Mars is the fourth Planet from the Sun, and of the Seven other Planets, is the one most like Earth, and the only one that a manned base is thought to be viable on for the near future [making bases anywhere else in the Solar System would require technology that is at least a century off into the future]. Mars is around half the size of the Earth, and because of this has considerably weaker gravity. This alone presents a problem, in that the human body is designed through Evolution to live only in an environment that has the exact amount of gravity that the Earth possesses. Attempting to live in an environment with gravity that is any weaker or stronger would cause serious problems to the colonists attempting it.
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This is known because of a little known fact about Astronauts. Spending extended periods of time in Outer Space is extremely hard on the human body for numerous reasons. One of these is that the microgravity causes the person's muscles to atrophy [they grow weaker and weaker until the person loses use of them completely]. This is because the daily tasks they are performing aren't giving them any exercise since the objects they are interacting with, as well as their own bodies, have little to no weight. The microgravity also causes a slow breakdown of their circulatory system, which is why humans can only spend so much time in Outer Space without risking death from Circulatory failure [your circulatory system uses gravity to know which way is up and which way is down, just in the same way as a budding seed does. It also uses it to aid in the actual pumping process, most significantly in the areas farthest from the Heart where its pumping alone isn't enough to keep the flow going]. Also, when in Outer Space, a person is exposed to high levels of radiation, even within the protection of a space shuttle or space suit, which is designed to provide as much protection as possible.
The Sun releases very high amounts of radiation from its surface constantly, being far more radioactive than any Nuclear Reactor here on Earth. The Ozone Layer in the Atmosphere of the Earth, combined with its Magnetic Field, blocks most of this radiation, and only a very small portion of it actually reaches the Earth's surface. When visiting the International Space Station however, which is outside of the Earth's Atmosphere and much of its Magnetic Field, they are exposed to considerably higher levels of Radiation, even when inside its walls. Because of this, Space Radiation has always been a problem, although studies have found no significant rise in Malignant Neoplasms among former Astronauts. One Peculiarity was that during the Apollo program, the Astronauts all reported seeing flashes of light when they closed their eyes, now believed to be reactions of rays of light from the Solar Wind with the fluid inside their eyes.
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Solar Phenomena have always posed a danger to Astronauts, the most poignant example of this being a specific CME [Coronal Mass Ejection, what is commonly called a Solar Flare] that occurred in between two of the Apollo Missions, which would have killed the Astronauts if they had been exposed to it. Since a mission to Mars would take at least Six Months with the best technology we have now, the Astronauts undertaking it would be exposed to the dangers of space for a very long time. Also, although few normal people worry about this, NASA, as well as the Russian Federal Space Agency are worried that spending Six Months confined closely together will have serious effects on the minds of the Astronauts undertaking the mission [after doing a simulation test, Russia decided it wouldn't allow women on its team]. Due to all these factors wearing on the Astronauts undertaking the mission, some in the industry worry that the Astronauts who undertake the mission won't even have the strength left to do it once they actually reach Mars.
This I don't know how to solve, although I guess they could provide them with entertainment of some kind, like TV or maybe even Video Games. This is a serious consideration though, as every single Pound/Kilogram of material that is taken is extremely expensive, with each one costing an exorbitant amount of money [1 Million+]. What I do note is that since the travel time is Six Months, there is a dangerously high chance that the shuttle could be hit by a CME during transit [the longer one stays in stellar space, the higher the chance they will be hit by one. This chance goes down the farther you are from the Sun, since the danger zone of a storm can be anywhere.]. Therefore, I would think that the people designing the shuttle will have to find some way of proofing the shuttle in case it comes into contact with one, which is a tall order since as far as I know, Satellites get knocked out when they're hit by one.
Moving on, as for Mars itself, let's first name the differences between it and the Earth, differences that anyone attempting to Terraform it would have to overcome. First, like I said, it is half the size of the Earth, which essentially means that anyone wanting to permanantly live their would have to actually be genetically modified so that they could withstand Mars' weak gravity indefinitely without having their body deteriorate from the atrophying of their muscles and other body tissues.
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This isn't the only problem, in fact its probably the easiest to solve [genetic engineering isn't that hard, whereas the problem I am about to discuss I see as exponentally more difficult to solve]. The main thing that someone terraforming Mars would have to change is the makeup and thickness of its atmosphere, which is currently quite thin and overwhelmingly made up of Carbon Dioxide, containing very little Nitrogen and only trace amounts of Oxygen [the coloration of the Martian Sky is the exact opposite of that on Earth, this being a result of the makeup of the compounds within it. It is red during the day due to all the Carbon Dioxyde, with a Blue Sunset due to the Nitrogen in its Atmosphere, while ours is Blue due to all the Nitrogen in our atmosphere, and Red, Orange, and Purple do to the Carbon Dioxyde and other compounds in ours]. Therefore, someone attempting to Terraform the Red Planet would have to release large amounts of Oxygen into the Atmosphere so that we could breathe. They would also have to heat it up so that we could live there as temperatures there are regularly colder than even Antarctica. It is generally agreed among the scientific community that the way to solve this problem would be to start a runaway greenhouse effect by somehow melting the Ice Caps at either or both of the Martian Poles. Large amounts of Methane as well as water are believed to be hidden under those poles, and so melting them would cause the methane to rise into the atmosphere and rapidly heat it. It has been suggested to maneuver an Asteroid or Comet into them to do this, or even for a few large nuclear reactors to be built there that could release large amounts of heat, albeit locally, to do it as well.
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Still, this does not address the bigger problem, the one that caused Mars' atmosphere to be thinned, and its oceans to disappear in the first place. That being Mars' lack of a Magnetic Field like the one possessed by the Earth. It is that lack of a magnetic field that has allowed the CMEs that periodically strike it to slowly chip away at its atmosphere and evaporate its oceans, which is why it is in the state we currently see it. Anyone attempting to Terraform Mars would have to either revive the planet's magnetic field, or find some other way of stopping the Solar Flares that will periodically hit it from simply undoing all the alterations they had just spent so much time and effort attempting.
For those who don't know, Mars does not have a Magnetic Field for two reasons. First, as I have repeatedly said already, it is considerably smaller than the Earth, and its core is therefore also considerably smaller than Earth's. There is a second reason however that Mars' is now inactive. Earth's Core actually composes most of its mass, with only the very thin crust being solid. The reason for this is the Big Splash event that happened Billions of years ago, near the final stages of the Planet's creation. The Big Splash was the event in which the Proto-Earth was struck by another Planet, now called Theia [one of the Titans in Greek Mythology, known as the Wife of Hyperion, Mother of Helios, and the Goddess of Light]. That event completely liquified the planet, so that even after four billion years, the planet is still mostly molten, barely having cooled at all from the incredible heat produced by the impact. Mars however never experienced such an event, and so its core was considerably smaller to begin with, and therefore cooled much faster, eventually cooling completely. This caused it to lose its magnetic field, which in turn caused its oceans to evaporate and its atmosphere to thin.
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I have thought of a couple ways that a shield against Solar Flares could be created, including an enormous satellite with some kind of actual sail shield on it that could block the charged particles from hitting the planet, as well as a team of smaller satellites armed with electromagnetic guns that when fired in unison could perhaps produce waves of electromagnetic energy that could deflect the flare away from Mars entirely. It may seem silly, but this a serious problem that anyone planning a Terraforming operation would have to deal with, as a direct hit from a Solar Flare could completely undo whatever Terraforming work was attempted on the planet.
I have many more things I'd like to talk about, even just regarding the potential Mars Mission, but I think that's enough material for now.