Perhaps the most successful practitioner of science fiction was one of its originators, French lawyer and mathematician Jules Verne. Writing “From the Earth to the Moon” in the 1860s, his Florida-based moon shot eerily resembled the flight of Apollo 8 a century later. Verne frequently resorted to the set piece duels to move his stories forward and “From the Earth to the Moon” begins in such manner. His 21st century counterparts probably understand interstellar flight as well he understood lunar flight (including the use of dramatic devices), but in each case their prospects of experiencing such within their lifetimes would be reckoned extremely low. In Verne’s case, another hundred years made a difference. Could the same be said for the vision of the writers of “Avatar”?
With the same energy and attention to detail he devoted to the maiden and final voyage of the Titanic, in his 2009 film “Avatar” James Cameron delivers us to far-away Pandora, a moon of a giant planet orbiting another sun. With the opening scene in 2154 AD of hundreds of sleeping space voyagers awakening in free-fall in orbit above their interstellar destination, we behold images of science fiction seldom brought to the screen, maybe not since “2001: A Space Odyssey”. Had this been a Star Trek installment, the crew would simply have paced about the ship’s bridge. Though truly a technical and artistic achievement creating a world, its flora and fauna and even a civilization through computer animation, many matters were given short shrift; some only mentioned in passing in interviews prior to film release. While 1960s viewers of Stanley Kubrick’s “2001” had some notion of the moon and Jupiter as places above the Earth, visible in the night sky, and subsequently how they could be reached owing to Apollo astronauts and robotic Pioneer and Voyager space probes, corresponding examples are absent with Pandora.
Of course, the “Avatar” script presents many matters to question: Will a 22nd academic researcher reach for a cigarette as she emerges from an intense avatar session? What’s the business model for mining “unobtainium” (technical slang much like “kluge”) or shipping light beer over interstellar distances? Why not repair Corporal Sully’s legs before transporting him across the same void? How are quarterly financial reports compiled for interstellar operations? Are communication time lags taken into account? What happened to the Star Trek notion of non-intervention in local planetary affairs? What kind of world was the Earth that dispatched marines to Nigeria or Venezuela and beyond the solar system as well? Could earthly conflicts have still involved oil? Or are these simply “motor effects” like Jules Verne’s duels?
Petroleum could not have propelled Jake Sully to Pandora, but “Avatar” does provide a wider stage for human follies than afforded by our own era. Even if motivational projections seem headed into an abyss, drama demands villains as well as sympathetic protagonists. While “Avatar” seems stridently Gaian, recall that a Marxist conflict advanced the “Titanic” story line despite its love interests and box office receipts. At Pandora the usual suspects of the military-industrial complex re-unite and re-enact the themes of “Dances with Wolves”, ”The Last Samarai”, “Mutiny on the Bounty”… even “Bambi”. But happily the special effects foray was not necessarily to incarnate super heroes from comic books, but science fiction, a literary laboratory to study the plausible. Whether as literature or just a literary genre, science fiction novels have addressed interstellar travel, life on other planets and avatars for decades, though with imagery usually left to book cover art and inner response to narrative As a rule, before its themes reach the screen the baleen whales of Hollywood filter feed on them to such extent that remains are likely only action sequences in exotic locales. So, though Cameron’s story of conflict might be conventional, movie reviews might be missing the most interesting film aspects by neglecting to examine the world constructed and the voyage traveled – whether based on fiction or facts.
Pandora across Space
Pandora in space and time is not as elusive as “long ago and in a galaxy far away”. In a pre-release interview, film director Cameron placed it in the star system Alpha Centauri. While our own solar system is composed of planets, moons, smaller bodies and the sun, whether Alpha Centauri has planets is as yet unknown; but it has two stars very similar to the sun ( Alpha Cen. A and B) fairly close to each other, and another smaller, much fainter star C or Proxima Centauri. In the skies of the United States they are visible in the far south (Hawaii and Florida) as a single star nearly as bright as Sirius. That Alpha Centauri is perceived as bright as it is is because it is the nearest star system known.
From reading astronomy books in grade school, several units of measure remain in memory in terms of English units: distances to the moon (238,000 miles); the sun (93 million) and the speed of light (186,000 miles per second). These days texts introduce these measures in metric units: 380,000 kilometers to the moon, 150 million to the sun and 297,600 kilometers per second for the speed of light. But by either measure, radio or laser beams aimed at the moon from Earth reach it in 1.3 seconds and the sun’s rays reach Earth in 8 minutes and 22 seconds.
Light from the suns of Alpha Centauri takes 4.2 years to reach the Earth.
