The Science Behind the “Blood Moon Tetrad” and Why Lunar Eclipses Don’t Mean the End of the World

A mosaic of the 2003 total lunar eclipse. photos by author.

 By now, you may have already heard the latest tale of gloom and doom surrounding the upcoming series of lunar eclipses.

This latest “End of the World of the Week” comes to us in what’s being termed as a “Blood Moon,” and it’s an internet meme that’s elicited enough questions from friends, family and random people on Twitter that it merits addressing from an astronomical perspective.

Like the hysteria surrounding the supposed Mayan prophecy back in 2012 and Comet ISON last year, the purveyors of Blood Moon lunacy offer a pretty mixed and often contradictory bag when it comes down to actually what will occur.

But just like during the Mayan apocalypse nonsense, you didn’t have to tally up just how many Piktuns are in a Baktun to smell a rat. December 21st 2012 came and went, the galactic core roughly aligned with the solstice — just like it does every year — and the end of the world types slithered back into their holes to look for something else produce more dubious YouTube videos about.

Here’s the gist of what’s got some folks wound up about the upcoming cycle of eclipses. The April 15th total lunar eclipse is the first in series of four total eclipses spanning back-to-back years, known as a tetrad. There are eight tetrads in the 21st century: if you observed the set total lunar eclipses back in 2003 and 2004, you saw the first tetrad of the 21st century.

The eclipses in this particular tetrad, however, coincide with the Full Moon marking Passover on April 15th and April 4th and the Jewish observance of Sukkot on October 8th and September 28th. Many then go on to cite the cryptic biblical verse from Revelation 6:12, which states;

“I watched as he opened the sixth seal. There was a great earthquake. The Sun turned black like sackcloth made of goat hair. The whole Moon turned blood red.”

Whoa, some scary allegory, indeed… but does this mean the end of the world is nigh?

I wouldn’t charge that credit card through the roof just yet.

First off, looking at the eclipse tetrads for the 21st century, we see that they’re not really all that rare:

21st century eclipse tetrads:

Eclipse #1 Eclipse #2 Eclipse #3 Eclipse #4
May 16th, 2003 November 9th, 2003 May 4th , 2004 October 28th, 2004
April 15th, 2014*+ October 8th, 2014 April  4th, 2015*+ September 28th, 2015
April 25th, 2032 October 18th, 2032 April 14th, 2033*+ October 8th, 2033
March 25th, 2043* September 19th, 2043 March 13th, 2044 September 7th, 2044
May 6th, 2050 October 30th, 2050 April 26th, 2051 October 19th, 2051
April  4th, 2061*+ September 29th, 2061 March 25th, 2062* September  18th, 2062
March 4th, 2072 August 28th, 2072 February 22nd, 2073 August 17th, 2073
March 15th, 2090 September 8th, 2090 March 5th, 2091 August 29th, 2091
*Paschal Full Moon
+Eclipse coincides with Passover

 

Furthermore, Passover is always marked by a Full Moon, and a lunar eclipse always coincides with a Full Moon by definition, meaning it cannot occur at any other phase. The Jewish calendar is a luni-solar based calendar that attempts to mark the passage of astronomical time via the apparent course that the Sun and the Moon tracks through the sky. The Muslim calendar is an example of a strictly lunar calendar, and our western Gregorian calendar is an example of a straight up solar one. The Full Moon marking Passover often, though not always, coincides with the Paschal Moon heralding Easter. And for that matter, Passover actually starts at sunset the evening prior in 2014 on April 14th. Easter is reckoned as the Sunday after the Full Moon falling after March 21st which is the date the Catholic Church fixes as the vernal equinox, though in this current decade, it falls on March 20th. Easter can therefore fall anywhere from March 22nd to April 25th, and in 2014 falls on the late-ish side, on April 20th.

To achieve synchrony, the Jewish calendar must add what’s known as embolismic or intercalculary months (a second month of Adar) every few years, which in fact it did just last month. Eclipses happen, and sometimes they occur on Passover. It’s rare that they pop up on tetrad cycles, yes, but it’s at best a mathematical curiosity that is a result of our attempt to keep our various calendrical systems in sync with the heavens.  It’s interesting to check out the tally of total eclipses versus tetrads over a two millennium span:

Century Number of Total Lunar Eclipses Number of Tetrads Century Number of Total Lunar Eclipses Number of Tetrads
11th

62

0

21st

85

8

12th

59

0

22nd

69

4

13th

60

0

23rd

61

0

14th

77

6

24th

60

0

15th

83

4

25th

69

4

16th

77

6

26th

87

8

17th

61

0

27th

79

7

18th

60

0

28th

64

0

19th

62

0

29th

57

0

20th

81

5

30th

63

1

 

Note that over a five millennium span from 1999 BC to 3000 AD, the max number of eclipse tetrads that any century can have is 8, which occurs this century and last happened in the 9th century AD.

