To celebrate Breakaway day 2019, we’re very lucky to have a guest blog from Dr Kevin Grazier. Kevin is a lifelong fan of Space:1999 and here he discusses the good, the bad, and the ugly of the science of Space 1999 – Breakaway!
Breakaway Science: The Good, the Bad, and the Ugly
On this solemn day, let us remember the 311 men and women who served, and may still be serving, on Moonbase Alpha, and who, on that calamitous day twenty years ago, left the Solar System to venture to distant shores unknown.
The pilot episode of Space: 1999 was groundbreaking in terms of special effects, verisimilitude, storytelling, but the science depicted in the show was a mixed bag. In commemoration of “Breakaway” Day, let’s examine three aspects of the pilot episode, and see what we can learn, and how well the storytellers did in the light of decades of subsequent scientific advancement and discoveries. Let us also keep in mind that science fiction stories have, since their inception, relied on audience “willing suspension of disbelief.”
The Good: Rogue Planets
With all that occurs in “Breakaway” to send our characters on their cosmic journey, it’s easy to lose sight that when we pick up the drama, Moonbase Alpha is supporting the upcoming launch of the Meta Probe—a deep space exploration of a rogue planet. The Meta Probe was the ninth such probe into deep space with the first being to Uranus, and the ninth to another rogue planet named Ultra (we see the aftermath of this in the episode “Dragon’s Domain”).
When the series aired, astronomers and planetary scientists (even though the disciplines are separate, we’ll use the term “astronomer” for both groups from here on) knew of no planets in the Universe outside of the nine known in the Solar System at the time. Back then, had you asked 100 astronomers about the likelihood of extrasolar planets, you would get a spectrum of answers from “they’re ubiquitous” to “they are extremely rare.” Today, between 10 and 20 rogue planets have been identified.
The notion of rogue planets—planets wandering the Galaxy, not in orbit around a star— was fairly anathema to astronomers across the spectrum. Our understanding of how the Solar System formed—planets accreted from a disk of gas and dust encircling a young Sol—was largely the same as it is today, but both theoretical and observational science has filled in or confirmed many of the details.
Without a star, how would a rogue planet like Meta or Ultra form? If it did form within a star system? How would it get ejected? (We’ll see later how difficult it is to eject a planet from the gravity well of a star.) That answer started to become clear when computers started to become powerful enough to do large-scale computational simulations.
In 2017, the first object of an unambiguous extrasolar origin passed through the Solar System, an object named 2017 U1, or Oumuaua. Astronomers were excited at the apparition of our first extrasolar visitor, but some felt “Well, its about time!” In the 1990s, computational astronomers performing simulations to understand the dearth of asteroid-like objects in the outer Solar System (objects whose orbits are exterior to Jupiter and interior to Neptune are collectively called “Centaurs”) found that most all outer Solar System objects in the voids between the outer planets are hurled out of the Solar System. Even the handful of Centaurs that exist today will be kicked into the inner Solar System, kicked into a portion of the Edgeworth-Kuiper Belt known as the Scattered Disk, or ejected from the Solar System entirely.
As these objects pass by the massive jovian planets, some trajectories have geometries that give them the same kind of gravitational boost that spacecraft navigators use to gravity assist spacecraft to the outer planets. It may take multiple passes (and this does happen), but all the outer planets are capable of ejecting objects like asteroids, comets, or planetoids into the depths of space. Presumably, much larger objects can be ejected in multi-star systems.
More recently, astronomers acknowledge that some rogue planets may form in much the same way as stars do: they condense from a nebula of gas and dust. They just condense from *really small* disks of gas and dust.
Apparently, rogue planetoids can also come into being by a massive explosion of nuclear waste. Although, at the time of “Breakaway”’s original airing, few astronomers would have been onboard with the idea of rogue planets, on this point, Space: 1999, gets, in the words of Alan Carter, a “Good on ya’.”
The Bad (but not really): Breakaway
Nearly every science fiction story has one “gimme”. One place where the story relies on science that is far beyond the breaking point—or, in the case of Space:1999, the Breakaway point—of what mainstream science believes to be true, or even knows for certain is factual. It’s the moment in the story where the audience is expected to go with the storyteller and apply “willing suspension of disbelief.” In the pilot episode of Space: 1999, that moment turns out to be the inciting incident or our series. Let’s analyze how much energy would be required for the explosion of nuclear waste disposal Facility #2 to push the Moon out of Earth’s orbit.
MATH WARNING. Sorry, can’t help it. The summary paragraphs are cast into bold font if math makes your head spin.