To dispense with miles and kilometers, we can move on to light years, astronomical units (AUs) and parsecs, each with its own type of insight. The sun is 1 AU away from the Earth while Mars and Jupiter are 1.52 and 5.2 respectively from the sun. At opposite ends of Earth’s orbit (180 degrees apart, say at summer and winter solstice), if a surveyor were to look off into space at plus and minus one degree deflections from the right angle line to that base, the lines would cross at 57.3 AUs out, nearly 20 AUs beyond the orbit of Pluto; at 1/60th of this deflection or an arc minute, 3437 AUs; at 1/3600th of a degree or an arc second, 206,264 AUs. This last distance, based on astronomical surveying techniques, is a parsec, equivalent to 1200 “light-days” or 3.286 light years, about one light year short of the Alpha Centauri system, 263,600 AUs away. Thus, for every mile or kilometer between the Earth and Moon, there are about as many astronomical units between the sun and the next nearest star, a distance ratio of about 100 million. One of the reasons many 16th century minds were skeptical about Copernican theory was the difficulty of detecting shifts in positions of stars. In the case of this nearest star, home world of the Na’vi, its position would shift less than an arc second – and it was not visible from Europe at all.
Like the astronauts in “2001” headed to Jupiter, the space voyagers in “Avatar” hibernated in a deep refrigerated sleep for several years, but the 22nd century voyage traversed a distance 100,000 times larger than the journey to the giant planet. In both cases the technical issue of human hibernation was similar, but the transport problem of “Avatar” was enormously more difficult. It is true that in the absence of drag and gravitational force, a spacecraft could be accelerated to very high speeds – and we know of means to reach higher speeds than have been demonstrated thus far – but even advanced nuclear propulsion systems pale to what is required to reach a place like Pandora in six years. This would require a significant breakthrough. Our descendants would have to get very lucky.
Pandora across Time
At first look, this six-year trip to another star was undertaken at better than two thirds the speed of light average, not taking into account relativistic effects. While light travels at 300,000 kilometers per second, human rocketry has not yet achieved changes of velocity equivalent to the Earth’s speed around the sun (30 kilometers per second). What is more, beside speeding up to travel, there would be the need to slow down near Pandora and stop. To obtain the velocity of light by accelerating at 1 g, it would take nearly one year (347 days); but due to all manner of physical limitations including those related to Einstein’s Theory of Relativity, a goal short of light speed would be required. If we take the 1-g case of acceleration and deceleration, then we can estimate that 694 days of the flight were undertaken at an average velocity of half light speed, traversing nearly a light year. Flight time from the standpoint of Earth with these assumptions exceeds 5 years. If velocity topped out at 80 to 90% of light speed, the journey would approach six years.
Geometry, mass and the passage of time are changed as objects approach such speeds. In both aerodynamics and relativistic mechanics, when speeds approach either that of sound or light, descriptive equations are ruined by “divisions by zeros”. Theory in such circumstances breaks down.
So, to an observer on Earth , if such a ship accelerated up to near light speed, cruised at such and then decelerated to stop, the voyage would take at least six years; most likely more. But from the standpoint of a voyager such as Jake Sully on board, on watch all during the voyage or eventually awakened by an alarm clock, the time duration would be less because of the time dilation effect of nearly light speed.
In the equations describing general relativity there is a recurring algebraic expression which affects lengths, mass and perceived time as function of relative velocity measured as a fraction of the speed of light: the square root of [1 –(v/c)^2] or [1-(v/c)^2]^0.5. If a spacecraft’s velocity is half the speed of light (c), and time at rest or near zero velocity (t0) is multiplied by this expression, then perceived time’s rate is only 86.6% of time at rest. If the speed is 90% of c, time’s rate shipboard is 43.6% of time at rest. Time continues to slow down as ship speed approaches the speed of light – at which point it would stop. But since quantities such as rest mass (m0) are also divided by this expression which heads them toward infinity, nature declares “game over” or else disallows things to approach this state of affairs in the first place.
Despite the analytical appearance of all this, I have to say that I do not know how the “Avatar” screenwriters intended to address these issues. Acceleration, for example, need not have been achieved at 1 gee. It could have been higher or lower or perhaps made irrelevant by a breakthrough regarding the effects of inertia (no acceleration perceived). Pandora’s strange floating mountains suggested anti-gravity concepts somewhere at work in “Avatar”; yet most human locomotive problems on Pandora were solved laboring against gravity with propellers or jet engines. So while it would be possible for clocks on Pandora to be synchronized with Earth, six years of elapsed time as a result of flight would not be the same elapsed time back on Earth. It would be longer with an exact answer depending on the Pandora flight plan filed. And naturally the corporate quarterly reports referred to in the movie would have to be written largely based on forecasts.
Welcome to Alpha Centauri
The solar system is not very cluttered. The earth and inner planets such as Mercury, Venus and Mars are much less massive than the sun. These planets hardly interfere with each other gravitationally. But Jupiter is ten times wider than the earth and 330 times more massive. The sun is about 100 times wider than the Earth and a thousand times more massive than Jupiter (330,000 Earths). The film “Avatar” identifies Pandora as a large moon of a planet that resembles Jupiter. If nothing else, we can infer that Pandora is a moon larger than any in the solar system owing to its atmosphere; also, that it is close to a star that provides as much heat or illumination as our own sun, one of those three Centauri suns. In comparison to the Earth, Pandora is located in a crowded portion of space full of celestial traffic.
