In the movie "Iron Sky", during the finale, the Nazi superweapon "Gotterdammerung" fires its main weaponry at the horizon of the Moon, blasting away a portion of the lunar surface and revealing the Earth above the new horizon. This paper calculates that the energy required for such a feat- on order of 1023J, would mean it would pose a critical threat to Earth

Bryan, Mark

Forster, James

Stone, Alex

English

University of Leicester Open Journals

Journal of Physics Special TopicsA2 7 The falling Iron SkyM. Bryan, J. Forster and A. StoneDepartment of Physics and Astronomy, University of Leicester. Leicester, LE1 7RH.Nov 18, 2012.AbstractIn the movie ”Iron Sky”, during the finale, the Nazi superweapon ”Go¨tterda¨mmerung” fires itsmain weaponry at the horizon of the Moon, blasting away a portion of the lunar surface andrevealing the Earth above the new horizon. This paper calculates that the energy required for sucha feat- on order of 1023J , would mean it would pose a critical threat to Earth.IntroductionDuring the final act of the satirical film ”Iron Sky”, a huge, city-sized flying fortress is revealed- theNazi superweapon Go¨tterda¨mmerung. It shows startling resilience- being hit by several low-yield nucleardevices without taking any visible external damage (although several miles away, the control room lightsare damaged). Its party piece, however, has to be its main guns, of which there are two mounted at thefront of the vessel. These weapons are fired only once in the movie, but their effects are cataclysmic.When used to destroy part of the Moon to allow a clear shot at the Earth, they tear an enormous holein the lunar surface, sufficient to view the Earth.Impulse calculationGiven that we know that the Earth is just below the horizon, we can work out the volume of the moonthat was blown away in the explosion. Geometry gives us the equation for horizon distance, d, for a givenheight to bed =√h(D + h) (1)where h is the height of the observer from the surface and D is the diameter of the sphere, in this casewe use the lunar diameter 3476km [1] and we say that the main cannon of the Go¨tterda¨mmerung is 1kmabove the surface of the moon, giving us a horizon distance of 59km. At lunar distance the Earth has anangular size of 0.0375 radians (from its diameter) so assuming the Earth was just touching the horizon,the blast would have to remove a spherical cap 2km deep (h) in order to see the Earth. The equation forthe volume of a spherical cap is given byVcap =13pih2(3R− h) (2)which gives a volume of 2.2× 1013m3. Given that the average density of the moon is 3.3× 103kgm−3 [1]this gives a total mass ejection of 7.5 × 1016kg. Assuming this mass is travelling fast enough to escapethe moon’s gravitational pull, this would make its velocity at least 2.4km/s [1], meaning that a lowerestimate the total momentum of the ejected mass is 1.8× 1020Ns.Specific impulse of the weaponIn order for this momentum change the explosive would have to have an enormous specific impulse.No specific scale information exists for the Go¨tterda¨mmerung but visual estimation place the size ofthe projectiles to be around 100m in diameter. A scientist in the movie is overheard saying that theprojectiles are metallic hydrogen, which has a density of around 1 × 103kgm−3 [2] meaning each of thetwo projectiles fired would have a mass of around 5 × 108kg. The theoretical specific impulse for theatomisation of metallic hydrogen is only around 1000Ns/kg [2], nowhere near enough to provide theenergy required to blast apart the moon. A rough estimate of the energy required can be estimatedfrom the momentum and mass of the ejected material to be on order of 1023J (assuming that the bindingenergy of the rock is negligible at that scale), well outside even the most powerful warheads ever producedon Earth, even if the metallic hydrogen could be forced to undergo fusion by some unknown mechanism,the energy yield would be (for complete protium-protium fusion to deuterium) on order of 1017J still farfrom enough energy to remove that amount of Moon. Even a more complex fusion chain would still failto produce the energy required with the mass of hydrogen estimated. The creators of the movie descibep-1The falling Iron Sky, Nov 18, 2012.the weaponry as ”relativistic” which would infer that a large portion of the energy in fact comes fromthe kinetic energy of the projectile.Fig. 1: The damage done to the moon at theend of Iron SkyDiscussionAlthough initially in the movie it appears that far less thana total spherical cap is removed from the Moon, during thecredits we see that considerably more of the moon was de-stroyed than estimated (which can be seen in figure 1). Suchdestruction should not be physically possible with even ther-monuclear weapons (the largest of which, Tsar Bomba, hadan approximate energy of 1018J [3]), as such it could be theo-rised that the explosion triggered the fusion of the Helium-3in the Moon so prevalent to the plot. If this were to happenin a large enough pocket, the resulting reaction should pro-duce enough energy. Additionally large pieces of the Moonappear to be orbiting it in the same scene, which would meanthat these chunks of lunar rock had not escaped from the lu-nar gravity well. With such a large outflow of matter, it isquite possible that the orbit of the Moon would be changedconsiderably, with quite a lot of the mass heading inwards ofthe orbit, it would be sufficient to increase the rate at whichthe Moon’s orbit is degrading outwards by a considerableamount (around 6cm/s). The debris from the fallout of theMoon could have serious impact on Earth if any large pieces of lunar material were accelerated sufficientlyto escape the Moon’s gravitational pull in the direction of Earth. Although such considerations are mootas later in the end credits we see the world in the process of thermonuclear war, making such impactevents a minor concern.ConclusionThe energy required to devastate the moon would have to primarily come from the kinetic energy of theprojectiles rather than any chemical or nuclear source. The effects of the damage done to the moon couldhave serious consequences for Earth both from the debris and the eventual loss of the satellite itself.With such displayed power, the Go¨tterda¨mmerung would have posed a serious threat to Earth had itmade it more than a few minutes into its flight. Although what use as a weapon of conquest it wouldhave been is questionable as if its effect on the Moon is to be considered representative of its power,the Go¨tterda¨mmerung would have caused apocalyptic amounts of damage to the Earth itself, making aninvasion rather difficult.References[1] http://solarsystem.nasa.gov/planets/profile.cfm?Display=Facts&Object=Moon accessed on21/11/2012.[2] http://www.nasa.gov/pdf/637123main_Silvera_Presentation.pdf accessed on 21/11/2012.[3] V. Khalturin, T. Rautian, P. Richards, W. Leith, A Review of Nuclear Testing by the Soviet Union at NovayaZemlya, 1955-1990, Science and Global Security, 13:142, (2005).p-2

A2_7 The falling Iron Sky

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A2_7 The falling Iron Sky

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