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The New Horizons probe just flew through its closest approach to Pluto, and is executing its minutely detailed plan. Fingers on keys and its robotic spirochetes are spacelike-separated events.

The detail in the most recent photograph of Pluto — radioed as an assurance of success in the event that something hit the spacecraft during the last few hours — leaves the impression of a world that has been painted. Eons of weak geysers, subtle rarefied winds, and the sepia tones of photochemistry have combined to produce the illusion of shadow, oil pigments and diffuse lighting that eerily evoke this newly discovered portrait by Rembrandt.

First thing every morning, I check the raw images from New Horizons. Today there is a fresh set. The Independence Day glitch has been left millions of miles behind, and only days remain until arrival.

Pluto’s current remove seems to lie at a point of heightened mystery. Mottled patches and curiously regular features are starting to fill the frame.

The detail seems reminiscent of Mars seen through a refracting telescope, and brings to mind Percival Lowell’s drawings that combined real features and artifacts in a tantalizing juxtoposition.

Lowell’s drawing is from 1894. It was still a lifetime — seventy years — before Mariner 4 rushed past Mars and radioed cratered, disappointing close-ups of of the Martian surface. Undaunted, I rode my paper route during the early summer of 1976, concocting vivid premonitions that the first pictures from the Viking I lander would provide some shocking, irrefutable vista of fossils, sandblasted ruins and crashed saucers.

A more quantitative, but effectively similar vein of speculation informed this article by Loeb and Turner from a few years ago:

We need wait only another hundred hours or so if there is to be a view of Pluto’s lit-up cities of the night.

This morning, June 21, 2015, a Google image search for Pluto brings forth inane cartoon dogs, blurry, best-effort HST images, over-the-top space-art landscapes, and a selection of shiny photo-realistic globes, clearly influenced by Ganymede, Io, and Triton.

The New Horizons spacecraft, on its ballistic pinpoint trajectory, is just 22 days, 16 hours, 14 minutes from arrival at Pluto, devouring its ever-shrinking gap at 30,800 MPH. A remarkable recent movie posted by the Mission Controllers imparts enough detail to see by eye that the system is tidally despun. And with the targets still effectively at infinity, the scale of the bodies and the orbit is perfectly illuminated. Perspectives during the encounter will use foreshortening and narrow field of view to optimal effect, obscuring the fact that any system with an orbital time scale of order a week is, when taken as a whole, of order dozens of times less dense than air. Effectively just empty space.

In less than a month, the same Google search will be dominated by a small handful of thousand-fold improved images, possibly even by a single best photograph impressed in the camera’s eye during the dramatic needle-threaded moment of urgency.

Pluto’s cultural status made the mission possible. Perhaps the spacecraft will reciprocate with image that will become a touchstone, a visual shorthand for distance, isolation, frigidity and exile.

I was struck by the image that NASA released several days ago, just before the Dawn Spacecraft braided itself into orbit around Ceres.

From a graphic standpoint, the photograph is perfect. The black expanse relays that the asteroid belt, and by extension the solar system, are mostly empty. Even more subtle is the message telegraphed by the crescent phase. We arrive to our first clear view of this world as outsiders, from a distance further from the Sun than Ceres itself. A consequence of the energetics and the constraints of the trajectory design to be sure, but metaphoric nonetheless.

Vladimir Arnold, he of the A in KAM Theory, wrote a classic graduate text entitled Mathematical Methods of Celestial Mechanics. This, as one might imagine, is a book that is not exactly a storehouse of easy homework assignments. There are, however, a scattering of problems that offer insights while, at the same time, not actually requiring the tough-guy methods that are the text’s primary focus.

During his walk in outer space [as part of the Voskhod 2 Mission on 18 March 1965], the cosmonaut Alexey Arkhipovich Leonov threw the lens cap of his movie camera toward the Earth. Describe the motion of the lens cap with respect to the spacecraft, taking the velocity of the throw as 10 m/s. Neglect the asphericity of the Earth.

(Ria Novosti/Science Photo Library)

Leonov’s space walk tipped off a hair-rising adventure which began with his being nearly unable to re-enter the spacecraft, and ended with a frigid way-off-course landing in the Siberian Tiaga, all of which is covered in a recent BBC documentary.

One can hand-crank the problem by noting that the radially directed, \({\bf v}_{i}=10\,{\rm m\,s^{-1}}\), launch of the lens cap exerts no torque, so that \({\bf r}\times{\bf v}_{i}=0\), whereas the total specific energy of the lens cap’s initial orbit, \(-GM_{\oplus}/2a\) is augmented by \(\frac{1}{2}v_{i}^{2}\). Given the new semi-major axis, \(a_{\rm new}\) and the before-and-after conservation of \(h=(GM_{\oplus}a_{\rm new}(1-e^2))^{1/2}\), one can solve for \(e\), and then proceed to all four orbital elements by noting that \(r=a(1-e\cos E)\) and \(M=E-e\sin E\), and then working out the longitude of pericenter, \(\varpi\), relative to the reference direction defined by the radius vector from the Earth’s center to the point where the lens cap was thrown. Clumsy.

