News Article | November 29, 2016
They’re a happy family after all. The three closest stars to the solar system all revolve around one another, astronomers say, resolving a century-long debate. The nearest of the three, Proxima Centauri, is a red dwarf 4.24 light years from us. It made a splash in August when astronomers reported that it hosts an Earth-mass planet where temperatures might be right for liquid water. Just beyond that, 4.37 light years away, shine two bright stars named Alpha Centauri A and B. They orbit each other every 80 years and glow yellow and orange respectively. To the naked eye, they blend together to appear as the third brightest star in the night sky. In contrast, Proxima Centauri is too dim to see without a telescope, so it was only discovered in 1915. Ever since, astronomers have thought Proxima Centauri might revolve around Alpha Centauri A and B – but couldn’t prove it. If Proxima is bound to them, then it must move through space with nearly the same velocity. Otherwise, the little star would escape their gravitational grasp. Proxima and the Alpha Centauri pair are 13,000 times further apart than the sun is from the Earth. In recent years, planet hunters have been able to measure extremely precise velocities as they hunt for the tiny shifts a small planet, like the one orbiting Proxima, induces in its star, tugging it towards and away from us. “That’s the reason why it is possible now to be sure that there is a gravitational link” between Proxima and Alpha Centauri, says Pierre Kervella at the Paris Observatory in France. Moreover, the work reveals Proxima’s orbit for the first time. The star revolves once every 550,000 years on an elliptical path. At its closest approach, Proxima is 4300 sun-Earth distances from its partners; at its farthest, the star is 13,000 sun-Earth distances out, which is where it is now. To determine precise velocities, Kervella and his colleagues had to worry about subtle effects that most observers neglect. For example, as photons escape a star’s gravity, they lose energy, slightly shifting their wavelengths to a redder colour. And the stars’ upwelling surfaces, on the other hand, make the photons shift slightly blue. After correcting for these effects, the scientists conclude that Proxima Centauri’s velocity through space differs from that of its bright partners by just 270 metres per second – half the speed it would need to escape their gravitational grasp. The three stars are definitely an orbital trio.
News Article | February 20, 2017
As far as anyone knew, the club of astronomical objects with rings only took guests of a certain calibre. Picture Saturn floating majestically over a soundtrack of strings and softly clinking silverware. Apart from Saturn, only the solar system’s other giant planets qualified. Then a weird little asteroid named Chariklo crashed the party. It pulled the tablecloth out from under theories of ring physics, forcing astronomers to ask: if this misfit thing can have rings, what else could? The discovery came in June 2013, when observers in Brazil, Chile and Argentina all trained their telescopes on Chariklo, a lumpy rock some 240 kilometres across that orbits the sun between Saturn and Uranus. As Chariklo crossed in front of a background star, they hoped to analyse its shape and maybe find evidence of comet-like jets of ice escaping its surface. But within a day of the data arriving in the lab of Bruno Sicardy at the Paris Observatory, it started to look as if Chariklo had two narrow, sharply defined rings encircling its main body. Maryame El Moutamid of Cornell University in New York, Sicardy’s graduate student at the time, remembers him sharing the news in a conspiratorial whisper. Sicardy had also co-discovered Neptune’s rings in the 1980s – could this new find be just wishful thinking? “I was like, ‘what did you smoke? You see rings everywhere’,” she says. But the analysis kept showing rings, and so have additional observations. It’s still hard to convey just how strange that is, says Mark Showalter of the SETI Institute in California. It made sense that giant planets could be ringed: their gravitational fields are smooth, which should help rings stay stable. But we had never seen rings around an atmosphere-free object, not to mention a misshapen lump like Chariklo with a correspondingly bumpy gravitational field. Some theorists doubted it was even possible. “It still boggles my mind,” Showalter says. Since then, the questions have only multiplied. Any rings around Chariklo should fall apart after just a few thousand years – so either we spotted them in an especially lucky cosmic instant, or some poorly understood process is keeping them together. And the rings aren’t sloppy, either. They are especially tight and neat, similar to those of Uranus. One way to keep them tidy is if they are flanked by as yet undiscovered shepherd moons only about a kilometre in size, their gravity tugging stray material back in line. Since Chariklo’s position puts it in front of the dense star fields at the Milky Way’s centre, there should be plenty of chances to learn more as it crosses background stars. But even as the mystery of Chariklo’s rings lingers, the discovery has shown us that rings can exist in a far wider array of environments than we knew. Apart from Chariklo, there are hints of rings around the neighbouring asteroid Chiron, Saturn’s moons Rhea and Iapetus, Mars, Pluto, and even the enormous exoplanet J1407b. And many more bodies are now under scrutiny: Sicardy’s team is looking at other asteroids, and the New Horizons probe is searching for ring systems in the farther reaches of the solar system. In the meantime, the list of confirmed ring-bearers is still small enough to count on one hand. There’s Jupiter, Saturn, Uranus, Neptune – and then Chariklo with a foot in the door, ushering in untold others.
