1.2 >> 2001: A Trojan Binary

obelisk-monolith2

In post 1.1 the storyline associated with season three/episode three of Star Trek (The Paradise Syndrome), which aired on 4 October 1968, was briefly detailed.  In addition to learning the crew of the U.S.S. Enterprise had traveled to the distant planet Amerind in an effort to deflect a massive asteroid on a collision course with the planet, we were also introduced to an enigmatic metallic obelisk, the purpose and composition of which were entirely unknown.

Mr. Spock’s perplexity at his tricorder’s inability to scan the obelisk or to even determine its age is very reminiscent of the circumstances portrayed in another 1968 production – the now classic sci-fi film 2001:  A Space Odyssey (hereafter 2001 ASO).  In this film, a scientist named Dr. Heywood Floyd describes the discovery of an alien artifact to an astronaut who’s just arrived in Jupiter space:

“Eighteen months ago the first evidence of intelligent life off the Earth was discovered.  It was buried forty feet below the lunar surface, near the crater Tycho.  Except for a single, very powerful radio emission, aimed at Jupiter, the four-million year old black monolith has remained completely inert, its origin and purpose still a total mystery.”

The enigmatic nature of the obelisk and monolith aren’t the only attributes the  Star Trek episode and 2001 ASO have in common.

In 2001 ASO’s opening Dawn of Man sequence, a group of primitive hominids or ape-men are depicted in an African desert as they gather around an Earth-based version of the black monolith that appeared before them while they slept through the night beneath a rock outcropping.  Having been startled awake by the presence of the alien artifact, the ape-men slowly begin to caress its smooth surface as their initial fear gives way to curiosity.  Shortly after making physical contact with the monolith, the hominids exhibit signs of increased intelligence as they begin to wield animal bones as weapons, with which they assert themselves against a trespassing tribe.  Closing out the scene, we see the hominid leader violently tossing an animal bone into the air as it loudly howls in triumph over its enemies.

vlcsnap-2014-01-23-01h30m14s157

In an interesting transition to the next segment of the film, the image of the airborne bone cuts immediately over to a bone-shaped spacecraft in orbit above the Earth millions of years later.  The obvious implication is the monolith served to spark a steep uptick in the hominid’s intelligence, promoting mankind’s development.

Similarly, we slowly learn over the course of The Paradise Syndrome episode that the enigmatic obelisk has promoted the development of Amerind’s humanoids.  As Mr. Spock ultimately discovers, the obelisk was left on the planet as a marker by a super-race known as the Preservers that passed through the galaxy, rescuing primitive cultures that were in danger of extinction and seeding them where they could prosper – on this particular occasion the obelisk ultimately serves as an asteroid deflector that saves the planet.

Having underscored some curious parallels existing between Star TrekThe Paradise Syndrome (S3/E3) and 2001 ASO, both of which were released for public consumption in 1968, one might wonder what explanation can be called upon to account for the remarkable similarities or synchronisms between the two.

As mentioned in post 1.1, Margaret Armen started to develop The Paradise Syndrome storyline in March of 1968, one month prior to the April 1968 release of 2001 ASO, which might suggest to some that, rather than having borrowed ideas from the Clarke/Kubrick film, Armen’s synchronous storyline was instead a prime example of a highly unlikely, yet  nonetheless realized, coincidence.  It should also be remembered, however, that Armen didn’t complete her final draft until June 1968, which is to say, two months after 2001 ASO’s theatrical release.  As a result, it seems quite plausible Armen’s original March 1968 outline didn’t include the obelisk but instead revolved more around the asteroid impact concept.  Under this scenario, Armen would’ve then seen 2001 ASO or heard about the specifics of the film secondhand prior to completing her final draft in June and subsequently incorporated the idea of an obelisk asteroid deflector into the script.  Unfortunately, additional background information concerning the episode’s development, which would eliminate the need for speculation, doesn’t seem to be available so there the matter will need to rest.  There is, however, one additional similarity between Gene Roddenberry’s television creation and the Arthur C. Clarke/Stanley Kubrick film that seems to have successfully hidden itself in plain sight.

