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In Search of Planet Vulcan — The Ghost in Newton’s Clockwork Universe, by Richard Baum and William Sheehan, is one of my favorite astronomy books. It certainly has one of the best overviews of the momentous events and controversies surrounding the discovery of Neptune in September 1846. I’ll take the liberty to quote Baum and Sheehan’s recounting of the exact moment of Neptune’s discovery.

On September 18, Le Verrier wrote to Johann Gottfried Galle, then an obscure astronomer at the Royal Observatory in Berlin. A year earlier, Galle had sent Le Verrier his doctoral dissertation, which concerned observations made by 17th-century Danish astronomer Olaus Roemer. Belatedly, Le Verrier wrote to acknowledge it. Among other things, he queried Galle about Roemer’s Mercury observations, but then came quickly to his point:

“Right now I would like to find a persistent observer, who would be willing to devote some time to an examination of a part of the sky in which there may be a planet to discover… You will see, Sir, that I demonstrate that it is impossible to satisfy the observations of Uranus without introducing the action of a new Planet, thus far unknown; and, remarkably, there is only one single position in the ecliptic where this perturbing Planet can be located… The actual position of this body shows that we are now, and will be for several months, in a favorable situation for the discovery.

Galle indeed proved to be his man. He received Le Verrier’s letter on September 23, and at once sought permission from the observatory’s director, Johann Encke, to carry out the search. Encke was skeptical but nonetheless acquiesced: “Let us oblige the gentleman in Paris.” A young student astronomer, Heinrich Ludwig d’Arrest, begged to be included, and joined Galle as a volunteer observer. That night, they opened the dome to reveal the observatory’s main instrument, a 9-inch Fraunhofer refractor aimed at the spot assigned by Le Verrier. Recalculated for geocentric coordinates, its position was at right ascension 21 h, 46 min, declination -13 deg 24 min, very close to the position occupied by another planet, Saturn.

The question arose: What maps were available? At first they could think of none but “Harding’s very insufficient Atlas.” D’Arrest then suggested “it might be worth looking among the Berliner Akademische Sternkarten to see whether Hora XXI was among those already finished. On looking among a pile of maps in Encke’s hall [Vorzimmer], Dr. Bremiker’s map of Hora XXI [already engraved and printed at the beginning of 1846 but not yet distributed] was soon found.” As d’Arrest later recalled, “We then went back to the dome, where there was a kind of desk, at which I placed myself with the map, while Galle, looking through the refractor, described the configurations of the stars he saw. I followed them on the map one by one, until he [Galle] said: and then there is a star of the 8th magnitude in such and such a position, whereupon I immediately exclaimed, that star is not on the map!”

Neptune’s moment of discovery, at 11 PM Berlin local time on September 23, 1846, corresponded to 22:07 UT, or JD 2395563.4215. The period of Neptune is 60,190.03 days, or 164.79132 years. The first “Neptunian anniversary” of the discovery is therefore CE 2011 July 10 22:49:26.4 UT Sunday, that is, right now.

In 1846, photography was still in its very earliest stages, and it would be nearly two decades until the publication of Jules Verne’s De la Terre à la Lune. The fact that we greet the completion of one orbit in the possession of photographs of a crescent Neptune is a marvelous indeed.

Image Source.

Certainly, an occasion for celebration! On Friday, I got an invitational e-mail from Gaspar Bakos, who is hosting a Neptune-at-One cocktail party in Cambridge, Massachusetts. I briefly perused airfares before sadly having to decline.

A well-known theorem states that there’s no such thing as a free lunch. A corollary is that interesting discoveries tend to be made at the ~3-4 sigma level of confidence, and this is especially true if the supporting data is drawn from the public domain. If a signal is stronger than 4-sigma, then someone else has invariably pointed it out. If it’s weaker than 3-sigma, it’s probably wishful thinking.

With those rules of thumb in mind, I’m very optimistic that Kevin Schlaufman has obtained a genuinely important insight into how the planet formation process works:

The plot shown is above is from a paper that Kevin and I submitted soon after the 1,235 Kepler planet candidates were announced last Spring. After going through review, it was accepted by the ApJ, and it was posted to astro-ph last week.