Back in the 1980s when I was engaged in developing tools for simulating the flight of spacecraft, I had cut and pasted programs to look at problems related to planets outside the solar system; namely, could earth-like planets find stable orbits in star systems like Alpha Centauri or other “binary” stars. Beside the fact that interesting close-by binary systems like Alpha Centauri, Sirius and Procyon were laid out over distances no larger than the solar system, these component stars orbited not in circles but in elliptic paths resembling the paths of short period comets with eccentricities of about 0.5. Additionally, since the stars had different masses than the sun and their luminosity was highly dependent on mass ( to the 3rd or 4th power), the regions where temperature belts similar to Earth’s could be established about these stars had to be re-computed for hotter, cooler, larger or smaller stars. All these considerations made such studies interesting for myself and others working in the field.
Subsequently observational astronomy underwent a related revolution in capability to detect companions to visible stars. Since 1995 about four hundred extra-solar planets have been discovered largely by watching for periodic doppler shifts in spectral lines of host stars. Prior to this the field was stymied by the limited results obtained by “astrometry”, the measurements that eventually came to the rescue of the Copernican hypothesis that the Earth and other planets orbited about the sun.
Astrometry’s contributions are based on the fact that pairs of bodies orbit around their common center of mass. Since stars have mass ratios often close to 1, this means that their center of mass might be a point in space midway between them, the barycenter. Since the Earth and Moon are separated by about 60 Earth radii and the mass ratio is about 81 to 1 in Earth’s favor, the center of mass for the Earth-Moon system is on the Earth-Moon line but below the Earth’s surface. Still, to an observer out in space, the Earth would appear to wobble or gyrate backward and forward over a lunar orbit or month. Many stars are observed to do that because of large companions of nearly the same mass. Sirius A, more than 20 times brighter than the sun, is paired with a white dwarf star less than a thousandth as bright, but their mass ratio is about 3 to 1. Even if the Sirius B is hardly visible in its partner’s glare, A’s movements due to B can be charted in the sky.
In the case of Alpha Centauri A and B, the period is about 80 years with an eccentricity of 0.5. While their mean separation is 23 AUs, it varies between 34.5 and 11.5. From Earth-bound observatories, these separations in the celestial sphere would be slightly smaller values in arc seconds.
Though stellar motion against the celestial sphere is one way to detect invisible companions, Doppler shifts of spectral lines provides another. Distinct lines can be shifted to “red” for receding motion; “blue” for forward motion. Observing the Doppler shift of distinct absorption lines in the spectrum of Sirius A, in line velocity measurements can show an orbital motion of about 49 years period with the fainter star – in addition to its slight motions in the celestial sphere over the same period. Since Jupiter takes 11.84 years for a 5.2 AU radius orbit, the sun is drawn through a countering revolution about their common barycenter 1/1000th the radius but with the same period. Thus, while Jupiter has an orbital velocity of 13.16 km/sec, the sun has a velocity in this motion 1/1000th the value, about 13 meters/second. Based on astronomical techniques available today, this would be near the limits of detectability and it would take over a decade to verify. Many or most of the planets discovered thus far are more massive than Jupiter but also much closer to their stellar primaries. The register of planets is full of “hot Jupiters” with orbital periods of less than a week. This does not necessarily mean that most planets fall into that category, but that they are easier to detect. Instead of a 13 meter/sec oscillation, astronomers are detecting oscillations 10 or 100 times larger, the basis for the recent extra-solar planetary harvest. Unfortunately, to detect Earth by means of solar Doppler shifts, one would need to look for the superposition of a 0.1 meter per second oscillation atop the Jupiter signal stretched over a period of a year. Visible spectral lines are not that sharp; such a signal would be lost in the noise. But the earth provides evidence of its existence with radio waves.
While there have been detections of massive planets like Jupiter at other nearby stars such as Epsilon Eridani, there have been no detections thus far for Alpha Centauri A, B or C. This does not rule out all planets, but makes it less likely that a Pandora there would be a moon of a body like Jupiter. Despite similarities to the sun, the surface temperatures, brightness and radii of A and B would result in some differences in where an Earth type planet would be placed. In the case of A, the largest and brightest star, an Earth or Pandora would likely reside at 1.25 AUs away with a year of about 484 days; for B, about 0.65 AUs (about where Venus orbits the sun) with a period of 204 days. In both of these cases the presence of the other star influences the orbits of these terrestrial planets, causing them to experience cyclic changes in their eccentricity over thousands of years, but a number of studies (beside mine) indicate stability, actually with B’s planet being less influenced by A than vice versa. A remaining issue would be how the planets would have formed in the first place, but this is an observational undertaking as well. There are many star-forming regions in the sky in which newly formed stars are surrounded by disks that appear to be forming into planets. Close binary stars add complications, but do not necessarily preclude planet formation.
With hundreds of star systems home to over four hundred planets thus far, some statistical patterns for formation have been sought. Among many observations coming to light was one with regard to the abundance of lithium in stellar atmospheres: where planets were observed, stellar atmosphere lithium was depleted. Alpha Centauri A possesses more lithium than the sun does while B possesses less. So there could be a planet or two lurking around Alpha Centauri B after all.