Had someone been approached to come up with an alternate title for Gene Roddenberry’s 1960s sci-fi television series that didn’t use the words “Star“ or “Trek” but connoted the same or similar meaning, one possibility that may’ve been offered up might’ve been Galaxy Quest, which, as it turns out, happened to be the name of a 1999 Star Trek parody, starring Tim Allen and Sigourney Weaver.  Another possibility – one that may very well have occurred to the reader by this point – would be Space Odyssey.  And with that, we’ll now segue to an intriguing analysis of 2001:  A Space Odyssey, a film released two years after the first episode of Star Trek aired on NBC, which might suggest to some that Clarke and Kubrick did a bit of borrowing themselves.

As described earlier, the opening sequence of 2001 ASO begins with an imaginary encounter between proto-humans and a sophisticated extraterrestrial artifact.  Following this opening sequence, entitled The Dawn of Man, we then jump several million years into the future, stopping to survey the situation at the dawn of the 21st century, a point in time at which the Moon has been colonized and meticulously surveyed.

Notwithstanding the now obvious fact the Clarke/Kubrick timetable of technological advancement was a bit too optimistic, we learn in the film that a second black monolith is discovered when scientists pinpoint an unusually powerful magnetic anomaly, leading them to excavate at a lunar site near the impact crater Tycho.  Shortly after excavating the lunar monolith a mission is mounted to Jupiter when a mysterious radio pulse, emanating from the alien artifact, is beamed directly toward the giant Jovian planet with pinpoint accuracy.

In light of the current study, of particular interest in relation to the 2001 ASO Jupiter Mission sequence is a short scene wherein the American spacecraft – U.S.S. Discovery One - is involved in a close encounter of sorts while en route.

The incident in question occurs while mission commander Dr. David Bowman prepares to board a small EVA pod in order to access the ship’s outer hull and retrieve a transmitter device know as the AE-35 for inspection.

Just prior to Bowman’s departure, the camera switches to a wide-angle, long-distance shot from outside the vessel.  At first the field of view is nearly empty save for the tiny image of the Discovery One spacecraft appearing in the screen’s upper right-hand quadrant against the dimly flickering star field in the background.

A second or two later, however, a small white point emerges from the star field, rapidly growing in size and quickly morphing into a tumbling asteroid that hurls overtop of the camera.  Following the first asteroid on a slight offset is a second of similar size.  This asteroid too barrels over the top of the camera and then returns us to the same nearly empty frame.

2001 binary 01

The composite image below provides a comparison with respect to the relative size of the two asteroids, making it quite clear they’re of nearly equal mass.

comp ast

Although the two asteroids appear to pass the Discovery One at a relatively safe distance, in astronomical terms such proximity would, without question, constitute what astronomers call a “near miss.”

As it turns out, the Jupiter Mission sequence from 2001 ASO was based in part on a 1949 short story by Arthur C. Clarke entitled Breaking Strain (aka, Thirty Seconds Thirty Days), which revolves around a space freighter, en route from Earth to Venus, being struck by a meteor which breeches the hull and depletes most of the ship’s oxygen supply.  Given the catastrophic meteor strike associated with the spacecraft in Clarke’s Breaking Strain, it seems plausible to suggest the meteor/asteroid near miss incorporated into 2001 ASO derives directly from Clarke’s earlier short story, although in this instance the ship narrowly escapes impact.

A celestial circumstance in which two asteroids in close proximity follow the same trajectory through the vastness of the solar system is a special one albeit now known to be more commonplace than originally thought.  Such objects are known by astronomers and astrophysicists as binary or double asteroids.  These asteroids are unique in that they consist of two bodies bound by gravity, rotating about a common center of mass in a fixed period of time.

Although astronomers long suspected the existence of binary asteroids, the first binary asteroid wasn’t observed with absolute certainty until 1993 when the Galileo probe photographed the main belt asteroid 243 Ida and its small satellite Dactyl.  This occurred as the spacecraft blazed by the binary system at nearly 28,000 MPH on its way to Jupiter.

