Monday, August 3, 2015

Extraordinary Near-Earth Asteroids II: 2010 TK7

Another denizen of the zoo of Near Earth Asteroids is a little rock called 2010 TK7.  The first clue to its unusual nature comes from its orbital period: 1.00039 Earth years.  The second clue is the orbit it pursues to permit it to avoid collision with Earth.  This 300-meter NEA follows the L4 Lagrange point on Earth’s orbit, 60 degrees ahead of Earth.  Its behavior is similar to that of the Trojan asteroids on Jupiter's orbit, 60 degrees ahead of and 60 degrees behind Jupiter: we can call it an "Earth Trojan". It circulates slowly around the exact L4 point because its orbit is quite eccentric (eccentricity 0.1908) and inclined (20.882 degrees).  As it ranges from perihelion, 0.8094 AU from the Sun (closer to Venus’ orbit than to Earth’s), out to aphelion at 1.1911 AU, its orbital velocity constantly changes

There have been numerous suggestions that this asteroid would be a very easy target for spacecraft missions from Earth.  The usual rationale is that, unlike most NEAs, it is always close to Earth and therefore easy to reach.  But this argument is simplistic and requires scrutiny.  Suppose the spacecraft departs from the Earth-Moon system with a relative velocity of 2 km per second.  The mean distance between Earth and the L4 point is 150,000,000 kilometers; to get there would then require 75 million seconds (about two and a half years), after which the spacecraft would fly by the asteroid at a relative speed of 2 kilometers per second, traversing the diameter of the asteroid in 1/7 of a second.   To reduce the flyby speed to the point at which the spacecraft could rendezvous with, orbit around, or land on the asteroid requires a velocity change (“delta V” to rocketeers) even larger than that required to take off from the Moon and get into orbit. 

The size of 2010 TK is poorly known.  Its apparent brightness and distance, measured at the time of discovery, permit us to calculate an absolute magnitude of 25.3, which is about 30 meters in diameter if the asteroid has “average” composition and reflectivity; probably 20 to 50 meters within the uncertainties of our data.

In case you haven’t seen the concept of “absolute magnitude” explained, it is the apparent magnitude a body would have if observed at a distance of 1 AU form Earth and 1 AU from the Sun.  The scale for measuring magnitude is an adaptation of the ancient naked-eye system: a bright star is “of the first magnitude”, a noticeably fainter star is 2nd magnitude, and so on down to the practical limit of naked-eye observation, 6th magnitude.  Every interval of 5 magnitudes corresponds to a factor of 100 ratio in the intensity of visible light.  Thus Vega is about magnitude 1, the faintest star your naked eye can see, about magnitude 6, provides 100 times less light, and a body of magnitude 26 is 25 magnitudes fainter than Vega, or five factors of 100 (10 billion times) fainter.

Is there anything about this rock that would attract the attention of explorers or miners?  Because of its orbit, it can never approach Earth closely enough to make it a practical target for spectroscopy or for radar observations.  If we needed to know what it is made of, its chemistry, mineralogy, and physical structure, we would have to go there.  In other words, to find out whether it would make sense to send a spacecraft there we would have to send a spacecraft.  This is not a compelling argument for planning a mission.

"The Day after Tomorrow" is no Closer

High on the list of things that Everybody Knows is the claim that the Gulf Stream is slowing down, delivering ever less heat to the Northeastern US and Western Europe and inevitably triggering a new Ice Age.  The “evidence” comes from proxy data and computer climate predictions; the reality of the problem was attested by the 2004 eco-porn movie “The Day after Tomorrow”, in which New York is eaten by a glacier.

There are just a few little problems with this story.  First, there is the use of the word “evidence” to describe the predictions of models and proxy estimates.  Let’s be clear about this: the way science progresses is to 1) collect data, 2) propose one or more ideas, called hypotheses, that might explain the data, 3) use quantitative models of these hypotheses to generate predictions of future observations, and 4) carry out a new round of experiments designed to test (and discriminate between) the competing hypotheses.  Steps 1 and 4 deal with evidence (data); step 3 is not evidence; it is informed conjecture, as-yet untested speculation, whose sole purpose is to motivate a search for critical new data, NOT to predict the future. 

Second, the role of disaster movies is not to teach science; it is to sell tickets.  Anyone who derives his understanding of climatology from disaster movies is a fool.  This judgement includes those whose knowledge of asteroids comes from Bruce Willis.

Third, (a most inconvenient truth): we actually have direct observational data on the flow of the Gulf Stream covering some 23 years of recent history.  Shock, horror: we don’t need to rely on hypothetical speculation!  A research team headed by an eminent expert on oceanic circulation, Prof. H. Thomas Rossby of the Graduate School of Oceanography of the University of Rhode Island and his team, have been measuring the speed of the Gulf Stream since 1992.  Their study was based on observations made on the Bermuda Container Lines’ ship Oleander, which makes weekly crossings from Elizabeth NJ to Bermuda.  The Oleander carries a Doppler current meter that directly measures currents to a depth of about 600 m.  And what are the results of their research?  They find no evidence whatsoever that the speed of the Gulf Stream has decreased over the time of their study. 

Why do we get so much bad science in the press? Because untested conjectures are often much more interesting than the truth. Which sells more papers (or movies), the "news" that we are on the verge of a new Ice Age, or the demonstrated fact that everything is going on normally? By ignoring the distinction between untested hypotheses and replicated fact, they mislead the public, misrepresent the science, and sell their undigested pap as news. 

Sherlock’s Debt to Giordano Bruno

             Followers of the excellent BBC Sherlock series (yes, you—it’s OK to admit it) have surely noticed the remarkable antipathy Sherlock holds against the “Napoleon of blackmail”, the reptilian Charles Augustus Magnussen.  But they also have perhaps been intrigued by the “memory palace” process of memorization that Sherlock and Magnussen have in common. 