I wrote about the underlying details of the plot in this post from several months ago. The basic idea is as follows: The 997 Kepler planet candidate host stars are divided up into two groups — (i) the less numerous group of stars that host a candidate with R_pl>5 Earth radii (red), and (ii) the more numerous group of stars that only host a planet (or planets) with R_pl<5 Earth radii (blue). The two groups of stars, along with a control sample of 10,000 non-candidate-bearing dwarf stars from the Kepler field (gray), are plotted in a color-color diagram (and then binned to create the diagram above):

The y-axis corresponds to the magnitude difference between a given star’s green (Sloane g filter) and red (Sloane r filter) colors. The x-axis charts the differences between the 2Mass J and H infrared colors for each star. Metal-rich stars tend to have redder optical colors than metal-poor stars, whereas the J-H index sorts the stars in terms of their overall temperatures (with cool stars to the right and warm stars to the left of the plot). Metal-rich stars thus lie along the upper part of the main-Sequence locus.

The binned version of the plot provides a confirmation of several trends that were already very well known. First, among host stars with masses similar to the Sun that harbor giant planets, there’s a strong preference for metal-rich stars. This is the classic planet-stellar metallicity effect. Second, among low-mass stars, there’s a dearth of giant planet candidates. This is the known giant planet-stellar mass effect. Finally, among the solar mass stars that host low-mass planets, there’s no discernible metallicity correlation.

The new result pertains to low-mass planets orbiting low-mass stars. The diagram shows that for this subset, there’s strong evidence for a metallicity correlation — At masses less than ~0.8 solar masses, higher metallicity stars are more likely to host low-mass planets. We take this as direct evidence regarding the overall bulk efficiency of planet formation for planets that aren’t required to bulk up via rapid gas accretion. Take a 0.7 solar mass with twice the Sun’s metal content and a typical 0.02 solar mass disk. The entire planet-forming disk contains about 150 Earth-masses worth of stuff heavier than hydrogen and helium. Kevin’s result is effectively saying that a good fraction of the time, a good fraction of this total burden of metals winds up in planets.

We had to be careful. There are a lot of systematic “gotchas” that can potentially throw a wrench into the exciting big-picture conclusions, and so much of the paper is devoted to considering potential show stoppers in turn. I think that the result is robust, and that it will hold up as the planet catalog continues to grow.

The French philosopher of science Isidore Auguste Marie François Xavier Comte (1798 – 1857) was the founder of sociology and is widely remembered for the doctrine of positivism, which holds that the scientific method can be used to understand both natural and social phenomena.

He’s well known to astronomers, however, largely because of the spectacularly incorrect statements regarding stars in his Cours de la Philosophie Positive (1830-1842):

On the subject of stars, all investigations which are not ultimately reducible to simple visual observations are … necessarily denied to us. While we can conceive of the possibility of determining their shapes, their sizes, and their motions, we shall never be able by any means to study their chemical composition or their mineralogical structure … Our knowledge concerning their gaseous envelopes is necessarily limited to their existence, size … and refractive power, we shall not at all be able to determine their chemical composition or even their density… I regard any notion concerning the true mean temperature of the various stars as forever denied to us.

Lots of fun to get your introductory lecture on stellar spectroscopy off to a snarky start with that particular zinger.

Comte’s pronouncements on planets are slightly more obscure, but now, given the many and varied successes of the Spitzer Telescope, they provide an equally rich vein for irony-with-20/20-hindsight:

The take away message seems to be “never say never”. Nowadays, an academic with Comte’s flair would certainly have the innate sense to leave some wriggle room in anticipation of unforeseen scientific advances.

In any case, in this evening’s astro-ph mailing, there’s a very interesting article by Brugamyer et al. that touches on the inferred chemical and mineralogical structure of extrasolar planets. The authors of the paper make a detailed examination of the relative oxygen and silicon abundances of stars known to host extrasolar planets.

The context comes from work back in 2006 by co-author Sally Dodson-Robinson which indicated that stars with high silicon abundances relative to iron show increased planet fractions at given metallicity:

The expectation was that stars with high oxygen abundances relative to iron would also show increased planet fractions at given overall metallicity. Oxygen is a key component of the core-building materials for giant planets, and so it stood to reason that the more water available, the more Jupiter-mass planets one ends up with. Remarkably, this turns out not to be true. Here’s the relevant diagram from the Brugamyer et al paper:

Statistically, it appears that an excess of oxygen relative to iron has no influence on the likelihood of a given star hosting a readily detectable planet. The silicon effect, however, is statistically robust and readily detectable in the Brugamyer et al. analysis:

So how does one explain the unexpected result? Brugamyer et al.’s hypothesis is that icy grain nucleation on silicon-rich dust, rather than the subsequent growth of the icy core-forming particles, is the key bottleneck in forming giant planets via core accretion.

