really, we don't know how bad this might get. It could be that just standing upright is enough to convince your bones not to go into growth mode, and if so, this is a non-issue.
Another potential problem is childbirth. Not being female, I'm not an expert, but I do know that kids skulls are subjected to some very intense pushing and smooshing on the way out, and that their skulls are soft enough on Earth that forceps delivery can sometimes cause skull fractures. If, as I suspect, low gravity means more fragile bones for the fetus, then mothers giving birth could potentially crush the skulls of their babies with the force of the muscles required to push them out. Lower gravity could also lead to an increase in breech births. The exact causes of breech births are unknown (We don't even know why most babies come out head first: I read everything from "the baby gets top-heavy" to "it's instinct" to "the mother just needed to role on the floor"), but it seems likely that there is a gravitational component involved in aiding babies when they determine which way is down. If that is the case (and I should stress again, I don't really know for sure), then lower gravity would make it harder, increasing complications.
All other complications aside, the real issue is bone and muscle mass and density. This is the problem we KNOW is real, and it would mean that Mars-born humans would have a lot of trouble making trips to Earth, which we know that someday they will probably want to do. Ergo, we must try defying gravity (teehee).
To get ideas for this, I looked into possible spacecraft designs. One major school of thought regarding interplanetary and interstellar spacecraft is to build torus shapes as habitations, and spin them to simulate gravity via centrifugal force. Build a big ring, spin it at the right speed, and stand people inside it, and they are pulled outward by exactly the same level of force that pulls us downward on Earth. The bigger the circle, the fewer the rpms need to be. Voila, microgravity problem solved. People can now stay in space as long as they want without getting all weak and breakable.
On a planet this becomes more difficult, because the planet is pulling down at the same time that the torus is pulling outward. You might have experienced a carnival ride where you stand in a padded, circular room, the room spins, and then the floor falls away. You don't fall out because you are pinned to the wall by centrifugal forces, but you can't move either, because the force needed to pin you to a wall safely is perhaps 2 Gs, and pulls you heavily into that padded wall. Less force, and you might fall out of the ride, because Earth's gravity is still present. We can only use centrifugal force to ADD gravity, we can't get rid of the existing gravity.
Mars gravity, however, is less. So we can reach Earth gravity if we can add the right amount. What we need to do is build a spinning house. Specifically, a spinning house with a curved floor. You see, the addition of two forces in different directions (in this case, one outward force, and one downward) can be seen as a single force that is their sum, a new vector, in a new direction that averages the old ones. So, if I spin a torus to add .62 g of force at a certain radius, while Mars pulls downward with .38 g, there will be a certain, perfect angle at which I can tilt the floor, where gravity will pull exactly 1 g perpendicularly.
The problem with this is that at all other radii, the force from the rotation will be different, and the angle will change. To account for this, the floor will need to be curved such that "down" is always perpendicular to the floor. If you make the radius big enough, and the rotation slow enough, the difference in angle becomes gradual, leading to a gentle upward slope away from the entrance to the building in the center. As you walk outward and up the slope, you will get heavier and heavier, but down is always directly beneath your feet. You can walk perpendicular to the slope of a hill, and a ball on the floor won't roll back down.
In fact, if the designers built the slope right, the ball would roll upward. You see, a human being sticks up off the floor, and a human's center of gravity is not at floor level. To optimize balance, it would be best to build the curve so that it fits a radius just under 1 meter less than the actual radius, so that our feet, below 1 m, are slightly heavy, and our heads, above 1 m, are slightly light, and on the whole, an average height person comes out to be Earth weight. This means objects at floor level will have more outward pull than the floor angle compensates, and will roll upward. Unfortunately, this also means that rolling office chairs will be a bad idea.
(WARNING: This paragraph may contain math type stuff.) The building itself will need to be HUGE, and the bigger it is, the better, because the bigger it is, the slower it can spin, and the less difference in weight and angle from one point on the radius to the next. At a radius of 50 m, .62 g is a rotation of 17.439m/s, a little less than 3 rpm, which, at a radius of 51 m will cause a velocity of 17.787m/s, for .632 g, increasing or decreasing by roughly 2% (.0124 g) per radial meter. So, a person 2 meters tall would have feet that were 4% heavier than his head, which might be dizzying, but would be tolerable.
This will be quite a construction project. Basically, it means building a spinning football stadium on Mars. And it can never stop, either. If the spin stops, all the furniture goes sliding down the slope. A difficult feat for engineers. This will have to be built with on-site martian materials, as shipping costs would render it completely impractical to build on Earth. Only the outer edges will really be good for human habitation. The center would make a very nice little park or low gravity playground or gymnasium. It will need a VERY reliable and substantial power supply, probably fusion, although current fission reactors would work, and I would want a triple fail-safe on the machinery, and would probably still bolt my furniture to the floor. It probably won't exist for a couple years after original Mars landing, due to all of these concerns.
However, aside from fusion power (which we could skip, but I don't want too), all of the technology is already achievable, it just needs a bit of scaling up in terms of size. Once that is done, gravity problems go away, and this can be the first apartment building on the red planet.
Ah, my science teachers would kill me; I ignored sig-digs. Every number here should be assumed correct only to two decimal places, since that was my precision with g.
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