The total gravitational energy of an orbiting object is the sum of its potential energy and kinetic energy:
For the Moon in orbit around Earth, its kinetic energy is given as:
The Moon is on an elliptical, but very nearly circular orbit and, on average, is 384,399 km from Earth. We make the simplification of a circular orbit, meaning its orbital speed is constant. The period or one lunar orbit is 27.3 days, meaning Luna is speeding along at 1024 m/s. Its mass is 7.36 × 1022 kg, so using those values in the equation above, its kinetic energy is 3.88 × 1028 joules.
The equation for the Moon’s gravitational potential energy relative to Earth is:
Where G is the Universal Gravitational Constant, or 6.67 97 × 10-11 m3/kg·s2. One Earth mass is 5.97 × 1027 kg, yielding a gravitational potential energy of –7.63 × 1028 joules. Summing the potential and kinetic energy, Luna has a total orbital energy of –3.77 × 1028 joules.
The value of the energy is negative because an object in a circular or elliptical orbit—known as a bound trajectory—always has negative total energy. Any celestial body, satellite, or spacecraft that has a trajectory with a positive total energy relative to another, in our case the Moon relative to Earth or Oumuamua relative to the Sun, is unbound and is travelling too fast to to be captured into orbit or to remain in orbit. What we have to determine, then, is how much of a kinetic boost does the Moon need to make its total energy relative to Earth a positive value.
The energy yield of all the exploding nuclear waste has to exceed +3.77 × 1028 joules to counter the Moon’s potential energy and to get it to Earth escape velocity. That is the explosive equivalent of nine trillion (9 × 1012) megatons of TNT (nine trillion 1 MT nuclear bombs), or 155 billion (1.55 × 1011) times the yield of the largest nuclear bomb ever exploded on planet Earth (the Soviet Union’s Tsar Bomb which came in at 58 MT). Using E = mc2, it would require the equivalent of converting 416 billion kg of matter (about the mass of a small asteroid) directly to energy.
This is not the first time a scientist has done the Breakaway calculation, but what is often overlooked is that in order for the Moon to go on its interstellar journey, leaving Earth’s gravity well is not the biggest hurdle. The Moon is also bound to the Sun, and escaping the Solar System, especially starting deep as within the Sun’s gravity well as Earth’s orbit, is a far more daunting task.
Performing the calculation for escaping the Sun’s gravitational influence is a little more difficult, since that number is time-varying, and dependent on the Sun-Earth-Moon geometry. We start with a quick overview of Earth’s orbit, and its position at Breakaway (Figure 1). In the figure, Earth’s eccentricity (a measure of how out-of-round an orbit is, with 0 being perfectly circular and 1 meaning the object is on an escape trajectory, never to return) is exaggerated. Earth’s aphelion (the farthest point from the Sun) and perihelion vary only slightly from one another, so although Earth does have an orbit around the Sun more eccentric compared to the Moon’s orbit around Earth, we will, again, make the simplification that Earth is on a circular orbit. This circular orbit approximation of the distance from Earth to the Sun (rEarth = 1.49 × 1011 m), and gives a constant orbital velocity (vEarth = 29,662 m/s).
Figure 1 The location of Earth relative to the Sun on September 13th.
Figure 2 shows two extreme cases for the geometry that would take the largest explosion and the smallest explosion (if the word “small” can be used, in any meaningful way, to describe an explosion that blows the Moon out of the Solar System). Proper shading due to solar illumination has also been added to the diagram, which becomes important later.
When the Moon is between the Earth and Sun, the unilluminated disk of the Moon faces Earth, and we have what is called a new moon. In that instance, the motion of the Moon is in the opposite direction of the motion of Earth, and this is the geometry that requires the biggest BOOM to send the Alphans on their journey. In that instance, the values for the energy calculations would be:
When the Moon is opposite the Sun as seen from Earth, the Moon is farther from the Sun, and feels its gravity less. The Moon’s illuminated face can be seen from its entirety from Earth, so this is a full moon. In this geometry, the Moon is moving the same direction relative to Earth as Earth is relative to the Sun, so its velocity would be added to that of Earth’s, giving us:
Figure TK.Y The relative Sun-Earth-Moon positions for the geometry requiring the largest and smallest explosions to boost the Moon out of the Sun’s orbit.
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 it escaping Earth with our new values. [SOME MATH HAPPENS) It turns out that it takes, between 7.4 quintillion (7.4 × 1015) and 8.3 quintillion (8.3 × 1015) megatons— between 830 and 960 times—more for the Moon to escape the Sun than it did to escape Earth to wander the Galaxy.
