P = 1,23 x 10⁷ {exp(-3170/T_pole)}    

This equation works as long as there is carbon dioxide in the polar cap.
 
 
 

Ways to heat up the planet 
 

The easiest way to heat up the planet is to build huge industries that exhaust vast amounts of greenhouse gases into the atmosphere. If we use gases without chlorine, the ozone layer doesn't get destroyed. A good gas is CF₄, which has the advantage of being very longlived in the upper atmosphere (10000 years). But such an enormous project would cost a lot of money and would need extensive work done by human beings. It would, of course, need a lot of energy, too.
 

An induced warming of 10K would probably be feasable if the required materials were found. The amount of energy required (4490 MWe) corresponds to the amount used by a big American city like Chicago. The extra 10K would be reached after about 30 years.




Orbiting Mirrors

The main reason why Mars is colder than earth is that Mars gets less sunlight than earth. So it seems logical to increase the amount of light that hits Mars surface. This could be done by stationing big mirrors in space.
These could be stationed at about 214000 km over the Martian surface. That way, the mirror would stay where it is: the sunlight pushes it outward, the Martian gravity pulls it inward.
But to increase the light that hits Mars by just 2%, a mirror the size of Texas is necessary. More logical to heat up only certain parts of Mars. Zubrin and Mc Kay have shown that a constant temperature rise of only 4 K on the south polar icecap would make the whole carbon dioxide reservoir evaporate to thicken the atmosphere by 50 to 100 mbars and heat up the planet by more than 20 K.
A mirror (or solar sail) with a diameter of 125km stationed at 214000 km over the south pole would heat up everything below 70' by 5 K.
This is more than enough to make the icecap melt. In 10 years, the whole icecap would be evaporated and some of the carbon dioxide that is now in the regolith below 70' , would also be liberated into the atmosphere.
So we can increase the temperature globally by more than 20 K by warming up the planet regionally.
A mirror of that size seems never the less enormous. Bur don't forget that Mars has a weaker gravity, which makes launch costs much cheaper, it has 2 satellites that orbit close to Mars and have almost no gravity which could be turned into giant solar sail industries if we take rising technology into account.
Another idea is to build bases on the moon that could build smaller sails and let them sail over to Mars. These bases could also export materials to Earth and Mars, like He3, which begins to be used medically.
Cargo that are send to Mars could use solar sails as propulsion. Instead of throwing them away after being used, they could be used ib the reflectors to heat up the planet.
Mars is close to the asteroid belt. If an aluminum rich asteroid was found, nuclear reactors with a capacity of 5 MWe (like the ones that will be used for manned flights soon) could rapidly build sails and send them to Mars.
Such sails are of a big importance in the terraforming of Mars.

To note is that the construction of such a mirror might be the only thing that needs to be build to terraform Mars. If the temperature needed to let the carbon dioxide that is captured in the regolith escape (also called T_d) is under 20 K, the melting of the south polar icecap might do the job of making all the carbon dioxide of the planet escape into the atmosphere.

But if T_d is higher, extra heating through greenhousing will be necessary.



The biological heating


There are bacteriae that can produce methane and oxygen with water and carbon dioxide, others produce ammonia and oxygen with water and nitrogen.
Both are greenhouse gases, that are far weaker than FCKWs, but far stronger than carbon dioxide.
Let's assume 1% of the surface is covered with such bacteriae and that those use sunlight with an efficiency of 0,1% to produce their greenhouse gas. This would cause one billion tonnes of ammonia and methane to escape into the atmosphere. That is enough to heat up the planet by 10 K in 30 years.
These gases would protect the surface from UV radiation, but would also be destroyed, which doesn't matter, because they'd constantly be replaced by the bacteria.
Through the heating caused by these gases, more carbon dioxide would be released into the atmosphere, which wouldn't only heat up the planet through greenhousing, but also make a much thicker ozone layer (carbon dioxide raises the formation of ozone), which would slow down the destruction of ammonia and methane, which would cause a higher concentration of these gases.

Further heating through organisms can be acieved by letting black organisms grow on the surface of the planet. This would lower the albedo and therefore heat up the planet.
Best would be to engineer organisms (e.g. lynchens) that are able to grow on the polar caps. This wouldn't only heat up the planet directly through albedo change but also through carbon dioxide release.
The major problem with this project is that no plants are known that would live in such cold regions, although there are lynchens that survive temperatures of -100'C and are still photosynthetically active (and therefore grow) at -24'C.
But if such organisms could be engineered, the result would be very helpul. No big mirror would have to be built in space, organisms would replicate and melt the polar caps on their own. The only human job would be to engineer and release them.



Albedo change

It is well known that dark objects heat up faster than light ones. So to heat something up, all you have to do is to paint it in black.
This might be of a big help to melt the polar icecaps. On Mars, there are vast regions of dark, almost black sand. Some of those regions are close to the icecaps.
Future terraformers could transport some of that sand to throw it on the icecaps.
Although more work needs to be done than with the release of black plants, the project would probably be simpler to realize than the construction of a big mirror in space.
One problem would probably be that winds would blow of the sand.

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