News Article | December 7, 2016
"All of these Cassini mission measurements are changing our view of the Saturnian system, as it turns our old theories upside down. It takes one good spacecraft to tell us how wrong we were in the past," said Radwan Tajeddine, Cornell research associate in astronomy and a member of the European-based Encelade (pronounced en-CELL-ad) scientific team that pored over the Cassini data and published a paper in the astronomy journal Icarus (January 2017). The Encelade team – lead by Valéry Lainey of the Paris Observatory – provided two key measurements in the research, "New Constraints on Saturn's Interior From Cassini Astrometric Data." The scientists measured Saturn's Love number (the rigidity of a planet) for the first time and confirmed Saturnian moons move away from the planet at a faster rate than expected. (Most moons, including Earth's moon, move away from their parent planet.) Using photographic images taken from century-old glass negatives and Cassini spacecraft observations, the group measured the Love number – named for Augustus E.H. Love, a famed British mathematician who studied elasticity – that describes the rigidity of the tidal bulge and the dissipation factor, which controls the speed at which moons move away. While Saturn is mostly a gigantic shroud of liquid hydrogen and liquid helium, it contains a rocky core – about 18 times the size of Earth, which responds to tidal forces from all of Saturn's major moons by bulging. The forces of the bulging core, in turn, push the moons slightly away. "Those two parameters – the Love number and dissipation factor – are difficult to separate," Tajeddine said. So the team detected and examined the orbits of four tiny moons associated with the larger moons Tethys (Telesto and Calypso) and Dione (Helene and Polydeuces). While these tiny moons do not affect the tidal forces on Saturn, their orbits are disturbed by Saturn's core tidal bulges. "By monitoring these disturbances, we managed to obtain the first measurement of Saturn's Love number and distinguish it from the planet's dissipation factor," Tajeddine said. "The moons are migrating away much faster than expected." Tajeddine explains that if Saturn moons actually formed 4.5 billion years ago, their current distances from the home planet should be greater. Thus, this new research suggests, the moons are younger than 4.5 billion years, favoring a theory that the moons formed from Saturn's rings. The team also found that Saturn moon Rhea is moving away 10 times faster than the other moons, which is the first evidence that a planet's dissipation factor can vary with its distance in relation to the moon. The scientists have no definitive explanation. After 13 years of cruising around Saturn, to explore its rings and moons, NASA will program Cassini's grand finale – a flight through the planet's rings and a dive into its atmosphere – for September 2017. "What we believe about Saturn's moons history might still change in the coming years with the finale of the Cassini mission," said Lainey, who suggested, "The more we learn about Saturn, the more we learn about exoplanets." More information: Valéry Lainey et al, New constraints on Saturn's interior from Cassini astrometric data, Icarus (2017). DOI: 10.1016/j.icarus.2016.07.014
Prigent C.,Paris Observatory
Comptes Rendus - Geoscience | Year: 2010
During the last decade, satellite observations have allowed significant advances in quantifying precipitation, especially with the contribution of the TRMM mission. Observations at different wavelengths (visible, infrared, and microwaves), in both active and passive microwave modes, are analyzed, and eventually coupled to produce records of precipitation estimates over the globe, with up to hourly time sampling. This article provides an overview of the techniques, the results and the perspectives. © 2010 Académie des sciences.