Of course, the visual appearance of a “Blood of the Moon” that’s possibly alluded to in Revelation is a real phenomena that you can see next week from North and South America as the Moon enters into the dark umbra or core of the shadow of the Earth. But this occurs during every total lunar eclipse, and the redness of the Moon is simply due to the scattering of sunlight through the Earth’s atmosphere. Incidentally, this redness can vary considerably due to the amount of dust, ash, and particulate aerosols aloft in the Earth’s atmosphere, resulting in anything from a bright cherry red eclipse during totality to an eclipsed Moon almost disappearing from view altogether… but it’s well understood by science and not at all supernatural.

The changing colors of a lunar eclipse: a mosaic of four eclipses. Photos by author.
The changing colors of a lunar eclipse: a mosaic of four eclipses. Photos by author.

Curiously, the Revelation passage could be read to mean a total solar eclipse as well, though both can never happen on the same day.  Lunar and solar eclipses occur in pairs two weeks apart at Full and New Moon phases when the nodes of the Moon’s ecliptic crossing comes into alignment with the Sun — known as a syzygy, an ultimate triple word score in Scrabble, by the way — and this eclipse season sees a non-central annular eclipse following the April 15th eclipse on April 29th.

And yes, earthquakes, wars, disease, relationship breakups and lost car keys are on tap to occur in 2014 and 2015… just like during any other year. Lunar eclipses marked the fall of Constantinople in 1453 and the World Series victory of the Red Sox in 2004, but they’re far from rare. We humans love to see patterns, and sometimes this habit works against us, making us see them where none exists. This is simply a case of the gambler’s fallacy, counting the hits at the cost of the misses. We could just as easily make a case that the upcoming eclipse tetrad of April 15th, October 8th, April 4th and September 28th marks US Tax Day, Croatian Independence Day, The Feast of Benedict of the Moor & — Michael Scott take note — International World Rabies Day… perhaps the final 2015 eclipse should be known as a “Rabies Moon?”

So, what’s the harm in believing in a little gloom and doom? The harm in believing the world ends tomorrow comes when we fail to plan for still being here the day after. The harm comes when something like the Heavens Gate mass suicide goes down. We are indeed linked to the universe, but not in the mundane and trivial way that astrologers and doomsdayers would have you believe. Science shows us where we came from and where we might be headed.  We’ve already fielded queries from folks asking if it’s safe (!) to stare at the Blood Moon during the eclipse, and the answer is yes… don’t give in to superstition and miss out on this spectacular show of nature because of some internet nonsense.

The upcoming lunar eclipse next week won’t mean the end of the world for anyone, except, perhaps, NASA’s LADEE spacecraft… be sure not to miss it!

 

Quasars Tell The Story Of How Fast The Young Universe Expanded

Artist's conception of how the Baryon Oscillation Spectroscopic Survey uses quasars to make measurements. The light these objects sends out gets absorbed by gas in between the receiver and the source. The gas is then "imprinted wiht a subtle ring-like pattern of known physical scale", the Sloan Digital Sky Survey stated. Credit: Zosia Rostomian (Lawrence Berkeley National Laboratory) and Andreu Font-Ribera (BOSS Lyman-alpha team, Berkeley Lab.)

For those who saw the Cosmos episode on William Herschel describing telescopes as time machines, here is a clear example of that. By examining 140,000 objects called quasars (galaxies with an active black hole at their centers), astronomers have charted the expansion rate of the universe — not now, but 10.8 billion years ago.

This is the most precise measurement ever of the universe’s expansion rate at any point in time, the science teams said, with the calculation showing the universe was expanding by 1% every 44 million years at that time. (That figure is to 2% precision, the researchers added.)

“If we look back to the Universe when galaxies were three times closer together than they are today, we’d see that a pair of galaxies separated by a million light-years would be drifting apart at a speed of 68 kilometers per second as the Universe expands,” stated Andreu Font-Ribera of the Lawrence Berkeley National Laboratory, who led one of the two analyses.

The researchers used a telescope called the Sloan Digital Sky Survey, a 2.5-meter telescope at Apache Point Observatory in New Mexico. The discovery was made during Sloan’s Baryon Oscillation Spectroscopic Survey, or BOSS, whose aim has been to figure out the expansion and acceleration of the universe.

The accelerating, expanding Universe. Credit: NASA/WMAP
The accelerating, expanding Universe. Credit: NASA/WMAP

“BOSS determines the expansion rate at a given time in the Universe by measuring the size of baryon acoustic oscillations (BAO), a signature imprinted in the way matter is distributed, resulting from sound waves in the early Universe,” the Sloan Digital Sky Survey stated. “This imprint is visible in the distribution of galaxies, quasars, and intergalactic hydrogen throughout the cosmos.”