243 ida

Interestingly, whereas the U.S.S. Discovery One voyage of the Clarke/Kubrick film portrayed the first manned mission to Jupiter to conduct an extensive scientific survey, to date the Galileo mission is the first and only unmanned mission to Jupiter to entail an orbital insertion followed by an intensive scientific survey.

Moreover, it should also be pointed out that 2001 ASO was the first (and possibly the only) film to depict – via special effects – a hypothetical binary system of asteroids whilst the Galileo probe was the first manmade device to actually image the once hypothetical construct and transmit those images back to Earth.

Additional specifics of the Galileo mission will be discussed a bit later as it has further relevance with respect to the current study.

In the author’s previous post (1.1), a curious synchronism existing between an episode of a 1968 science fiction series (Star Trek) and a 2001 scientific paper was underscored.  Continuing along these lines, in this post we’ll explore yet another intriguing synchronism existing between 1968′s 2001 ASO and a 2001 scientific discovery.  As with the previous synchronism, this one too deals with the subject of asteroids.

On the basis of a prima-facie screening of 2001 ASO, it’s relatively clear the binary asteroid encounter takes place at some point near the midpoint of the Jupiter Mission sequence and, interestingly, enough information seems to be available to answer the question of when with surprising accuracy.  Working from details deriving from the movie, the movie’s 1965 script and Clarke’s 1968 novel of the same name, fans of the film have successfully synthesized an intriguing timeline of events.  Utilizing this timeline in conjunction with images from the film as well as statistics culled from NASA’s Galileo Mission to Jupiter, it’s then possible to determine specifics with respect to the trajectory and destination of the film’s hypothetical binary asteroid.

Although the procedures involved in attempting to determine the trajectory of the film’s hypothetical binary asteroid could be a bit complicated, the process can be vastly simplified by employing a straightforward computer model.

Using a 3D modeling program and a low-resolution model of the U.S.S. Discovery One (built to approximate scale), it’s possible to duplicate the 2001 ASO film frame depicting the close passage of the hypothetical binary asteroid.

2001 ASO model

Once the film frame is reconstructed in virtual space, it’s then a simple matter to view the scene from any angle.  For our purposes, a bird’s eye perspective, looking down on both the spacecraft and the passing binary asteroid is essential.  When we carry out this task, we arrive at the top down view included in the image below.

birdseye

As we know the binary asteroid’s traveling directly toward the camera, we’re in a good position to determine the angular orientation of the Discovery One relative to the camera’s primary axis (which is the equivalent of the asteroid’s trajectory).  All we need to do is simply extend a straight line along the spacecraft’s primary axis until it intersects the binary asteroid’s trajectory line.

At this point, it’s then a simple matter to use a virtual protractor to calculate the spacecraft’s angular orientation relative to the asteroid’s trajectory and, when we do so, we learn this angular orientation is equivalent to 139°.

birdseye2

birdseye3

In order to then determine the destination of the Clarke/Kubrick hypothetical binary, we next need to pinpoint the whereabouts of the Discovery One in relation to its elliptical path of travel or Jupiter-bound trajectory.

In order for a space probe or spacecraft to intercept a planet, it’s necessary to launch the space-bound vehicle into an elliptical orbit around the Sun – one that intercepts the target planet’s orbital path.  The figure included below is taken from NASA’s 2003 Galileo Mission press kit and the highlighted red line depicts the Galileo probe’s final Jupiter intercept trajectory (when looking down on the plane of the ecliptic).

galileo traj

After the final slingshot maneuver around the Earth/Moon system (8 Dec 1992), the Galileo probe acquired a final burst of speed, accelerating from 79,000 MPH to 87,200 MPH, which significantly elongated its orbital parameters.  This increased velocity is represented by more widely-spaced hash marks drawn perpendicular to the trajectory line.  The distance between each pair of lines represents an interval of one month and, as is apparent from the figure, this distance starts out further apart, becoming closer together as the probe approaches Jupiter.