Dasyra K.M.,Paris Observatory |
Combes F.,Paris Observatory
Astronomy and Astrophysics | Year: 2012
We present deep observations of the 12CO(1-0) and (3-2) lines in the ultra-luminous infrared and radio galaxy 4C 12.50, carried out with the 30m telescope of the Institut de Radioastronomie Millimétrique. Our observations reveal the cold molecular gas component of a warm molecular gas outflow that was previously known from Spitzer Space Telescope data. The 12CO(3-2) profile indicates the presence of absorption at -950 km s -1 from systemic velocity with a central optical depth of 0.22. Its profile is similar to that of the Hi absorption that was seen in radio data of this source. A potential detection of the 0 → 1 absorption enabled us to place an upper limit of 0.03 on its central optical depth, and to constrain the excitation temperature of the outflowing CO gas to ≥65K assuming that the gas is thermalized. If the molecular clouds fully obscure the background millimeter continuum that is emitted by the radio core, the H 2 column density is ≥1.8 × 10 22 cm -2. The outflow then carries an estimated cold H 2 mass of at least 4.2 × 10 3 M ⊙ along the nuclear line of sight. This mass will be even higher when integrated over several lines of sight, but if it were to exceed 3 × 10 9 M ⊙, the outflow would most likely be seen in emission. Since the ambient cold gas reservoir of 4C 12.50 is 1.0 × 1.0 × 10 M ⊙, the outflowing-to-ambient mass ratio of the warm gas (37%) could be elevated with respect to that of the cold gas. © 2012 ESO.
News Article | February 22, 2017
MADISON, Wis. -- Plumbing a 90 million-year-old layer cake of sedimentary rock in Colorado, a team of scientists from the University of Wisconsin-Madison and Northwestern University has found evidence confirming a critical theory of how the planets in our solar system behave in their orbits around the sun. The finding, published Feb. 23, 2017 in the journal Nature, is important because it provides the first hard proof for what scientists call the "chaotic solar system," a theory proposed in 1989 to account for small variations in the present conditions of the solar system. The variations, playing out over many millions of years, produce big changes in our planet's climate -- changes that can be reflected in the rocks that record Earth's history. The discovery promises not only a better understanding of the mechanics of the solar system, but also a more precise measuring stick for geologic time. Moreover, it offers a better understanding of the link between orbital variations and climate change over geologic time scales. Using evidence from alternating layers of limestone and shale laid down over millions of years in a shallow North American seaway at the time dinosaurs held sway on Earth, the team led by UW-Madison Professor of Geoscience Stephen Meyers and Northwestern University Professor of Earth and Planetary Sciences Brad Sageman discovered the 87 million-year-old signature of a "resonance transition" between Mars and Earth. A resonance transition is the consequence of the "butterfly effect" in chaos theory. It plays on the idea that small changes in the initial conditions of a nonlinear system can have large effects over time. In the context of the solar system, the phenomenon occurs when two orbiting bodies periodically tug at one another, as occurs when a planet in its track around the sun passes in relative proximity to another planet in its own orbit. These small but regular ticks in a planet's orbit can exert big changes on the location and orientation of a planet on its axis relative to the sun and, accordingly, change the amount of solar radiation a planet receives over a given area. Where and how much solar radiation a planet gets is a key driver of climate. "The impact of astronomical cycles on climate can be quite large," explains Meyers, noting as an example the pacing of the Earth's ice ages, which have been reliably matched to periodic changes in the shape of Earth's orbit, and the tilt of our planet on its axis. "Astronomical theory permits a very detailed evaluation of past climate events that may provide an analog for future climate." To find the signature of a resonance transition, Meyers, Sageman and UW-Madison graduate student Chao Ma, whose dissertation work this comprises, looked to the geologic record in what is known as the Niobrara Formation in Colorado. The formation was laid down layer by layer over tens of millions of years as sediment was deposited on the bottom of a vast seaway known as the Cretaceous Western Interior Seaway. The shallow ocean stretched from what is now the Arctic Ocean to the Gulf of Mexico, separating the eastern and western portions of North America. "The Niobrara Formation exhibits pronounced