How much air do we need to add to Mars?
From NASA's Mars Fact Sheet, surface density of the Martian atmosphere is about .02 kg/m3. That is about 1.5% of Earth's surface air pressure of 1.27 kg/m3. Mars' atmosphere is virtually a vacuum.
Mars surface gravity is about 38% earth gravity. That means given an atmosphere of comparable temperature and composition, Mars atmosphere scale height is 264% earth atmosphere scale height. But Mars surface area is about about 28% that of earth's. 2.64 * .28 is about .75. To get comparable air density, we would need Mars' atmospheric mass to be about three quarters that of earth's atmosphere.
The total mass of the Martian atmosphere is about 2.5 x 1016 kg. Earth's atmosphere is about 5 x 1018 kg. So to make Mars surface air density earth like, we'd need 3.6 x 1018 kg of air added to Mars.
But do we need sea level air density? No, there are people who survive at higher elevations. This list of the world's highest cities show several places at around 5000 meter elevation. Granted the dwellers of the highest city La Rinconada, Peru don't live comfortably. But they demonstrate humans can endure air density half that of sea level. If half is sufficient, Mars only needs 1.8 x 1018 additional kilograms of air.
Would be Mars terraformers like to point at the frozen CO2 at the Martian poles. If Mars temperature is raised just a little, they hope the vaporized carbon dioxide would create a greenhouse effect that would cause more carbon dioxide to be vaporized. Their hope is that a runaway greenhouse effect could substantially boost Mars' atmosphere from frozen volatiles already in place.
According to Wikipedia, there is thought to be a 1 meter thick layer of CO2 at Mars north pole, a cap about 1,000,000 meters in diameter. At the south pole there is an 8 meter thick layer of CO2 over a cap having a 350,000 meter diameter. That's about 1.6 x 1012 cubic meters of CO2. Dry ice has a density of 1.6 thousand kg/m3. If all of that CO2 is vaporized (an optimistic assumption) that totals about 2.5 x 1015 kg of atmosphere. Short by almost 3 orders of magnitude, a miniscule contribution toward the needed 1.8 x 1018 needed kilograms.
Zubrin and McKay believe runaway greenhouse could boost Mars atmosphere to 300 to 600 millibars. Besides the polar dry ice, they also mention CO2 in Martian regolith. I believe most of Zubrin's optmistic estimates are influenced more by wishful thinking than hard data. But for the sake of argument I'll grant 300 millibars of CO2. 300 millibars of CO2 is not breathable. But let's say green plants combine Martian water and CO2 to make sugars and starches plus oxygen. Taking the carbon out of 300 millibars of CO2 leaves about 220 millibars of oxygen. Earth's 1000 millibar atmosphere is 1/5 oxygen, so perhaps a 220 millibar oxygen atmosphere would be breathable. But it would also be an extreme fire hazard. Apollo 1 taught us a pure oxygen atmosphere isn't a good idea.
Even with Zubrin's very optimistic scenario, it seems we'd still need to import 1.5 1x 1018 kilograms of nitrogen.
Can we add to Mars' air with comets?
Zubrin and McKay suggest it'd take .3 km/s to nudge an ammonia asteroid in the outer solar system towards Saturn and then Saturn's gravity could throw the ammonia snowball Marsward.
"Consider an asteroid made of frozen ammonia with a mass of 10 billion tonnes orbiting the sun at a distance of 12 AU. Such an object, if spherical, would have a diameter of about 2.6 km, and changing its orbit to intersect Saturn's (where it could get a trans-Mars gravity assist) would require a DV of 0.3 km/s. If a quartet of 5000 MW nuclear thermal rocket engines powered by either fission or fusion were used to heat some of its ammonia up to 2200 K (5000 MW fission NTRs operating at 2500 K were tested in the 1960s), they would produce an exhaust velocity of 4 km/s, which would allow them to move the asteroid onto its required course using only 8% of its material as propellant. Ten years of steady thrusting would be required, followed by a about a 20 year coast to impact. When the object hit Mars, the energy released would be about 10 TW-years, enough to melt 1 trillion tonnes of water (a lake 140 km on a side and 50 meters deep). In addition, the ammonia released by a single such object would raise the planet's temperature by about 3 degrees centigrade and form a shield that would effectively mask the planet's surface from ultraviolet radiation. As further missions proceeded, the planet's temperature could be increased globally in accord with the data shown in Fig. 12. Forty such missions would double the nitrogen content of Mars' atmosphere by direct importation, and could produce much more if some of the asteroids were targeted to hit beds of nitrates, which they would volatilize into nitrogen and oxygen upon impact. If one such mission were launched per year, within half a century or so most of Mars would have a temperate climate, and enough water would have been melted to cover a quarter of the planet with a layer of water 1 m deep."
This scheme presupposes we could land a 20 gigawatt power source on a rock in the outer solar solar system. For comparison the Palo Verde Nuclear Power Plant, the largest nuclear power plant in the United States, produces about 3.3 gigawatts. So we're sending 6 Palo Verde Nuclear Power Plants out past Saturn. McCay's scheme stipulates using the comet's mass as reaction mass. So now we have a mining and transportation infra structure on the comet that digs up the ice and places this reaction mass in the nuclear rocket engine.
If we have the wherewithal to establish such infrastructure, we certainly have the ability to build habs on these rocks.
Asteroidal Real Estate
How much asteroidal real estate could 1.5 1x 1018 kilograms of air give us? An O'Neill cylinder 8 kilometers in diameter and 32 kilometers long would give us 804 square kilometers of real estate. Such a cylinder would have a volume of 1.6e12 cubic meters. On earth's surface, our air has a density of about 1.27 kg per cubic meter. So that volume at 1 bar density would be 2e12 kilograms of air.
1.5e18/2e12 = 750,000. Three quarters of a million O'Neill habitats. Recall each cylinder has 804 square kilometers of real estate. 750,000 * 804 km2 = 603 million km2. Mars' surface area is 145 million km2. So if we put the asteroidal resources to use where they're at, we get 4 times as much real estate.
Some would point out that O'Neill cylinders are very extravagant pieces of mega-engineering. I completely agree! It's my belief that humans don't need a full g to be healthy, I believe .4 g (a little more than Mars' gravity) would suffice. In which case the hab radius could be 1.6 km. Such a hab would have only 321 km2 of real estate but a volume only 2.6e11 cubic meters. 2.6e11 m3 * 1.27 kg/m3 = 3.3e11 kilograms. 1.5e18/3.3e11 = ~4.5 million. 4.5 million of the smaller O'Neill habitats. 4.5 million * 321 = 1460 million square kilometers. Or about as much real estate as 10 Mars planets.
If the goal is to provide more real estate and resources for humanity, terraforming Mars is an extravagant waste. We should ditch planetary chauvinism and go for the small bodies.
Robert Walker also takes a look at terraforming Mars.