The guiding center approximation revives the old idea of epicycles to describe the motion of a particle (in this case, the lens cap) on a low eccentricity orbit. For modest \(e\), the true Keplerian motion is approximated as a compound of the circular motion of a “guiding center” and the counter-directed motion about the guiding center on a 2:1 ellipse, where the semi-minor axis is oriented radially, and has length \(ae\). Both motions complete once per orbital period. Here’s the basic idea, drawn for an orbit with \(e=0.3\), which is actually quite a substantial eccentricity:

For the lens cap problem, the guiding center materializes at a distance \(2ae\) ahead of the launch point. The motion associated with the guiding center is the superposition of two simple harmonic motions. For the radial oscillation, \(\frac{1}{2}v_{i}^{2}=\frac{1}{2}n^{2}x^{2}\rightarrow v_{i}=nae\), which works out to \(e=0.0013\). To first (and very good) approximation, the lens cap arrives back 88 minutes later in the close vicinity of the spacecraft, after inward and outward radial excursions of 8.4 km, and after leading the spacecraft by as much as \(4ae=34\) km. The small total gain in orbital energy lengthens the lens cap’s orbital period slightly, which means that the cap fails to catch up by a few tens of meters at the end of a full one-orbit epicyclic oscillation.

In Michael Rowan-Robinson’s Cosmology (3rd ed.) Oxford University Press. pp. 62–63, one finds, “It is evident that in the post-Copernican era of human history, no well-informed and rational person can imagine that Earth occupies a unique position in the universe.”

If one insists on a strictly inertial frame, I guess that’s true, but non-inertial frames often have more value. Thousands of extrasolar planets have been found, and not one of them is remotely habitable. Many lines of evidence are beginning to point toward an Earth that is unique, probably in the galaxy, and perhaps, even, in the accessible universe. In the post-post Copernican era, epicycles (2:1, rather than 1:1) have a certain appeal. And indeed, there’s nothing inherently wrong about the Tychonic model of the solar system, it simply subscribes to an Earth-centered point of view. Don’t we all?

On the topic of epicycles, I have to say I wasn’t a fan of the article on “retrograde beliefs” that appeared a few weeks ago in the New York Times Magazine. Obviously, astrology is a bunch of bunk. It’s known to be wrong. One can make the argument that taking it down in the genteel and informed confines of the NYT magazine amounts to shooting fish in a barrel. Satire is probably the best approach. Aside from this stylistic quibble, the writing in the NYT piece seems incoherent, somehow second-hand and artless. An intricate 1756 diagram by James Ferguson (who is no longer around to defend his work) is given a rather underhanded misrepresentation:

The full title of Ferguson’s book is Astronomy Explained Upon Sir Isaac Newton’s Principles, And Made Easy to Those who Have Not Studied Mathematics. The diagram reproduced in the NYT is not the product of some recalcitrant Ptolemaic view as implied in the caption, but rather appears in a chapter entitled “The Phenomena of the Heavens as seen from Different Parts of the Solar System”. It shows the intricate motions of the inferior planets in a co-rotating Earth-centered frame, and Ferguson gives a fascinating description of the analog-computational method he used to create the diagram:

One tends to roll one’s eyes when the topic turns to Georges-Louis Leclerc, Comte de Buffon, the French encyclopedist and pre-revolutionary intellectual luminary.

Buffon sounds regrettably similar to Buffoon, especially considering that The Comte is best-known for some memorable blunders. For example, Georges-Louis came out on the losing side of a tussle with Thomas Jefferson regarding the general valor of the New World fauna. From the wikipedia article:

At one point, Buffon propounded a theory that nature in the New World was inferior to that of Eurasia. He argued that the Americas were lacking in large and powerful creatures, and that even the people were less virile than their European counterparts. He ascribed this inferiority to the marsh odors and dense forests of the American continent. These remarks so incensed Thomas Jefferson that he dispatched twenty soldiers to the New Hampshire woods to find a bull moose for Buffon as proof of the “stature and majesty of American quadrupeds”

Buffon also speculated, in 1778, that the solar system’s planets were the result of a collision between a comet and the Sun, a hypothesis that is completely incorrect. Even in the 1750s, perturbation analyses (such as those carried out by Alexis Claude Clairaut in connection with the successful predictions of the return ephemeris for Halley’s Comet) had made it clearly evident that cometary masses are far smaller than planetary masses.

Buffon, however, was definitively not a buffoon. He came remarkably close to having a full command of all the scientific disciplines, and some of his efforts still sparkle. He calculated that the chance of the Sun rising tomorrow is \(1-(1/2)^x\), where \(x\) is the number of consecutive days that it has risen to date. In his treatment of probability theory, he also stated that one chance in 10,000 is the lowest practical probability — an enormously useful bon mot, on par, say, with Andy Warhol’s remark that “when you think about it, Department Stores are kind of like Museums.”