rhythmic rock layering due to changes in the relative abundance of clay and calcium carbonate," notes Meyers, an authority on astrochronology, which utilizes astronomical cycles to measure geologic time. "The source of the clay (laid down as shale) is from weathering of the land surface and the influx of clay to the seaway via rivers. The source of the calcium carbonate (limestone) is the shells of organisms, mostly microscopic, that lived in the water column." Meyers explains that while the link between climate change and sedimentation can be complex, the basic idea is simple: "Climate change influences the relative delivery of clay versus calcium carbonate, recording the astronomical signal in the process. For example, imagine a very warm and wet climate state that pumps clay into the seaway via rivers, producing a clay-rich rock or shale, alternating with a drier and cooler climate state which pumps less clay into the seaway and produces a calcium carbonate-rich rock or limestone." The new study was supported by grants from the National Science Foundation. It builds on a meticulous stratigraphic record and important astrochronologic studies of the Niobrara Formation, the latter conducted in the dissertation work of Robert Locklair, a former student of Sageman's at Northwestern. Dating of the Mars-Earth resonance transition found by Ma, Meyers and Sageman was confirmed by radioisotopic dating, a method for dating the absolute ages of rocks using known rates of radioactive decay of elements in the rocks. In recent years, major advances in the accuracy and precision of radioisotopic dating, devised by UW-Madison geoscience Professor Bradley Singer and others, have been introduced and contribute to the dating of the resonance transition. The motions of the planets around the sun has been a subject of deep scientific interest since the advent of the heliocentric theory -- the idea that the Earth and planets revolve around the sun -- in the 16th century. From the 18th century, the dominant view of the solar system was that the planets orbited the sun like clockwork, having quasiperiodic and highly predictable orbits. In 1988, however, numerical calculations of the outer planets showed Pluto's orbit to be "chaotic" and the idea of a chaotic solar system was proposed in 1989 by astronomer Jacques Laskar, now at the Paris Observatory. Following Laskar's proposal of a chaotic solar system, scientists have been looking in earnest for definitive evidence that would support the idea, says Meyers. "Other studies have suggested the presence of chaos based on geologic data," says Meyers. "But this is the first unambiguous evidence, made possible by the availability of high-quality, radioisotopic dates and the strong astronomical signal preserved in the rocks."
News Article | August 30, 2016
An unusual radio signal from a Sunlike star has prompted alien hunters to take a closer look at the system, located just 94 light years away. The 11 gigahertz radio burst, lasting two seconds, was picked up on May 15, 2015 by the RATAN-600 radio telescope in Zelenchukskaya, Russia, and was kept under wraps for well over a year. Until now. Over the weekend, interstellar spaceflight expert Paul Gilster broke the news that a team led by astronomer Nicolai Bursov of the Special Astrophysical Observatory—and including famed Search for Extraterrestrial Intelligence (SETI) astronomer Claudio Maccone—has been analyzing the signal, and will be presenting findings at the 67th International Astronautical Congress in Guadalajara, Mexico, on September 27. “No one is claiming that this is the work of an extraterrestrial civilization,” Gilster cautioned, “but it is certainly worth further study.” To that end, SETI has trained both its Allen Telescope Array in California and the Boquete Optical SETI Observatory in Panama toward the star, named HD 164595, which is within 100 light years of Earth, in the constellation Hercules—a cosmic stone’s throw away. Adding to the excitement is the star’s status as a veritable “solar twin” to our own Sun, differing in mass by only one percent, and “almost identical” in metallicity, according to Gilster. We also know it hosts at least one planet, a hot Neptune-sized world about 16 times more massive than Earth, with a year of 40 days. Sunlike star with at least one confirmed planet? Check. Near enough to Earth for two-way communication to theoretically take place, albeit over several generations? Check. Strong radio signal at a frequency that is unusual for a natural astronomical source? Triple check. Even the fact that researchers who first recorded the signal kept it a secret smacks of some grand alien-related conspiracy. Maybe it is. But probably not. False positives are a well-known occupational