The widely spaced lines translate to high speed and lines positioned nearer together represent low speed as it requires more time to travel the same distance the further along its trajectory the probe travels.  The reader will recall that at the final Earth/Moon slingshot of 8 December 1992, the probe was traveling at 87,200 MPH but, as the probe approach 243 Ida nine months later, it had been slowed to a meager 28,000 MPH or, about a third of its earlier velocity (see previous figure).

If the planet Jupiter wasn’t present when the probe reached the outer edge of its orbital ellipse, instead of hitching a ride in the planet’s gravitational field, the slowly moving probe would gradually begin tumbling back toward the sun with ever increasing velocity.

The Discovery One’s elliptical trajectory would be much like that of the Galileo probe but we know from the film, film script and novel that it accelerates away from the Earth/Moon system at a much greater rate, ultimately attaining a much higher velocity.  We know this as, following Galileo’s final slingshot, it took three years to reach Jupiter whereas Clarke’s 1965 script states the transit time is 257 days and the novel indicates the mission is to be a 2-year round trip, meaning the transit time would be closer to a full year.

Although either figure would work with respect to the current discussion, an average transit time will be calculated on the basis of these two figures.

The following Discovery One trajectory incorporates a total transit time (average) of 311 days and uses an elapsed mission time of 148 days for the asteroid encounter.  This 148-day estimate is reached via the accumulation of days relating to a series of logged chronological events beginning with the time of the spacecraft’s departure and culminating in the radio delay time associated with a key transmission from the spacecraft to Mission Control.  This transmission concerned the AE-35 unit and occurred the day prior to the asteroid encounter.  The stated delay time of 25 minutes equates to a distance of 284.9 million miles from Earth.

The time interval between trajectory “dots” in the diagram is 25.9 days and the “X” marks the point of the asteroid encounter.

orbit 1

Having established Discovery One’s approximate location along its trajectory at the time of the binary asteroid encounter, we can now incorporate the angular data obtained previously to plot the trajectory of the binary asteroid.

Given the close proximity of the asteroid and the spacecraft in relation to the vastness of the solar system, the bird’s eye version of the movie frame showing both the asteroid and the Discovery One (see previous figure) is reduced to a single point defined by two intersecting lines – one line representing the asteroid’s trajectory and the other representing the orientation of the Discovery One’s primary axis.

The spacecraft’s axial orientation relative to its orbital trajectory can be considered equivalent to a line drawn tangent to the semi-ellipse defining its travel path.  Once this tangent line is established and plotted, the binary asteroid’s trajectory can then be plotted by incorporating the 139° angle calculated previously.

orbit 2

At this point, the reader may be wondering why all this effort was put into estimating the trajectory of 2001 ASO’s binary asteroid.  To understand the significance of the asteroid’s trajectory, we must first note the point of intersection between the asteroid trajectory line and the orbital trajectory of Jupiter as depicted in the figure above.  With this intersection point firmly in mind, we now need to learn a bit more about the Sun-Jupiter gravitational system.

Born 25 January 1736 in Turin, Sardinia-Piedmont (Italy), Giuseppe Luigi Lagrangia (Joseph-Louis Lagrange) was inspired at an early age by a memoir penned by English astronomer Edmond Halley of Halley’s Comet fame.  Greatly motivated by his chance reading of Halley’s chronicle, Lagrange was drawn into the world of science and mathematics and, by 1761, was widely considered one of the greatest mathematicians living.

lagrange

In 1772, Lagrange happened upon an unusual upshot of Newton’s Law of Gravitation when applied to two bodies orbiting one another.  According to Lagrange’s calculations, there should be two locations along the orbital trajectory of the smaller body wherein objects will oscillate rather than succumb to the gravitational fields of either entity and fall toward one or the other.