Buffon’s Histoire Naturelle, which aimed to exhaustively cover all of the natural sciences, ran to 44 quarto volumes, eight of which were written and which appeared after he died, and all of which were out of date the moment they were printed. Even in the 1700s, scientific knowledge was accumulating so rapidly that it was impossible to keep up.

It has been recently hammered home to me that the same situation also now holds true for extrasolar planets. Jack Lissauer and I just finished a review article on exoplanets for the forthcoming second edition of Elsevier’s Treatise on Geophysics. A pre-print is up on today’s arXiv listing. In writing the article, it was painfully clear just how large the literature is, and how fast it is growing…

When I lived in Japan, I visited Hokkaido University in Sapporo to give an astronomy colloquium. While there, I immediately noticed that an odd motto, “Boys, Be Ambitious!” is attached (in English) with great frequency to the various affairs, both large and small, of the University. One of the astronomy graduate students had the phrase written on a post-it note attached to the screen of his computer. In another building, there was a large mural showing a stern, stiffly dressed 19th-century gentleman exhorting a group of reverent students with a longer version of the phrase:

“Boys, be ambitious! Be ambitious not for money or for selfish aggrandizement, not for that evanescent thing which men call fame. Be ambitious for that attainment of all that a man ought to be.”

Which, upon reflection, seems to be reasonable advice…

The gentleman in the mural, it turns out, is William Clark Smith, the founder and first president of the University of Amherst, Massachusetts. In the mid 1870s, he was enlisted by the Japanese Meiji Restoration government as an Oyatoi Gaikokujin, or “hired foreigner”, to establish an agricultural college in Sapporo (now Hokkaido University) and he made an impression that has lasted well over a century. The Wikipedia article is extensive and quite interesting. On the origination of the motto:

“On the day of Clark’s departure, April 16, 1877, students and faculty of SAC rode with him as far as the village of Shimamatsu, then 13 miles (21 km) outside of Sapporo. As recalled by one of the students, Masatake Oshima, after saying his farewells, Clark shouted, “Boys, be ambitious!”

Upon returning to the United States, and flush with the organizational successes and appreciation that he had garnered in Japan, Clark left his academic career, cultivated an interest in gold and silver mining, and embarked on an abrupt, ambitious, and ultimately disastrous foray into the business world. In 1880, he teamed up with a junior partner, John R. Bothwell, to found what might best be described as a 19th-century incarnation of a metals hedge fund. From offices on the corner of Nassau and Wall Streets in Manhattan, the firm of Clark & Bothwell acquired interests in a slew of silver and gold mines across North America, for which they assumed management and issued stock. Clark, as president, got his contacts and colleagues to invest in the venture, and for a period during 1881, the stocks issued by Clark and Bothwell ran up into multi-million dollar valuations. A classic example of a bubble.

Clark travelled around the country, promoting the company, acquiring new mines, and seeing to their management, while Bothwell appears to have been responsible for back-office operations. Clark, who had no experience in finance, and little real knowlege of mining geology seems to have spun his wheels, while Bothwell, who had a shady history, actively mismanaged the companies. The operation got into debt, with the outcome being all too typically familiar along the lines of When Genius Failed. By the Spring of 1882, they were facing insolvency, investor lawsuits, fraud allegations, and various other problems. Bothwell disappeared on a train trip to San Francisco, never to be seen again, leaving Clark holding the bag. The story played out to the delight of the Massachusetts and national press.

From the Springfield Republican, May 29, 1882:

… it appears form the beginning that he, as manager of the mines has allowed Bothwell, as treasurer, absolute control of the books and finances of the several companies. It doesn’t appear that he ever examined the books, nor had anybody do so for him, or inquired into the financial condition of each mine, or what was being done with their profits; neither has he required from Bothwell such bonds as the latter’s position should require for the safe handling of moneys entrusted to him..

The scandal made the New York Times, which wrote several articles about the affair, including this one, from May 29th, 1882, which I dug out of the archive:

The scandals eventually ruined Clark’s health, and he died four years later, in 1886, at age 60. A cautionary tale for academics everywhere with ambitions to leave the Ivory Tower in search of glittering lucre…

I’ve been putting the finishing touches on a review article covering extrasolar planets that will be posted to arXiv in a few days. The list of to-do’s involves updating the figures, including the one shown just below, which charts \(M\sin i\)‘s of the RV-sourced planets in dark gray and simple radius-derived mass estimates of the transit-sourced planets in red. The steady Moore’s Law-like progression toward ever-lower masses has definitively reached Earth-mass (not to be confused with Earth-like) planets. The process took up only two decades, and was among the more impressive scientific advances of the recent past.

Here’s an elaboration of the above figure that doesn’t make it into the article, but is interesting nonetheless. On the y-axis is \(K/rms\), which is reasonably well correlated with the signal strength of Doppler velocity discoveries. One can certainly detect planets with confidence at low \(K/rms\), but it requires a large number of independent Doppler velocity measurements. The color corresponds to “astrobiological interest” — surely naive, and probably misplaced, but nonetheless quantifiable by my planet valuation formula.