hazard for alien hunters, as SETI director Seth Shostak eloquently demonstrated in a recent Air & Space article about a “dry run” in 1997. The enormous RATAN-600 facility that detected the signal in May 2015. Image: александр с кавказа “The incident demonstrated that any promising signal will become public knowledge immediately, even though it will be days or weeks before it’s rigorously confirmed,” Shostak pointed out. “While that fact should quiet those who think that any detection of alien intelligence would be kept under wraps to avoid panic among the populace, the corollary is that in the future, you should expect to hear about some signals that look good but, after a few days of checking, don’t pan out.” “As soon as an interesting signal tickles a radio telescope, scientists will start tweeting and blogging,” he added. “You can bet on it.” This is a prophetic observation in light of the traction that the HD 164595 signal is already gaining around the world. Though the RATAN-600 researchers neglected to communicate their findings to the wider scientific community for several months—a lag time that has some scientists miffed—the cat is now out of the bag. Naturally, stories about how this unbagged cat is definitely an alien from a Kardashev Type II civilization are rife across the internet. But though the signal is absolutely worthy of further investigation, odds are it has a completely natural explanation. For instance, Jean Schneider, an astronomer based at the Paris Observatory, has proposed that HD 164595 may be intensifying a background radio source via a process called gravitational microlensing, in which powerful gravity fields magnify phenomena behind them from Earth’s perspective. Interference from our own radio communication devices has also not been ruled out as a possible source for the signal. There’s nothing wrong with getting excited over weird feedback from outer space. But the frenzy does recall a timeless lesson that Carl Sagan doled out in the fourth episode of Cosmos: A Personal Journey. "I can't see a thing on the surface of Venus,” Sagan said, channeling over-eager planetary scientists. “Why not? Because it's covered with a dense layer of clouds. Well, what are clouds made of? Water, of course. Therefore, Venus must have an awful lot of water on it. Therefore, the surface must be wet. Well, if the surface is wet, it's probably a swamp. If there's a swamp, there's ferns. If there's ferns, maybe there's even dinosaurs." “Observation: You couldn’t see a thing,” he sums up. “Conclusion: Dinosaurs.” I’m not one to put down any theories about extraterrestrial dinosaurs, but Sagan’s point remains relevant to this day. Our tendency to put the cart light years beyond the horse when it comes to anything alien says much more about the human yearning for connection with other intelligent lifeforms than it does about those speculative civilizations.
News Article | November 14, 2016
The unusually big and bright moon happens when the Earth's satellite rock is full at the same time as, or very near, perigee—its closest point to our planet on its monthly ellipsis-shaped orbit. At a distance of 356,509 kilometers (221,524 miles), this is the closest it has been to Earth since 1948, creating what NASA described as "an extra-supermoon." The phenomenon was visible first in Asia, sending astronomy enthusiasts and photographers flocking to the best viewing spots, hoping the chronic pollution that blights many of the region's cities would not spoil the fun. Sydney's eastern Bronte suburb became an unexpected magnet as thousands of people armed with picnic mats and cameras packed its small beach after a Facebook invite went viral. Loud cheers went up among the crowd as the moon made brief appearances between heavy, gray clouds before disappearing. "It's really nice," Aidan Millar-Powell told AFP of the festive community atmosphere at the beach. "People don't usually come together like this in Sydney for a natural phenomenon." Tourists, office workers and couples crowded the Hong Kong waterfront as the supersized moon rose over the skyscrapers of the financial hub, while in the Chinese capital Beijing the moon climbed spectacularly over the city's skyline. 