ScienceThe Science Of Breakaway
Scienceby Marcus Lindroos
Although the special effects and visuals of Space:1999 generally have aged extremely well, the series has a bad reputation for being scientifically illiterate. Much of the criticism undoubtedly originates from the basic concept of the show, i.e. a giant nuclear explosion blasting the Moon out of Earth orbit, into interstellar space. The famous sci-fi author and scientist Isaac Asimov ridiculed this element of the "Breakaway" episode in a New York Times article in 1975.
This article examines the science of Breakaway and the Moon's journey through space while suggesting some alternative solutions.
The main problem is that the Moon is way too big and massive for the basic premise of the first Space: 1999 episode to work. Even if the current global stockpile of 30,000 nuclear warheads were brought from the Earth to the Moon and then simultaneously detonated there, it would merely create another crater.
The Moon has a mass of 7.35e22 kilograms and consequently accelerating it away from the solar system would be enormously difficult. The solar system escape velocity is approximately 1.41 times the heliocentric velocity of the Earth/Moon system, i.e. 1.41 x 29.8km/s ~42.1 kilometres per second. The minimum requirement then becomes a velocity increase of 12.4km/s assuming the Moon departs in the same direction as the Earth's orbital motion around the Sun, in which case we will get the 29.8km/s component "for free". This is somewhat simplified as we also have to account for the Moon's orbit around the Earth (1km/s) but it is good enough for our purposes. The diagram illustrates the minimum energy escape trajectory.
The Breakaway explosion begins at 20:15 lunar time and ends approximately four minutes later according to the communications posts seen in the episode. The resulting acceleration then has to be slightly more than 50 metres per second, i.e. 5-6 earth gravities!
Bergman states that the nuclear explosion "has been acting like a gigantic rocket motor, pushing us out of orbit". Let's start by estimating how much rocket propulsion would be required. One of the most ambitious nuclear bomb propulsion schemes proposed to date is the British Interplanetary Society's Project Daedalus from the 1970s. The 180-metre Daedalus booster rocket had a projected dry mass of 4000 tonnes and would have carried 46,000 tonnes of small nuclear fusion charges (deuterium/helium-3 pellets). Using Tsiolkovsky's rocket equation, it can be shown that some 2000 billion billion (2e12) Daedalus rockets clustered on the far side of the Moon would be required. Unfortunately, the Moon's surface area (3.79e13 square metres!) is too small by three orders of magnitude as 2e12 number of rockets arranged side by side would occupy some 5e16 square metres. The total mass of those rocket stages would be about the same as for the largest asteroids, i.e. 1e20 kilograms. The explosion rate also would have to be speeded up by a factor of 270,000 as each Daedalus unit normally operates for 2.05 years before its supply of bomb pellets has been exhausted.
The most powerful explosive known to man is antimatter, which does not exist naturally on Earth since mixing of matter and ordinary matter leads to the immediate annihilation of both. The reaction of a single kilogram of antimatter with 1 kg of matter would produce 1.8e17J (180 petajoules) of energy (by the mass-energy equivalence formula E = mc2), or the rough equivalent of a 43 megaton nuclear bomb! This is 255 times more efficient than the Project Daedalus deuterium/helium3 fusion reaction.
Let us assume some unknown process related to the nuclear waste (and perhaps Matter of Life and Death) somehow starts transforming lunar soil into antimatter, which then immediately annihilates. Each matter electron and antimatter positron annihilation produces two gamma ray photons. These depart in random directions, but one of them will be absorbed by the lunar surface on average. The Moon will then receive successive boosts from the gamma ray momentum transfer. Smith and Webb (ref 1) gives the velocity as a function of the fraction of the spacecraft's mass used for the matter/antimatter annihilation --
velocity = 300,000km/s * ( (x-1) / (x+1) )
where
x = (1 / (1 - fraction) ) ^ 2/PI
Consequently, a mass fraction of 0.015% will produce a solar system escape velocity of 14.3km/s. For the Moon, this translates to about 1e19 kilograms of annihilated matter and antimatter -- approximately twice the mass of Saturn's 300km wide moon Hyperion. The total energy released is also astronomical: approx 9.92e35 Joules over just four minutes or 4e33 Joules per second radiated by Nuclear Waste Disposal Area Two. In contrast, the Sun's *total* output per second is "only" 3.846e26 J. The explosion would thus be comparable to the most powerful star flares ever observed visually, and it would undoubtedly immediately kill all life on the Moon as well as the Earth itself. The only possible solution would be if the lunar farside somehow could reflect all the deadly gamma rays away without absorbing any of the radiation, but no known physical material can act as a "gamma ray mirror".
