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If you wanted to give Mars an atmosphere as dense as Earth's, you would have to find a lot of gas somewhere. How much is "a lot"? Call it about 4,000,000,000,000,000—that's four quadrillion—-tons of gas.
That's a lot in human terms, all right, but rather little in the larger numbers used by astronomers. Fortunately it doesn't all have to come from the Oort. There's a fairish supply on Mars itself.
The principal things you need to make a planet capable of sustaining life are what scientists call "volatiles," principally water and air.
If you look at the composition of the planets of the solar system, you can see that these volatiles are distributed in a fairly orderly way. Mercury, the planet nearest the Sun, has practically none; whatever it may originally have had of them has long since been volatilized by the Sun's heat and—because the hotter volatiles get the more rapidly their molecules move, thus attaining enough speed to overcome the pull of the planet—they have been lost into space.
Venus and Earth, being farther from the Sun and also a lot bigger than Mercury, are luckier; they have retained much of their volatiles. Then, when you get farther out, past the asteroid belt, you find that practically all of the volatiles have been retained; in fact, the gas-giant planets, from Jupiter through Neptune, are essentially nothing but volatiles . . . but, partly because they are so large and their gravitational grip is therefore so firm, and also because these planets are so far from the Sun, and therefore so cold, the volatiles haven't been able to escape.
All of that is quite orderly and sensible, and fits the pattern of how the solar system was supposed to develop—with one exception.
There's the unusual case of the planet Mars.
Mars seems to have been shortchanged on volatiles. It ought to have more than it does. It did have, once. There are clear indications of river valleys on Mars, which means that there must have been liquid water at some time. Indeed some of these features, like the Valles Marineris, are huger than anything on Earth. They look like a magnified Grand Canyon, and if, like the Grand Canyon, they were carved out by the erosion of liquid water flowing, that amount of water must have been very great. In fact it must have been enough, once, to have given Mars great oceans. How great? Enough, if the water involved had been spread evenly over the surface, to cover the planet half a kilometer deep. It wouldn't have been spread evenly, of course; it would have collected, like Earth's oceans, at low points. But it would have been a lot.
So where did those volatiles go?
Most of them must have been lost to space, simply because Mars's weak gravity could not hold them forever. They weren't all lost, though. Visibly, there is still enough of them left to make the Martian polar ice caps. Invisibly, bound into the minerals of the Martian surface, there is a great deal more.
That's where the Oort program gets its biggest bonus. Once enough comets are dumped on the surface to raise the surface pressure and the surface temperature a little, all those locked and frozen invisible volatiles can begin to become visible again.