'More super than others' The supermoon was visible across much of India although residents of New Delhi, the world's most polluted capital, struggled to see it clearly through the toxic smog that has been shrouding the city in recent weeks. In Thailand, astrologers were variously predicting the supermoon would bring disaster or great fortune. The supermoon means a stronger high tide, something that gets surfers giddy with excitement, not only at the prospect of riding bigger waves, but doing so at night. In Florida, tides were unusually high and flooding was reported along some beachside streets near Miami and Fort Lauderdale. NASA published a photo of the moon appearing as a giant orange orb behind Russia's Soyuz rocket at the Baikonur Cosmodrome launch pad in Kazakhstan, ready to propel a Russian cosmonaut, a European and an American astronaut to the International Space Station later this week. "Supermoon adorns our rocket," tweeted Peggy Whitson, the NASA astronaut who will be on that flight. Astronomers say it can be hard to notice that the moon appears brighter than usual. Once it is high in the sky, it can also be hard to tell it is larger. To get the best view, Pascal Descamps of the Paris Observatory advised choosing somewhere with a well-known landmark in the foreground for comparison. Supermoons are actually quite common—there is one every 14 months on average. "But some supermoons are more super than others," said Descamps. After Asia it was the Middle East, Africa, Europe then North and South America's turn to peer upwards, with eager moongazers on all continents heading to popular landmarks to see the supermoon up close—with mixed results. In Athens, the hundreds gathered at the ancient Acropolis were treated to the sight of the massive orb rising between the monument's famous columns, bathing the site in its glow. But thick clouds spoiled the show in several European capitals including London, Paris, Berlin and Rome. Amateur photographers took up positions on London's Waterloo Bridge hoping to see the moon rise above St Paul's Cathedral, but cloud had blanketed the sky all day and mobile apps were the only way to track the moon's progress. In Poland, the great rivalry between Warsaw and the old royal capital Krakow reared its head as heavy clouds thwarted moongazers in the former. But in Krakow, further south, the massive moon rose victoriously above the clouds. "I think the moon is more golden than usual—it doesn't have the usual cold silver color," said Roman Kwiatkowski, a Krakow psychotherapist making use of his large balcony to enjoy the spectacle. Parts of east Africa also had an excellent view, from Nairobi to Dar es Salaam. Johannesburg got a storm instead, with one disgruntled Twitter user, @Runningflyhalf, renaming the phenomenon "supercloud." But in Cape Town, thousands of people were rewarded for making the hour-long trudge up Lion's Head mountain with the sight of the huge moon reflecting off the glimmering bay below. "I think it's well worth waiting another 34 years to see it," tourist guide Leslie Edgar, 30, told AFP. "I will do it again. It was spectacular." Explore further: There's an 'extra-super' Moon on the rise
News Article | February 21, 2017
Hold on to your hats, my friends, because I have discovered a secret mathematical holiday to observe the last day of this month. This year February 28 happens to be both the day before Lent starts in the western Christian calendar and the 139th anniversary of the birth of mathematician Pierre Fatou (1878-1929). Due to this auspicious confluence of math history, astronomy, the church calendar, and the English language, this year’s Fat Tuesday is Fatou’s Day! Assuming the Vatican and other church authorities don’t alter the way Easter and related holidays are calculated, this concurrence will only happen once more before 2100: in 2090. (It also happened in 2006, but I wasn’t blogging yet, so how would you have known?) You’re going to want to make it count. I believe my first encounter with Fatou was in an analysis (read: beefed-up calculus) class when I learned about Fatou’s lemma. This helpful result in calculus is in a family I think of as commutativity statements. (Commutativity is about whether you can do things in a different order and get the same same answer. In math, as in life, one cannot always interchange operations and expect good results. Ask anyone who has sleepily tried to put on their shoes before changing out of their PJs into their real pants. If life were commutative, it would work!) Fatou’s lemma is about the relationship of the integral of a limit to the limit of an integral. Specifically, it says that if the correct conditions are met, then the integral of the limit inferior of a sequence of functions is less than or equal to the limit inferior of the integrals of the functions in the sequence. (For more rigor, check out Wikipedia or Math3ma.) Fatou is also famous for his contributions to complex dynamics. Basically, he was trying to figure out what happens if you plug a complex number into a function and then plug the output into the same function, lather, rinse, and repeat. I wrote a little more about that idea in my post from a few years ago about fractal kitties and last month’s post about the Mandelbrot set. Basically, sometimes points