From a geometric perspective, these points lead and trail the body in question by 60° and lie along the body’s orbital path as illustrated in the figure below, which depicts Earth’s Lagrange points (L4 – leading; L5 – trailing).

earth lagrange

Although the larger body in our current scenario is still the Sun, the smaller body is the planet Jupiter and Jupiter’s Lagrange points (L4 and L5) have attracted the attention of a great many scientists in the wake of Lagrange’s prediction for reasons we shall soon see.

The exceptionally wide gap that exists between the orbits of Mars and Jupiter is familiar to astronomers due in large part to the fact that, rather than containing an essentially empty void, it contains a relatively large population of orbiting bodies – 243 Ida included among them.  This relatively dense band of orbiting bodies, beginning just outside the orbit of Mars (1.5 AU) and extending out to around 3.3 AU (Astronomical Units), is known collectively as the main asteroid belt.

main belt

Although the main asteroid belt consists of a vast number of primordial bodies or minor planets, it’s not the only celestial cache of interplanetary debris in the solar system.  Just as the Earth has leading and trailing Lagrange points along its orbit, so to does the planet Jupiter.  Unlike Earth’s Lagrange points, however, Jupiter’s Lagrange points are centered within relatively large clusters of asteroids that are locked perpetually into the planet’s orbit, leading (L4) and trailing (L5) the planet by 60°.  The leading group of Lagrange asteroids is known as the Greeks and the trailing group, the Trojans.

L4 - L5

Combining the information included in the figure above with the previous determination concerning the binary asteroid’s trajectory, we derive the following diagram.

comp

On the basis of the figure above, what’s important to understand about 2001 ASO’s hypothetical scenario is that, at about the time Discovery One’s arriving at Jupiter, the binary asteroid is nearing the planet’s trailing Lagrange point, which is to say, finding itself nestled deeply within the very heart of Jupiter’s Trojan asteroid population (L5).

Although at this point it no doubt seems to the reader as if a great deal of time and effort has been spent carrying out calculations of no consequence, providing just a modicum more information may profoundly impact one’s perception of the matter.

As previously mentioned, astronomers had long suspected the existence of binary asteroids and, in 1993, the first known binary asteroid was photographed by the Galileo probe on its way to Jupiter.  Despite this remarkable initial confirmation, it would be another 5 years before the second binary asteroid would be discovered.  In the years following this second discovery, additional Main Belt and Near-Earth binary asteroids were found but no Trojan’s could be counted among them.

Then, it happened…

The same year that saw a massive surge in the ground-based detection of binary asteroids also saw a team of astronomers, led by Dr. William J. Merline, utilize the 8.1-meter Gemini North telescope to discover the first ever Trojan binary.

One thing that was unique about this breakthrough was the fact that, unlike most binary asteroids discovered (e.g., 243 Ida), the components of this binary system (617 Patroclus) were nearly identical in size – an astonishingly rare occurrence.

What was far more extraordinary about the find, however (in light of the author’s alleged 1968/2001 temporal nexus), was the year in which the discovery was made.

The year of the discovery was 2001!

The image below was created by space artist Lynette Cook for the Keck Observatory in the wake of the Trojan binary’s discovery.  With respect to the Clarke/Kubrick film 2001:  A Space Odyssey, the only thing missing from the painting is the artist’s rendition of the slightly angled tail-end thruster assembly of the U.S.S. Discovery One, positioned between the binary asteroid and Jupiter (see inset) on its way toward the massive planet.

617 Patroclus

comp ast

What’s the likelihood a 1968 science fiction film, depicting a hypothetical binary asteroid (of nearly equal-sized components) en route to Jupiter’s Trojan asteroid population, would reference in its title the very year the first and only Trojan binary asteroid (of nearly equal-sized components – a rarity) would be discovered (i.e., 2001)?  Moreover, what mechanism can be called upon to account for the fulfillment of this seeming 33-year-old prediction from the realm of science fiction?

Once again, the presence of this synchronism might be explained by invoking coincidence when considered in isolation but, when coupled with the asteroid-related, fiction/fact, 1968/2001 synchronism discussed previously (post 1.1), it becomes much more unlikely.  Is it possible the proliferation of these synchronisms are not random events?

More to come…

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