If the "massive nuclear explosion" will not hurl the Moon into extrasolar space, what will? The Andersons' original Zero G script assumed hostile aliens somehow could reduce the Moon's gravitational pull. This would supposedly cause the Moon to break out of Earth orbit and leave the solar system. Unfortunately, this will not work either. If it were possible to reduce lunar gravity, it would mean that the lunar tides on Earth immediately would disappear and that the Moon would start orbiting the Earth rather than the Earth/Moon centre of mass which is located some 1700 kilometres beneath the surface of the Earth. This would have a noticeable impact on everyday life here on Earth, but it would not result in the Moon going out of orbit.
Fortunately, there is one realistic alternative that does not require new physics. If a massive extrasolar planet (for example Meta) would pass sufficiently close, its gravity might eject the Moon from our solar system. Computer simulations suggest such events are very common in young solar systems and consequently the number of ejected "interstellar wanderers" ought to be enormous, but the likelihood of encountering such a runaway planet would of course be very small. The Alphans would have ample time to evacuate their moonbase before the disastrous encounter takes place, but they might be prevented from doing so by e.g. a disaster in the nuclear waste disposal area.
It seems we have finally discovered a realistic (albeit improbable) mechanism capable of sending the Moon into interstellar space. Unfortunately there is still a big catch: the universe is way too big! The Moon will be travelling much too slowly to get anywhere within the lifetimes of the men and women on Alpha. It will be moving at approximately the same velocity as NASA's unmanned Pioneer and Voyager probes which means the Alphans will need at least 15 years to cross the orbit of Pluto. The travel time to the nearest stars would be several hundreds of thousands of years so Moonbase will be empty and lifeless long before it finally reaches another solar system, which obviously ruins the drama. Therefore, we need to find a celestial body capable of accelerating the Moon to a significant fraction of the speed of light.
At this stage we have to turn to speculative concepts that (unlike antimatter or extrasolar planets) have never been detected in nature although the laws of physics do not seem to rule them out. The first such concept is negative matter, which are particles that have negative mass. Negative matter was initially suggested in 1957 in a scientific paper by the Anglo-Austrian mathematician Hermann Bondi. The implications of negative matter have recently been explored in some detail by the late astrophysicist and sci-fi author Robert L. Forward, who claimed (2) the concept does not violate fundamental physical laws such as the conservation of linear momentum and energy (negative matter is assumed to have negative rest mass, negative momentum and negative kinetic energy). Negative matter is not antimatter, which as far as is known has normal (positive) mass just like regular matter. However, the gravitational field of negative matter would cause all forms of matter, including negative, to move away from it whereas the gravitational field of normal matter causes all forms of matter (positive and negative) to move towards it. Forward speculates that there may in fact be very small amounts of negative matter particles in our part of the universe, and these are continuously drawn to large positive masses such as our Sun. The resulting additional heating might perhaps explain why the amount of fusion neutrinos coming from the Sun is only one-third of the calculated amount assuming all solar energy is generated by thermonuclear fusion plus gravitational contraction...
If an extrasolar planet having a negative mass of -7.35e22 kilograms approaches the Moon (whose positive mass is of the same magnitude), the negative mass will repel the positive mass while the positive mass will attract the negative mass (see illustration above, the negative mass is dragged along by the positive mass). The end result will be that both planets go off in the same direction with a constant acceleration equal to the gravity force between them. For the Moon, the gravitational acceleration will only be a few tens of centimeters per second at most but it is nonetheless fast enough for the moon/"anti-moon" pair to move away from Earth and the solar system in a comparatively short period of time.
Forward claims (3) that a negative matter drive could accelerate a spaceship to 70% of the speed of light if the electrostatic force between electrically charged positive and negative masses were used (gravitational forces will be much too weak except for planet sized objects). If the Moon were "hijacked" by another moon made of negative matter, it would open up interesting sci-fi storytelling possibilities. Moonbase Alpha would be transformed into a kind of "Flying Dutchman" doomed to sail the universe while travelling ever closer to the speed of light. If the Alphans however learn to develop a negative matter space drive, they would still be able to explore and perhaps colonise other nearby star systems as no spacecraft energy source or reaction fuel mass would be required.
Negative matter is probably the best scenario if faster than light space travel proves to be impossible. Unfortunately, there are still some drawbacks. It is not clear if negative matter exists at all in our universe (Forward speculated that it might be the dominant form of matter in distant regions of space which seem to be almost totally devoid of galaxies; the positive matter would gradually be "repelled" into distinct regions where it forms normal galaxies and stars). Also, in the Breakaway scenario depicted in the previous paragraphs, the Moon/antimoon pair would need more than a decade to reach a significant fraction of the speed of light since the gravity force and hence acceleration is quite small. The final result is that the Alphans would experience lots of weird phenomena such as time dilation as they reach old age and the Moon is moving almost at the speed of light in deep space, but the first few decades on Alpha would be rather boring.