will stay relatively close to where they start, and sometimes they’ll spiral out wildly to the far reaches of the complex plane. Is there a way to figure out which points do what? The study of complex dynamics eventually led to the definition of Fatou sets and Julia sets. (Julia sets are named after French mathematician Gaston Julia, who studied complex dynamics around the same time as Fatou, though they worked independently.) The Julia set of a polynomial consists of the points that have chaotic behavior near them. That is, some points near them will tumble out to infinity under iteration, and some will stay close. The Fatou set is the complement of the Julia set: all the points surrounded by neighbors who act like they do. They either all flutter away or all stay close to home. Julia and Fatou sets are often beautiful fractals, as you can see in the gorgeous online book Pictures of Julia and Mandelbrot Sets. Furthermore, they give the most obvious way to connect Fatou’s Day to Fat Tuesday: fractal pancakes. Nathan Shields, whose Saipancakes are #pancakegoals, gives some inspiration at the top of this post. If you don't have his pancake skills, don't worry. Not all Julia and Fatou sets are as photogenic as the Mandelbrot set. It will probably be easier to replicate a pancake resembling one of the components of the Fatou set for the polynomial f(z)=(z+z2)/2 at home. Michèle Audin’s book Fatou, Julia, Montel: The Great Prize of Mathematical Sciences of 1918, and Beyond explains a lot of the ins and outs of Fatou’s and Julia’s work on complex dynamics, putting it in context and addressing questions of priority. It also contains a biographical chapter on Fatou that mentions that he was a music-lover and, at least according to family lore, had a parrot. If you want to do a Fatou deep-dive for Fatou’s Day, I highly recommend that book. For those looking to make a pilgrimage, Fatou’s birth and death cities are both in Brittany, France: Lorient and Pornichet, respectively. He studied at the École Normale Supérieure in Paris and worked for the rest of his life at the Paris Observatory. He lived at 172 Boulevard du Montparnasse, just around the corner from the observatory, for several years. There is no plaque for him, but I know from experience that it is possible to visit the address and make people look at you weird while you try to get the best possible selfie in front of what is now a dental practice. Sadly, there is no Rue Fatou among the nearly 100 Paris streets named for mathematicians, but there is a Rue Fatou in Meaux, a town about 25 miles northeast of Paris. The administration of the city of Meaux has not yet answered my email (undoubtedly in bad French) inquiring about the origin of the street's name, so I do not know whether it was named in honor of the mathematician. So for a perfect Fatou's Day, integrate a sequence of functions, draw some fractals, and eat mathematical pancakes!
News Article | August 31, 2016
The phenomenon, known as an annular solar eclipse, happens when there is a near-perfect alignment of the Earth, Moon and Sun. But unlike a total eclipse, when the Sun is blacked out, sometimes the Moon is too far from Earth, and its apparent diameter too small, for complete coverage. "At the eclipse's peak, all that will be visible is a ring of light encircling the black disk that is the Moon," said astronomer Pascal Descamps of the Paris Observatory, in the French Indian Ocean island of Reunion to witness the event. "That will be the magic moment," he told AFP. Daylight should be slightly dimmed, as on a very cloudy day. Only people along a very narrow, 100-kilometre (62-mile) band stretching across central Africa, Madagascar and Reunion will see the full effect of the ring, or annulus. Anyone north, south, east or west of the band will see only a partial eclipse, or none at all. The display will start at 0613 GMT in the south Atlantic, passing over Gabon, the two Congos, Tanzania and the northern tip of Mozambique and Madagascar. Reunion island will get a good view before the eclipse ends around 1200 GMT over the Indian Ocean, said the Paris Observatory. At the eclipse's peak, between 1008 and 1011 GMT, the Moon will cover about 94 percent of the Sun. The experts warn that sunglasses offer insufficient protection for looking at the Sun, even when it is partly masked. "Looking at the Sun without special protection, even for a few seconds, can cause irreversible damage to the retina", even blindness, said Descamps. Special eclipse glasses can filter out the Sun's harmful ultraviolet and infrared rays. One could also use a pinhole camera, which can be easily built at home—basically a box with a hole on one side for light to pass through and project an inverted image on the opposite side.