Everyone’s heard the cliché about lemons and lemonade. NASA’s K2 Mission exemplifies it.

For brighter stars, the photometric light curves from K2 have precision on par with the original mission, and the data is completely free for everyone to look at. No secret repositories, no loose lips sink embargoed publications. Individual planets are so numerous that they are beginning to resemble the pages of names in a phone book. Six years ago, the light curve for EPIC 210508766 with its uninhabitable 2.747d and 9.997d super-Earths would have been cause for non-disclosure agreements and urgent Keck follow up. Now, given the ho-hum V=14.33, these planets will wind up as anonymous lines in a catalog paper — weights for gray scale dots in big data plots. Mere dimidia:

(EPIC 210508766 b and c, discovered earlier this week by Songhu Wang and Sarah Millholland)

A few years ago, I wrote a number of posts about a “valuation” equation for getting a quantitative assessment of the newsworthiness of potentially habitable planets. The equation folds qualities such as planetary size, temperature and proximity into a single number, which is in turn normalized by the dollar cost of the Kepler Mission.

The equation, when thoughtlessly applied to Earth, nearly got me into serious hot water when the now-defunct News of the World ran a story with it (which stayed, fortunately, behind a pay wall).

Now that Kepler’s prime mission has been complete for a substantial period, it’s interesting to calculate the values implied by the equation for the up-to-date table of Kepler’s KOI candidates. The cumulative sum runs into the tens of millions of dollars, with single objects such as KOI 4878.01 exceeding $10M. Such worlds are truly the candidates that the Kepler Mission was designed to find.

With K2, which has many bright M-dwarfs within its sites, it’s quite plausible that some very high-profile planets will soon turn up. I’ve set up a K2 prediction market at metaculus.com that canvases the likelihood that such a discovery is imminent…

Sign up and make your prediction count!

If nothing else, the extrasolar planets comprise a thoroughly alien cohort, albeit one that is hitched awkwardly to a naming scheme of utilitarian expedience: Tres-4b, Gliese 876e, HD 149026b, and so forth.

When it comes to exoplanets, I’m somewhat chagrined to realize that I fall into the old timer category, and so predictably, back in the old days, I stuck up for the conservative, default naming convention. In this post on exoplanet names back in 2008, I wrote:

A sequence of letters and numbers carries no preconception, underscoring the fact that these worlds are distant, alien, and almost wholly unknown — K2 is colder and more inaccessible than Mt. McKinley, Vinson Massif or Everest.

The International Astronomical Union, however, just issued official crowdsourced names for 31 exoplanets.

Some of them might take a some getting used to. Fortitudo, Orbitrar, Intercrus. “Son, that’s not 51 Peg b, that’s Dimidium.”

So will the names come into general use? I’ve set up a prediction market at our new website Metaculus to determine whether or not it’s likely:

www.metaculus.com/questions/38/

What do you think? Sign up and make your prediction count…

There are of order 500 million hot Jupiters in the Milky Way. Swollen and massive, with blisteringly short periods, they crowd the tables and the diagrams showing extrasolar planets. The first of their number were career-cementing front page news, trophies of planet roving planet hunters. Two decades on, they slip into the census with little fanfare and less notice.

Conventional wisdom holds that hot Jupiters form at large, Jupiter-like distances, where water ice is stable and where the orbital clock runs slowly. Then they migrate radially inward, either gradually, by interacting with the disk that produced them, or, even more gradually, via the Kozai process, or perhaps, violently, as a consequence of dynamical instabilities that toss giant planets to and fro.

When the first hot Jupiters were discovered, their presence was so strange, so unpredicted and so uncomfortable that there was a certain need for a point of contact with the familiar. It seems more sensible that a planet should form in the right environment and then go astray, rather than defy odds and logic to emerge spontaneously in a location where it obviously shouldn’t be. It’s a short leap from the Copernican principle to the idea that the Solar System has no special distinction. We have nothing orbiting at forty days, not to speak of four.

Yet there is a tantalizing gap in the mass-period diagram that hints that short-period super-Earths that reach fifteen or more Earth masses might engage in rapid gas accretion. Such promotions need happen less than once in a hundred tries. In the spirit of trying to go against the grain, in the perverse hope of eliciting a paradigm shift, Konstantin, Peter B. and I have been working to make the case that many hot Jupiters might just form where they’re found.

The details are all in a paper that we just posted on arXiv.

Image Source

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: