The Martian atmosphere is composed of approximately 95% carbon dioxide, 2.7% nitrogen, less than 0.13% oxygen, and other trace gases. With the addition of hydrogen, all the ingredients needed to produce methane are in place. The methane/oxygen reaction works very well for rocket propulsion, producing only carbon dioxide and water as byproducts—no messy, toxic byproducts result.
The scenario might look something like this. A spacecraft descends to the Martian surface, does whatever it is designed to do (it can be either robotic or human-tended, the premise is unchanged), and is ready to return to space. Rather than load onto the spacecraft at Earth all the propellant needed to launch from the Martian surface back into space— lugging it on the voyage to Mars and paying a heavy (literally) price to land it on the surface—we launch the craft with its Mars ascent fuel tanks empty. We then land the spacecraft near some sort of tanking station on the surface that has been producing methane rocket fuel from in situ Martian resources for this very purpose. The methane is transferred to the ascent stage, the rocket is lit, and the payload returns to space.
To make this happen, a miniature chemical plant, using well-understood chemical processes, will be placed on the surface to produce rocket fuel. In order to be economical, the plant should be able to support one large human-scale mission or multiple robotic scale missions. The first ingredient, methane, is extracted from the carbon dioxide in the atmosphere by reacting it with hydrogen, producing water in the reaction. The hydrogen comes from one of two places: (1) since it is of low molecular weight, the spacecraft brings it along—which partially defeats the objective of weaning ourselves from the home planet, or (2) we get it from local Martian water. Recent observations of Mars are causing many to believe that large reservoirs of subsurface water might exist there. If it does, then the hydrogen component of water can be easily liberated by using the same method we discussed for generating hydrogen on the Moon: electrolysis.
Rocket fuel ingredient number two, oxygen, required to "burn" the methane, comes from either the water produced in the hydrogen/carbon dioxide reaction used to produce the methane fuel or from other, similar chemical processes. Recall that oxygen is present in water, carbon dioxide, and many other compounds found to exist on Mars.
It is important to note the significant potential impact of this approach to space exploration. The amount of fuel needed to return to Earth from Mars for a human expedition is significant. Making the fuel required for the return leg of the trip in situ, rather than lugging it with you, might be the difference between making the mission happen, or not. The launch mass savings, hence cost savings, are enough that mission planners are already taking notice and seriously considering this option for future missions.
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