An all-time classic of the literature is Alar and Juri Toomre’s 1972 ApJ study of colliding galaxies. With an exceptionally simple physical model — the restricted three body approximation, in which test particles orbit in the joint potential provided by two massive bodies on a conic 2-body trajectory — the Toomre brothers were able to construct startlingly plausible explanations for bizarrely irregular galaxies such as the Antennae.

One is hard-pressed to think of a better example of seeing the essence of a manifestly complicated phenomenon so precisely nailed by a simple model. The take-away lesson seems to be: Keep an eye out for situations in which glorious non-linearity has had of order one Lyapunov time to unfold.

ApJ 178, 623 also presents some of the finest astronomical diagrams ever. They are masterpieces of visual scientific communication. Every single detail conveys information, and nothing is superfluous.

In 1998, when I was a post-doc in Berkeley, my working routine was considerably less hectic than it is now. On the foggy morning of May 29th of that year, I remember buying a copy of the New York Times, and settling in at a Cafe on Telegraph Avenue for a relaxed 11AM coffee. A picture and a slew of familiar names jumped off the front page:

The story, which became a huge media event — even President Clinton made a passing mention of it — stirred up a uniquely unsettled, uniquely urgent feeling of being completely involved and completely left out all at the same time. A runaway planet clearly would have formed via gravitational instability, and I had spent several years studying gravitational instabilities for my PhD thesis. I gulped down my coffee, scooped up the paper and ran to my office in Campbell Hall. The phone was ringing when I got there. Doug Lin was on the line, buzzing with excitement. “It’s a tidal tail! Look at Alar’s ’72 paper!”

There was not a moment to waste… Doug called the editor at Science and informed him that we had an important interpretive result in the works. I stayed up all night putting together SPH simulations. It seemed completely feasible that one could explain the observation with a collision between two protostellar disks, in which the runaway planet formed via gravitational collapse in the tidal tail. We got the paper off to Science in short order, and boy was it exhilarating!

The Toomre brothers’ influence soaks right through the figures that I made for our paper. Thirteen years on, they remind me of listening to a cover of Sympathy for the Devil done by a competent Stones tribute band.

Sadly, a year or so later, it became clear that the TMR-1c runaway “planet” is, in actual fact, an unfortunately placed background star, and the TMR-1c fiasco is commonly used to illustrate the flaws in the publication by press conference model. Our Science paper has languished in obscurity, to the point where one can extract it from behind Science’s formidable pay wall with only a modestly compromising registration agreement to receive e-mail and no money down…

But hope springs eternal. Like everyone else in the community, my eyes lit up upon reading the recent microlensing result that the galaxy is teeming with of order 200 billion rogue planets. Processes like the one that we outlined in our paper may well be operating after all…

It’s Sunday afternoon here in Santa Cruz, meaning that GMT-wise, it’s already June 6th, and the next transit of Venus is exactly one year away. Seems like an appropriate moment to recall a quote by astronomer William Harkness from 1882 (by way of Stephen J. Dick’s Sky and Ocean Joined: The U.S. Naval Observatory 1830-2000).

We are now on the eve of the second transit of a pair, after which there will be no other till the twenty-first century of our era has dawned upon the Earth, and the June flowers are blooming in 2004. When the last transit season occurred the intellectual world was awakening from the slumber of ages, and that wondrous scientific activity which has led to our present advanced knowledge was just beginning. What will be the state of science when the next transit season arrives God only knows. Not even our children’s children will live to take part in the astronomy of that day. As for ourselves, we have to make do with the present.

There’s something oddly appealing about the nonintuitive spacing of Venusian transits, a 243 year repeating pattern, with transits occurring eight years apart, then a gap of 121.5 years, followed by an eight year interval and then a 105.5 year spacing. I’m certainly looking forward to June 6th 2012, when a healthy fraction of the transit will be visible from Lick Observatory on Mt Hamilton. For updates, be sure to bookmark the Transits of Venus Project website, which launched today.

