Mars has a magnetosphere but it's much weaker since its core is cooler and slower and smaller.
If we nuked the polar ice caps (or similar method to warm + evaporate them) it would generate enough of an atmosphere for the external pressure to be livable - maybe even breathable.
Since the magnetosphere is still weak, this atmosphere would be eroded over time, but we're talking tens of thousands of years or more.
That would be a far cheaper and less disruptive way of keeping an atmosphere on Mars.
edit: Here you go: http://www.orionsarm.com/eg-article/4851d85e0791b
Source?
Even granted that would be possible, it would be an enormous waste. Let's say it's possible to use the polar ice caps to create a breathable atmosphere, why do it for the whole planet instead of using it strategically to pressurize domes where people actually live? Added bonus: The domes provide partial shielding for the radiation on Mars. If you believe the ice on Mars can sustain a breathable global atmosphere for ten thousand years, how long will it last when used in closed systems like domes?
what's wrong with Zubrin's plan?
> not enough gravity.
what's gravity got to do with it?
ADDED: if you're going to tell me the gravity is necessary to hold onto the atmosphere, great, i'm actually familiar with that mechanism. i assert that mars' proclivity for losing the lighter atmosphere over millions of years isn't relevant, and that it'll hold onto everything important for Long Enough.
When the speed of molecules in the atmosphere (thermal, and thus dependent on molecular weight) approaches escape velocity for the body, the atmosphere starts to leak that component. Gasses like N2 (molecular weight 28) and oxygen (32) will "stick" to Earth where Helium (4) won't. Mars can hold CO2 (44) but not O2.
and only hydrogen and helium are currently prone to jeans escape on mars. the current dominant mechanism for atmospheric loss is the solar wind. which eats away ~1/3 megaton/century. mars has teratons of atmosphere remaining. and it can be added faster than that rate of loss.
(once warmed up, oxygen may begin to escape the atmosphere again. not necessarily faster than it can be replaced, though.)
Gravity got the following to do with it: Lower gravity makes it easier for the atmosphere to escape to space, especially since Mars has a very weak magnetosphere. Second, to have a human-breathable atmosphere you need not only the right composition, but also the right pressure, and to get that pressure on Mars you'd require an atmosphere more than 2,5 times the mass of Earth's. Where are you going to get it from? Even if it was available to you, using it to make Mars globally breathable would be an ENORMOUS waste compared to simply pressurizing domes and bunkers instead.