There is a near-Earth asteroid named Toutais that could potentially impact Earth one day. If you had Toutais, and two identical clones, converted them all to energy, that is about the energy required for the Moon to leave the Solar System. Alternately, if 1 MT nuclear warheads came in a basketball-sized variety, which is unrealistically small for 1 MT devices, they would fill a sphere with a radius just smaller than four Earth radii (6371 km × 4 = 25,484 km).
This being 2019, we know where the Moon was on September 13th,1999, see Figure TK.Z. For those who saw the Moon set on that day, before the catastrophe, they would have seen a moon just past new, and only a thin crescent was visible as the Moon set shortly after the Sun. This means that the energy requirements to push the Moon out of the Solar System at its position on Breakaway Day is towards the 8.3 quintillion joules end of the range calculated above.
Figure 3 The relative Sun-Earth-Moon positions on September 13, 1999.
Now, if the Moon had a close flyby, or several close flybys, to any of the jovian planets, and received a gravitational boost—like the gravity assists discussed in the rogue planet section—then it is possible that the Moon may have wended its way through the Solar system for year before, ultimately, being given the gravitational kick to become a rogue planet. If the Moon can escape Earth, there are plausible non-thrust-based ways it could have left the Solar System.
Which brings us to a final point. In the opening of Breakaway, the heading implies that the nuclear waste disposal areas are on the dark side of the Moon. This turn out to be by coincidence, not by design.
Our Moon, in fact most moons in the Solar System, is tidally locked to its planet—meaning that the same face of the Moon perpetually faces Earth. This, in turn, means that each part of the lunar surface spends roughly two weeks in sunlight, followed by the same amount of time in the dark. There is no permanently dark side of the Moon, sorry Floyd fans. It simply turns out that on September 9th, when our story picks up, the waste disposal areas were in darkness. That would not have been true in two weeks.
The final news broadcast heard from Moonbase Alpha is of a reporter describing the disasters that have befallen Earth. The positioning of the waste disposal areas contributed to the nature and severity of the disasters, but that is an entry for another Breakaway Day.
FIGURE 4: Still from the opening of “Breakaway”.
The Ugly: Fractal Explosions
When nuclear waste dump #2 explodes, it’s ugly. It’s a major catastrophe for those stationed on Moonbase Alpha, and there are serious long-term ramifications for those on Earth. It is, however, a beautiful screen example of the concept of fractals. An object is said to be fractal if it appears the same at many different size scales. Snowflakes are fractal: zoom in, continue zooming it, and the same patterns will recur at successively smaller size scales. Mountains are also fractal, as are shorelines and mineral crystals.
It turns out that, as depicted in Breakaway, the explosions that blasted the Moon out of the Solar System were fractal. We see the initial explosion, like a blasting cap, then the effects on the waste dump infrastructure and a few Eagles, then we see the dump in its entirety as it erupts. The next shot steps back to encompass a larger field of view, and we see a very similar explosion pattern. Another step back, another pattern of blasts similar to the first two. Hence, fractal.
A famous fractal pattern—a different iteration of which is featured on the first page of every chapter in the novel Jurassic Park—is known as the Dragon Fractal.
This video shows beautifully how complexity arises from simplicity, the explosions in Breakaway show how a real-life fractal phenomenon might manifest.
In summary, is the idea that exploding nuclear waste could generate enough thrust to propel the Moon out of Earth’s orbit, and out of the Solar System even remotely plausible?
No, but who cares?
It’s become de rigueur to criticize the science in any science fiction or science-themed film or television series the instant it is broadcast. Online, and on social media, experts (and “experts”) clamour over one another to be first to criticize the science in new series and films. The important question is, “Is the science so bad that it pulls me out of the drama, leaving me saying ‘Oh, PLEASE!’?” In the case of “Breakaway”, most watching the show for the first time likely knew the premise going in.
Sometimes the science depicted in TV and film is educational, sometimes understanding why something is wrong—or doing the math to understand how wrong—is useful if presented correctly. Science fiction series aren’t intended to be documentaries, and it has always been the case that science fiction stories require that the audience but into at least one fantastic premise so that the storytellers can tell the story they want to tell. In the case of “Breakaway”, blowing up the nuclear waste dumps isn’t plausible, and I don’t care. Blow that puppy up, and let’s go for a ride!
Dr. Kevin Grazier is a planetary dynamicist whose research entails large-scale simulations of early Solar System evolution and dynamics. He was also an Investigation Scientist on the NASA Cassini/Huygens Mission to Saturn and its moon Titan. Grazier has been the science advisor on several television series and feature films and is a co-author on the Hollyweird Science series of books that explores the depiction of science, scientists, and the culture of science in TV and film.