I can’t help feeling uneasy, however, thinking about the state of affairs on Dec. 10-11 2117…

As Mick Jagger famously remarked, you can’t always get what you want. Kepler’s photometric transit observations provide excellent measurements of the planetary orbital periods, the transit epochs and the planet-to-star radius ratios, but they are stingy and tight-lipped when it comes to the planet’s masses, eccentricities, and longitudes of periastron.

Occasionally masses can be inferred from transit timing variations, especially if a system contains more than one transiting planet. Alternately, one can assume a planetary mass-radius relation (keeping in mind, of course, what happens when u assume). For example, M=R^2.06 in units of Earth masses and radii works quite well in our solar system for V-E-S-U-N. Or, dispensing with the trickery, one can pony up and measure radial velocities.

With photometric data alone, information about the orbital eccentricity distribution of the planet census can be deduced by statistically comparing transit durations to orbital periods. The idea is a full elaboration of the simple observation that if a central transit that is substantially shorter than expected, then it’s quite possible that the planet is occulting the parent star near the periastron of an eccentric orbit.

In one of the flurry of Kepler-related papers that accompanied the February data release, Moorhead et al. (2011) implemented just such a program, and generated a statistical analysis of the distribution of transit durations for the Kepler exoplanet candidates. They assumed that the eccentricities conform to a Rayleigh probability distribution function:

where the controlling parameter, sigma, is is related to the mean orbital eccentricity through

To get a sense of what the Rayleigh distributions look like, here are examples for e_av=0.05, e_av=0.21, and e_av=0.50, compared to the distribution of eccentricities in the exoplanet.eu catalog:

Ignoring planets that are likely tidally circularized, the best fit occurs for e_av=0.21. This model, however, underproduces planets at high eccentricity — ’606 wouldn’t have turned up if e_av=0.21 were a hard truth. Moorhead et al.’s analysis of the Kepler data comes up with plausible best-fit values for e_av ranging from 0.1 through 0.25, for cooler stars with effective temperatures less than 5100K. So there is rough agreement, even though the two catalogs have radically different sampling biases.

A significantly non-zero value for average orbital eccentricity has some interesting consequences for transit surveys. At a given semi-major axis, eccentric planets have (on average) a higher chance of transiting. This is easily seen by comparing an e=0.5 orbit with a circular orbit having the same semi-major axis.

For a population of planets having a specific Rayleigh distribution of eccentricities, the average transit probability at a given semi-major axis is increased by a factor

where the normalization factor, N, is given by

For e_av=0.25, this boosts the total population of planets by about 10% over what one would infer from the standard 1/a circular orbit scaling.

I’ve been reading a textbook on ore-forming processes as part of an attempt to get a little more fluent in geology, and I ran across a plot that is certainly well known to many, but was an eye-opener for me:

The plot charts the solubility by weight of water in several common igneous rocks as one moves deeper into the lithosphere. The take-away message is that even at modest depths, rocks can be very heavily hydrated and are capable of harboring a very large amount of water.

The plot brought to mind something that, to my highly inexpert eye, has always seemed a remarkable coincidence. The volume of water in Earth’s oceans has an average depth of ~4000 meters, leading to a sea-level that does a pretty fair job of outlining the continental margins (which mark the boundaries between denser (but thinner) basaltic crust and lighter (but thicker) granitic crust. Only about 20% of the total continental crust is overlaid by water.

In the extrasolar planet context, an interesting question is whether the situation here on Earth is unusual. Many of the planets that Kepler has found (and will be finding) contain water mass fractions that are considerably larger than Earth’s. Is it reasonable to expect that they’ll have deep oceans that uniformly cover the planets, or is there some sort of mechanism involving water of hydration that maintains a seafloor-continent dichotomy even in the presence of a lot of water? As far as I can tell, this question hasn’t been answered definitively.

The naive answer seems to be along the following lines. Imagine that a terrestrial planet forms in such a manner that the mantle rock is heavily hydrated. Given that mantle rock can easily retain a water mass fraction measured in tens of percents, one could start out with a planet that contains many oceans worth of water, but in which substantial portions of the surface are dry.

When rock melts, the water of hydration is squeezed out. (Migration of this water into the surrounding country rock leads to the mineralized veins that are the basis for many of Earth’s great ore deposits.) On an ongoing volume-weighted basis, most of the melting is taking place beneath the spreading centers that form the mid-oceanic ridges. Every year, of order 300 cubic kilometers of melt are produced, several cubic kilometers of which are erupted to form fresh ocean crust. Coupled with mantle convection, this means that the mantle unburdens its water on a timescale of order a billion years. Some of the water is subducted back down, but this sink is less effective than the source, meaning that the water likely ends up on or near the surface.