            The revival of this ancient memory technology traces back to Giordano Bruno’s “Art of Memory”, in which ideas, people, and images are inserted into the context of a house or palace with many rooms.  This process was described and elaborated in Frances A. Yates’ wonderful book, “Giordano Bruno and the Hermetic Tradition”.

            But the technique is of far more ancient origin.  Cicero and Aristotle wrote of this technique, as did the famous Jesuit Matteo Ricci.  They in turn provided the inspiration to Bruno, whose ideas were again brought to current awareness by Yates’ scholarly writings.  And, as so often happens, these ideas were again “invented” by the writers of Sherlock, who surely were familiar with Bruno’s contribution, but who, in proof if their freedom from stuffy academic conventions, passed them on to us free of scholarly attribution.

            This oversight is perhaps made more understandable when we realize that the inscrutable Mycroft Holmes, in his assumed persona of Mark Gatiss, is the producer and one of the writers of Sherlock.  Surely he has some game afoot, if only we knew what it was…

            Perhaps all will become clear in Season 4, if it ever materializes.

The Alinda Family of Asteroids

The asteroid 887 Alinda has long been known to follow an orbit that is nearly resonant with the orbital periods of both Jupiter and Earth: its orbital period of 3.915 years is close to the 1:4 Earth resonance and close to the 3:1 resonance with Jupiter.  In recent years the rate of discovery of previously unknown asteroids has been enormous, with thousands of new asteroid discoveries each year, so it is not surprising that a number of other Alindas have been found.  Membership in this family requires an orbital period very close to 4 Earth years, which in turn requires that the mean distance from the Sun (the orbital semi-major axis) must be close to 2.54 AU.  That places these bodies in the inner asteroid belt—except for the excursions brought about by the eccentricities of their orbits. 
Orbits close to a Jupiter resonance are not only subjected to the gravitational perturbations exerted by Jupiter on all asteroids, but experience repeated perturbations with the same approximate geometry.  This allows, like the resonant pumping of a child on a swing, a constant buildup of self-reinforcing disturbances, which cause a constant growth in the eccentricity of the asteroid’s orbit, making an ever more elongated ellipse. Eventually, this growth in eccentricity imperils the asteroid by extending its orbit inward to perihelion distances ever closer to the Sun, crossing the orbits of one or more of the terrestrial planets, while also stretching the orbit outward so that its aphelion distance can approach Jupiter.  Close encounters with any planet can seriously disturb an asteroid’s orbit; the closest encounters, resulting in collisions, are fatal to the asteroid and may be seriously disruptive to the target planet.
The 23 Alindas now known include eleven in low-eccentricity orbits (e ranging from about 0.30 to 0.34).  These bodies roam the reaches of the Solar System from about 1.7 to 3.4 AU from the Sun, spending most of their time in the asteroid belt and never approaching any planet closely. They are the "young" Alindas, recently nudged into resonant orbits.  In such orbits their resonant relationship to Jupiter causes their orbits over time to gradually become more eccentric.  They are not in immediate danger except for the small probability of colliding with other asteroids, but they are in for serious trouble in the long run.
Three of the known Alindas (6318 Cronkite, 8709 Kadlu, and 6322 1991 CQ) have orbital eccentricities between 0.465 and 0.475, sufficient to have them cross the orbit of Mars.  These three Alinda Mars-crossers do not cross the orbit of any other planet; Mars has a small mass and cross-section area, and cannot remove these bodies as rapidly as Jupiter can replenish them and move them on to even more eccentric orbits.
Then there is the namesake of the family, 887 Alinda itself, with an eccentricity of 0.564.  Its perihelion distance (q) of 1.084 AU qualifies it as a near-Earth asteroid (NEAs by definition have q < 1.300 AU).  It grazes but does not cross Earth’s orbit, making it an Amor asteroid as well as an Alinda family member.
Even more pumped-up Alinda clan members include eight (with eccentricities between 0.57 and 0.75) that cross Earth’s orbit: at perihelion they are closer to the Sun than Earth is at aphelion, 1.017 AU.  They are therefore Apollo-family NEAs as well as Alindas.  Since all Alindas are Earth-resonant, they may fly by Earth repeatedly at close range at 4-year intervals for decades at a time, affording radar observation and spacecraft launch opportunities—and collision opportunities—over that time period.  One such asteroid is 4179 Toutatis, which was the target of a close flyby by the Chinese Chang-e 2 spacecraft in 2013.  Two members of this group, 7092 Cadmus and 8201 1994 AH2, could be termed Venus-grazers, having perihelia inside 0.76 AU.  The most eccentric of the Alindas is 3360 Syrinx, a Venus-crosser with e = 0.743.  Its orbit makes six crossings of planetary orbits every four years (twice each for Mars, Earth, and Venus), a highly unstable situation that suggests a short life expectancy.  Interestingly, all three of these most-eccentric Alindas have aphelia close to 4.3 AU.  None of the Alindas approach Jupiter closely, a wise precaution.  A close encounter with Jupiter could swallow the asteroid whole, kick it out of the Solar System permanently, or wreak other orbital havoc.
The Alindas serve as a reminder of the role Jupiter plays in sending hazardous bodies toward us; a fringe benefit is the opportunity to have many repeated launch opportunities to a given asteroid.  The Alindas are loose cannons, subject to disturbance by Jupiter, Mars, Earth, and Venus.  These asteroids are both carrot and stick, guaranteeing that we will hear a lot more about them in the future--such as when Toutatis comes by again in 2016!