An Atmosphere is vital for any terraformed planet. Unfortunately, there are many planets who lack it. Creating it is possible in two ways: by adding it from other sources (diverting comets or carrying it from other celestial bodies) or by creating it from existing rocks.
Volume required Edit
Earth's atmosphere has a large volume, but if we freeze it, it will not be so large. The weight of Earth's atmosphere is equal with a layer of 10 meters of water. So, if you compress Earth's atmosphere up to water density, you will only get a global layer of 10 meters. Its total mass is 5.15*10^18 kg. Rosetta's comet has a mass of 10^13 kg. So, you will need 515000 Rosetta comets filled with gas to create Earth's atmosphere.
If you compress all Earth's atmosphere to water density, you will get 5.15 millions cubic km, or a cube with a side of 173 km.
Of course, one can see that in order to create an atmosphere around other celestial bodies you will need more or less gasses. However, using formulas on the Atmosphere Parameters page, you can see that, in order to get Earth's pressure on the surface, you won't need much less to create Atmosphere around small bodies. This is because with less gravity, the atmosphere builds-up a much wider and much more diffuse structure. Around a planet with higher gravity, the gas layer will be more compressed and so you will not need much more gas.
On the other hand, terraforming can be done with more or less gas. With less gas, you will have an atmosphere like on Earth's highest mountains, while with more gas, the effect will be the opposite. However, humans can adapt to these conditions.
How to bring water in Edit
There are many ways to do this:
Diverting comets and other icy objects Edit
Comets are known to be made of dirty ice. They contain water ice, solidified gasses, salt and dust. They contain all ingredients needed for oceans and an atmosphere, but in different amounts.
Before everything, we must pick the best candidates for diverting. Some comets might contain too much deuterium, which will affect life. Other comets might have high amounts of toxins. Choosing the right celestial bodies for diversion is very important. And we could divert one singe object as well as we could use millions of small comets.
Also, we must look at other icy objects found nearby. This can include Centaurs and icy moons. They are closer then Kuiper Belt objects and might be more easy to transport.
An advanced civilization will use a refinery. This way, some components will be left and others will be carried. First, volatile gasses like nitrogen and carbon dioxide can be covered with a layer of water ice, protecting them from immediate outgassing.
Basically, we have to send a spaceship where the icy celestial body is located. In the Kuiper Belt, objects move relatively slow, with about 4 km/s. Further away, the speed is much slower. At Sedna's orbit, celestial bodies move much slower, with less then 1 km/s. In case of icy moons that orbit around gas giants, we first must pull them away, into heliocentric orbit, then we will slow them. Overall, it will be more easy to divert a further object then to use a closer one, but also it will be faster to divert a closer object then a more distant one.
With current technology, one good way for transport is the use of ion engines, which are slow but highly efficient. We could also use water from the surface, split it into hydrogen and oxygen and use it in a chemical engine. In both cases, we will need nuclear power generators. And we will need to be patient.
The diverted object will travel together with the spaceship. Small trajectory adjustments need to be made from time to time. As the object gets closer to the planet, it starts outgassing and that can push it away from trajectory. Transport phase in the inner solar system must be fast, because outgassing will make us lose some of the volatiles and it might break the comet apart.
When the diverted object comes close to the planet, there are two scenarios. In the first one, it impacts the planet with full speed. The impact might be strong enough that debris will escape into space, both from the planet and the impactor. Also, this will alter the Geography by creating a huge crater and re-activating volcanoes. It is possible to alter rotation axis, rotation speed and even orbit. The second scenario is for a more advanced civilization, which slows down the impactor until it becomes a satellite. Then, it is de-orbited slowly, for a much softer impact.
Stealing atmosphere Edit
A more advanced civilization would be able to extract gasses from a giant planet and transport them to the planet and moon they want to terraform.
Using local rocks Edit
Some celestial bodies like Mars have water and gasses trapped in rocks and beneath surface. Heating might in some cases just be enough to create an atmosphere. In other cases, a combined heating and impacting process could be used.
Some of the moons that orbit gas giants have large amounts of ices and gasses trapped within ice. For them, the best solution is to bring a small amount of gas (for example, impacting with a comet with a diameter of 7 km). The impact will create a tenuous atmosphere, which might be enough to allow us deploy Greenhouse Gases. Then, as temperature would increase, the ice will start to melt, releasing trapped gasses from the ice. The process will continue until it will reach an equilibrium phase.
Atmospheric balance Edit
What would happen immediately after we add an atmosphere? Some gasses will be absorbed in the rocks or will make chemical reactions with them. This process will occur soon after we create an atmosphere and will slow down soon too. We have to consider this when we calculate how much gas we need.
If we brought the air with an impactor, we also create a massive increase in temperature, melting all ices. At this point we have to start working on terraforming the atmosphere. We will add greenhouse gasses as the temperature is still high.
We also have to consider that once we produce oxygen, it will react with many rocks on the surface and might ignite gasses in the atmosphere, like methane. This will affect atmospheric composition and mass.
A third thing that will happen is, when we create oceans, that gasses can be dissolved into water. This works for oxygen and nitrogen, but in much larger concentrations for carbon dioxide. Gasses can exist in the first ocean we create and can escape into the atmosphere. Also, gasses from the atmosphere can get into the ocean.
It is possible to add gasses later, to replenish the atmosphere, but, if possible, it is better to estimate how much air will be absorbed in the rocks, in the oceans and how much will be lost in space in the first moments, when the atmosphere can be very hot.
Maintaining a terrafomed world can be costly. Around small planets and moons, atmospheres are not stable and will need to be replenished. This can easily be done by diverting other comets. However, a large impact will not be a good thing for local communities. s the planet gets colonized, settlers will look for new technologies to do this, which will try soft landing of a comet on their planet. A terraformed Moon will require about 50 Rosetta comets every year to replenish its atmosphere. And each time a comet lands, it releases many gasses, some of them toxic for humans. Maybe, at that time, there will be refineries in orbit, that will refine comets and will send to the planet only what needs to be replenished: water, oxygen, nitrogen and small amounts of carbon dioxide.
On an airless planet, the first step in terraforming is creation of an atmosphere. Nothing can be done without this step. All other steps, like setting the correct temperature, creating oceans, ameliorating ground features and insertion of life, cannot be done unless we have an atmosphere with the correct pressure. Even atmospheric composition can be later improved, if we have one.