So one can imagine planets (perhaps with mantle convection less vigorous than Earth’s) in which continents are gradually submerged as water is squeezed out of the mantle. Not, perhaps, a bad way to go. The world’s best beaches are those of the Seychelles islands — a handful of granitic specks in the vastness of the Indian ocean — the highest peaks of the submerged continental Mascarene Plateau.

Klaus Nomi and David Bowie (Image source and backstory)

I was in the middle of my dynamics lecture this past Monday morning, explaining the Fokker-Planck approximation to the collision term on the right-hand-side of the Boltzmann equation, when my phone started buzzing and vibrating in my pocket. Good thing I had remembered to turn the volume off. Without having to look at who might be calling, I knew it was likely some media outlet, BBC? KCBS? There was a sudden, all-to-familiar sensation of queasy uneasiness which made it very hard to focus on the second-order terms I had just written on the whiteboard.

Back in 2001, I naively and foolishly spoke to a reporter at the London Observer about the “relative ease” of accomplishing strictly hypothetical orbital engineering in the context of a billion-year time frame. The resulting article contained an alarmingly incorrect cognitive leap from the ultra-long term to the immediate near-term:

The misconception came exactly at the time when George W. Bush was visiting Europe, explaining his position regarding the Kyoto Protocol. The Observer story became a huge, completely nightmarish story in Europe, which then echoed across the Atlantic, where it was seized upon by the Drudge Report, Rush Limbaugh and others. Here’s an example editorial from the Manchester New Hampshire Union-Leader:

For nearly a week, the story managed to survive, zombie-like through successive news cycles. Eventually, Gary Condit appeared on the scene, and finally, the media’s full attention was diverted elsewhere.

As readers likely know, I’ve been writing on this web log about a planet valuation formula, which is designed to give a quantitative assessment of whether a newly discovered planet is worthy of significant media attention. Last month, I had a detailed conversation with Lee Billings, which was published on BoingBoing as a part of Lee’s series of posts on planets (which are well worth reading!)

Several weeks after the BoingBoing article appeared, I got a very politely worded e-mail from a reporter at News of the World.

[...] I found your article on the value of the Earth which popped up on a UK blog late last week.

From what I can ascertain, your findings and formula haven’t really had the coverage they deserve in the UK media and I was hoping to rectify that…

After a look at the Wikipedia page on News of the World, my heart was pounding. “Wacko US Prof Sez: Sell Earth for 3 Quadrillion Quid!” I sat down at the computer, and it took a long time to compose a reply.

Turned out that the reporter was admirably interested in getting the story right, and the final version (which is behind a paywall) is quite fair. After all, given the possibly arch, arguably pretentious tone here on oklo.org, I did pretty much have it coming.

Predictably, newspapers in Britain saw the News of the World story and immediately picked it up. As is to be expected, successive iterations tend to lose focus on the exoplanets, and gain focus on the value of Earth. Radio stations are calling, trying to set up interviews about how much Earth is worth. Angry e-mails drift into my inbox. Google news is at 61 articles and counting.

I think it’s time to look into installing Google’s AdSense…

Image Source.

In the midst of all that excitement surrounding the Kepler data release, it was easy to overlook the article by Martin & Spruit, Inflated hot Jupiters from merger events, that showed up on astro-ph earlier this month. This paper proposes a sure-to-ruffle-feathers explanation for the radius anomalies of the hot Jupiters. The idea is that stellar mergers (arising from orbital decay in very close binaries) shed angular momentum via an “excretion” disk, from which one or more short-period giant planets manages to form. In this picture, short-period, anomalously inflated planets are large because they are young — their formation dates to the binary star merger that created their parent star, and they are headed inward for destruction on timescales significantly shorter than the typical several-billion year age of planet-bearing main-sequence stars.

Image Source: Tylenda et al. 2010.

It’s believed that the anomalous novae V1309 Sco (which occurred in 2008) and V838 Mon (which made a big splash in 2002, and whose light echo is shown in the image at the top of the post) were both caused by binary mergers. In the case of V1309 Sco, the more massive of the two progenitor stars was probably similar in mass to the Sun, whereas for V838 Mon, a primary of order 8 solar masses was involved. Numerical simulations, such as the ones shown below by D’Souza et al. (2006), suggest that two distinct stars merge into a single star surrounded by a disk-like structure over an action-packed phase that lasts ~10 orbits.

