|Fig. 1: Martian North Pole, which is primarily made up of ice with a top layer of dry ice. In my calculations, I estimate this pole's layer as a cylinder. (Courtesy of NASA, Source: Wikimedia Commons)|
In an interview with Steve Colbert, Elon Musk proposed an unconventional idea to terraform Mars: transform the planet to be habitable for future generations. Musk proposed sending nuclear weapons to Mars' North and South Poles, which encapsulate frozen water and carbon dioxide (CO2).  As discussed by McLaughlin, the theory behind a thermonuclear attack on Mars is that the energy released by the nuclear weapons would vaporize the elements trapped in the ice into the atmosphere creating a greenhouse effect.  Similar to global warming on Earth, the energy from the sun, and the infrared radiation reflected by the planet would be trapped by the particles and slowly warm the planet. This initial increase in heat caused by the nuclear attack would then catalyze a chain reaction where more ice would melt, releasing more carbon dioxide, and further increasing the temperature and pressure of the planet until liquid water would exist.  I will now investigate the feasibility of this theory by estimating how much energy it would take to vaporize the frozen carbon dioxide.
The North and South Poles on Mars consist of ice with a top layer of frozen CO2, or dry ice.  From high-resolution thermal images obtained by the Mars Odyssey and Mars Global Surveyor, it has been concluded that the Martian North Pole, as pictured in Fig. 1, is 1000 km in diameter, and the CO2 layer is estimated to be about 1 m thick in the winter. The South Pole is smaller, with a diameter of 350 km with an estimated CO2 layer that is consistently 8 m thick.  The total voluae of froxen CO2 is thus
|North Pole CO2||=||π × (500,000 m)2 × 1 m||=||7.85 × 1011 m3|
|South Pole CO2||=||π × (125,000 m)2 × 8 m||=||3.96 × 1011 m3|
|Total Martian Frozen CO2||=||1.18 × 1012 m3|
Although a thermonuclear attack would surely melt and vaporize the water and rock trapped beneath the top layer dry ice, this analysis will primarily focus on the vaporization of the solid carbon dioxide, a molecular compound key in creating a greenhouse effect in the Martian atmosphere. In order to vaporize the 1.18 × 1012 m3 of solid carbon dioxide in the Martian Poles, the dry ice would need to sublime from its solid state to a gas. The heat of sublimation for solid carbon dioxide is 2.63 × 104 j mol-1.  With the density of dry ice being 1620 kg m-3, the energy required to vaporize all of the frozen carbon dioxide in the Martian poles is 
It is estimated that across nine countries, including the United States and Russia, there are about 15,000 nuclear weapons on Earth as of 2017.  Let us assume each of these nuclear weapons t be equivalent to the nuclear weapon recently tested by North Korea in 2017 - to account for modern trends in weapon size.  The nuclear test yield would then be about 250 kilotons of TNT.  With these assumptions, the total energy of the world's nuclear weapon arsenal is
This is significantly less than the energy it would require to vaporize all the frozen carbon dioxide on Mars.
Assuming that the energy estimates above are correct, there is there is not enough energy in the world's nuclear weapon stockpile to vaporize all of the solid carbon dioxide trapped in the Martian poles. However, would 1.6 × 1019 J of energy be enough to vaporize some carbon dioxide and initiate the chain reaction of the green house gas effect? This would likely not be the case, as much of the energy released by a large nuclear attack would be lost to the sky, even in the very thin Martian atmosphere. Thus, it is likely only a small fraction of the 1.6 × 1019 J of energy would be absorbed by the solid carbon dioxide, which will not be enough to initiate a greenhouse effect in the Martian atmosphere. Additionally, a thermonuclear attack on Mars would not be advisable as many risks are involved. First, any complication in sending thermonuclear weapons into Earth's atmosphere for transport to Mars would be catastrophic. Also, a large nuclear blast on Mars would damage its geography, and perhaps any traces of life on Mars, if it exists. Thus in conclusion, it would not be advisable to execute Elon Musk's proposition to deplete Earth's entire nuclear energy storage to nuke Mars. Other avenues of terraformation might be explored.
© Charlotte Philp. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
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