Even if objects cannot move faster than the speed of light, it seems space itself (according what is currently known about general relativity) can. Space can expand faster than light-speed, carrying very distant galaxies away from the solar system faster than light even if they are at rest relative to their local neighbours in space. It seems spacetime can be made to expand or contract at any speed. Faster-than-light space travel would then be possible simply by expanding space behind e.g. the Moon and contracting space in front of it. This would be achieved by applying enormous amounts of negative energy (negative mass, negative gravity) outside a "warp bubble" of normal surrounding the object, see illustration above. To an observer on Alpha, the Moon itself would appear to be moving at the same velocity in local space as it always does but it might traverse five light years in a matter of minutes as spacetime is "warped" (see the Space Warp episode. The Mexican physicist Miguel Alcubierre has demonstrated that the concept is possible at least in principle, but in practice it seems to require impossibly large quantities of negative energy. E.g. propelling even a small ship might exceed the total energy available in our entire galaxy. Nonetheless, we might postulate that God-like omnipotent aliens (perhaps capable of harnessing the energy of an entire universe) possess the capability. "Space warps" might explain how the Moon was able to quickly leave Earth orbit and apparently reach other distant star systems within weeks of Breakaway.
"Wormholes" also require negative energy. A Wormhole is a "tunnel" connecting two different points in spacetime in such a way that a trip through the wormhole could take much less time than a journey between the same starting and ending points in normal space. The ending point might be located somewhere in the past or the future of our universe, or even in a totally different universe. In the Journey To Where episode, Koenig, Helena and Alan apparently travel back to Earth through a wormhole, i.e. a shortcut through space and time (wormhole like phenomena are also alluded to in Space Warp, A Matter of Balance and The Taybor). In this case, the wormhole "mouth" connected to Alpha would have been rapidly accelerated through space whereas the one leading to Texas City remained almost stationary. Einstein's theory of relativistic time dilation would result in the accelerated wormhole mouth ageing less than the stationary one as seen by an external observer (the Alphans have been in space only approx 18 months whereas 121 years have passed on Earth). Thanks to the wormhole, direct communication and travel between widely separated locations in space and time becomes possible. Wormhole "time machines" have been described in Black Holes and Time Warps (1994) by Kip Thorne, who notes that one significant limitation is that it is only possible to go as far back in time as the initial creation of the machine, i.e. this particular wormhole must have existed since at least 1339.
As with space warps, the big problem is that enormous quantities of negative energy would be required to keep the wormhole "throat" open. Wormholes are thought to occur naturally but they are so short-lived and small that not even the tiniest amount of matter could pass through.
It seems there are Breakaway scenarios that, at least on paper, do not appear to violate the laws of physics. The most useful concepts involve negative energy in the form of space warps or wormholes, but both seem to require impossibly large quantities of negative energy. In Isaac Asimov's famous novel The Gods Themselves (4), fantastically advanced beings in another universe governed by different laws of physics start beaming "free" energy to our universe, where it is collected by grateful humans on planet Earth. The main characters of the novel eventually propose to send the Moon into interstellar space by importing kinetic energy "for free" from another universe (perhaps negative energy could be obtained from this source as well). So it seems Asimov himself actually came up with a theoretically viable solution to the problem.
The energy yield of all the exploding nuclear waste has to exceed +3.77 x 1038 joules. That equates to the equivalent of nine trillion (9x 1012) megatons of TNT, 692 trillion (6.92 x 1014) times the energy released by the Hiroshima bomb. Using E=mc2, it would require the equivalent of converting 416 billion kg of matter (equivalent to a small asteroid) directly to energy.
He then calculates escaping the Sun's gravity
In order to calculate how much energy it would take for the Moon to escape Sol, we apply the same energy calculations as we did for escaping Earth. We find that it takes, between 7.4 quintillion (7.4 x 1015) and 8.3 quintillion (8.3 x 1015) - a factor between 830 and 960 times — more 1 megaton nuclear warheads than it did for Earth in order for the Moon to escape Sol and wander the Galaxy. Since the Moon's phase was a waxing crescent on September 13, 1999, the day it was blown free of the Solar System, the energy it took have been closer to the 8.3 quintillion MT end of that range.
Assuming an acceleration of 8 G (80 m/sec2) over an on-screen duration of 2.5 minutes, the moon's velocity is 12km a second, less than the escape velocity from the solar system of 40km/second. The kinetic energy involved (0.5 x mass x (velocity)2) would be 5 x 1030 Joules, or 1 quadrillion megaton bombs, or 13,000 the energy of the sun.
Plait notes that the "mysterious unknown forces" must have been working hard.