The idea that merging stars can give rise to planets shows up prominently in the literature in the 1980s, with a series of papers in Soviet Astronomy by A. V. Tutukov, who had a number of speculative ideas regarding planet detection and planetary systems that have turned out to be quite on the mark — he did detailed calculations of the prospective yield of M-dwarf transit surveys, and he argued that ~25% of stars should harbor planetary systems. In several papers (including here) he advocated the idea that excretion disks can give rise to planet formation.

It occurred to me that in the event that stellar mergers do indeed serve as an effective formation channel for short-period planets, then blue stragglers should be very high-grade ore for photometric transit searches. The blue stragglers are main-sequence stars in globular clusters that lie above the main-sequence turn-off in the Hertzsprung-Russell diagram, and which are generally found near the cluster core. It’s believed that they owe their relative youth to being the product of binary mergers.

One of the most important early exoplanet-related results was the Gilliland et al. 2000 HST photometric survey of the rich nearby globular cluster 47 Tucanae. The Hubble telescope was trained on the cluster for 8.3 days, and time-series photometry (taken through two filters) was analyzed for ~34,000 individual stars. If the occurrence rate of hot Jupiters in 47 Tuc was similar to the occurrence rate in the solar neighborhood, then 17 transit planets were to be expected. None were found. This null result is generally attributed to the cluster’s low metallicity and to the possibility that planet formation was inhibited by the dynamical interactions and intense UV radiation that occurred during the cluster’s star formation phase.

A close up look at the 47 Tucanae color-magnitude diagram indicates that the 2-color HST imaging of cluster contains about twenty blue stragglers. Interestingly, it’s not entirely clear whether the blue stragglers have been folded for transits. In the Gilliland et al. 2000 paper, it appears that only the conventional main-sequence stars in the cluster were included in the analysis. The paper states: “For the results discussed further below only the 34,091 stars falling within a bright main-sequence box as shown were analyzed for time series.”

If hot Jupiters are commonly forming from binary merger events, then it seems like there should be a good chance that there could be a transit among the 20-odd blue stragglers observed with HST. Because this handful of stars are much smaller than the red stars at the same luminosity, the transit depths could likely be detectable, given the quality of the HST photometry and the brightness (I=16-17) of these stars. If the planet occurrence rate for merger remnants is 50% one would expect to find one transit among the tweny stars, given the ~10% a-priori geometric probability of transit. As a first step, certainly, it’ll be interesting to see whether these stars were analyzed in any of the follow-up work that was done with the Gilliland et al. dataset.

Earlier this year, in the New York Times Magazine, there was a very lengthy, very glossy advertising insert devoted exclusively to high-end watches. I leafed idly through it, and picked up a new concept, that of a complication. Where watches are concerned, a complication refers to any feature that goes beyond the simple display of hours, minutes, and seconds. According to the Wikipedia,

The Patek Philippe Calibre 89 is a commemorative pocket watch created in 1989, to celebrate the company’s 150th anniversary. Declared by Patek Philippe as “the most complicated watch in the world”, it weighs 1.1 kg, exhibits 24 hands and has 1,728 components in total, including a thermometer and a star chart. Made from 18 carat (75%) gold, it has an estimated value of $6 million, and took 5 years of research and development, and 4 years to manufacture. Four watches were made; one in white gold, one in yellow gold, one in rose gold and one in platinum.

The Calibre 89′s complications include such must-haves as the equation of time (yielding the instantaneous difference between apparent solar time and mean solar time), the date of Easter, and a 2800-star celestial chart. And just imagine the convenience of being able to pull your 2.42 lb watch out of your pocket whenever the need strikes to see what century it is!

It occurred to me that the 1,235 Kepler candidates could conceivably provide a bonanza for the high-end mechanical watch industry. The candidates, with their particular periods, transit durations, transit depths, effective temperatures, and radii offer endless opportunities for unique horological complications. In this spirit, at the link below, I’ve made a 1,235-complication applet which charts the appearance and disappearance of transits, timed from the start of Kepler’s Q0. The horizontal direction is mapped to orbital period, and the vertical direction is mapped to M=R^2 in Earth units. It’s mesmerizing to watch…

Click here to watch the animation.