Font-Ribera and his collaborators examined how quasars are distributed compared to hydrogen gas to calculate distance. The other analysis, led by Timothée Delubac (Centre de Saclay, France), examined the hydrogen gas to see patterns and measure mass distribution.

You can read more about Font-Ribera’s team’s research in preprint version on Arxiv. Delubac’s research does not appear to be available online, but the title is “Baryon Acoustic Oscillations in the Ly-alpha forest of BOSS DR11 quasars” and it has been submitted to Astronomy & Astrophysics.

Source: Sloan Digital Sky Survey

Can You Escape the Force of Gravity?

Can You Escape the Force of Gravity?

It feels like you just can’t get away from clingy gravity. Even separated by distances of hundreds of millions of light years, gravity is reaching out to all of us. Is there a place you could go to get away from gravity entirely?

Fortunately for our space intolerant tissues and terrible oxygen dependency withdrawal symptoms, gravity binds us to our sweet, cozy home with breathable air, the Earth. Its collective mass is trying to accelerate you towards its center, that way, at 9.8 meters per second squared. But the Earth isn’t the only one looking to cuddle.

You’re also being pulled at by the Moon, and if it weren’t for the Earth here, that pull could hurl you far off into deep space, or crash you into its cold dusty surface. In fact, as the Moon passes overhead, you’re being imperceptibly tugged upwards. This possessive tug o war isn’t just between the moon, and the earth fighting over you like an older brother keeping a small doll out of reach a younger sibling.

The Sun is also in on this shenanigan. Gravity from there is pulling at you from a distance of 150 million km. Well, aren’t we popular. So how far would you have to go to escape this gravitational custody battle completely?

Even At 2.5 million light years distance, gravity is still reaching out and being a clingy creeper. The Milky Way and Andromeda are pulling towards each other. The gravity between these two bodies is strong enough to overcome the expansion of the universe. Which will result in a galactic smash-up derby a few billion years from now.

There’s no end to it. Gravity appears to be madly greedy and long armed. Members of the Virgo Super cluster are connected to each other, and they’re dozens of millions of light-years apart. Objects in the Pisces-Cetus Super cluster complex are even connected to each other by our invisible and obnoxiously possessive friend. And they are hundreds of millions of light years apart…

In fact, you’re so popular that you are gravitationally pulled towards even most distant object in the observable Universe. And they, in turn, are linked to you. As a result, without the outward expansion and acceleration of the Universe, everything would fall inward to a common center of gravity. Newton thought that gravity was instantaneous and if the Sun disappeared, the Earth would immediately fly away. Einstein realized that gravity is distortions of spacetime caused by mass. And as it turns out, gravity moves at the speed of light.

Artist's impression of gravitational waves. Image credit: NASA
Artist’s impression of gravitational waves. Image credit: NASA

If the Sun disappeared, Earth would continue to follow the curved spacetime distortion for 8 whole minutes. Interactions between massive objects, like when black holes collide, cause ripples in spacetime called gravitational waves. As a gravitational wave passes through, you get warped in spacetime, like a wave in the water. The amount is so slight we’ve never seen them directly. However, the decay of pulsar orbits have shown them indirectly.

The ground-based LIGO experiment might someday detect a gravitational wave, but there’s been no luck so far. The Space-based LISA experiment should detect gravitational waves with more precision. The first version will launch in 2015, but the real experiment probably won’t be operational until 2030.

Everybody wants a piece, and I don’t know about you, I just want to be left alone. Gravity’s is reach is amazingly far. It’s everywhere, all the time, and it’s having none of that. What do you think? If you had the power to remove yourself from Gravity’s pull, what would you do? Tell us in the comments below.

If You Could Ride on the Outside of a Rocket, Here’s Your View While Blasting Into Space

Separation of the third stage during the Sentinel-1 launch in April 2014. Credit: Arianespace/European Space Agency /Roscosmos (YouTube/screenshot)

Imagine clinging on to the side of a rocket, somehow able to hang on despite the high speeds and diminishing oxygen. Looking down, this is what you’ll see — the view in the video above. This incredible sequence shows Sentinel-1a during its initial climb to orbit last week and, if you wait long enough, you can even see the separation of the third stage.

“Arianespace’s successful Soyuz Flight VS07 — which deployed Sentinel-1A to Sun-synchronous orbit — gave the world a front-row seat in space,” the company stated on YouTube. “Cameras mounted on the Soyuz’ Fregat upper stage captured the spectacular footage … as Sentinel-1A was separated at approximately 700 km [434 miles] above the Earth to commence its life in orbit.”

Sentinel-1a is the first of a series of environmental monitoring satellites overseen by the European Space Agency, a set that promises views of the Earth in high-definition.

Read more about the mission here. You can also see more video views of Sentinel-1a in this story.

Carnival of Space #348

This week’s Carnival of Space is hosted by Peter Lake at the AartScope blog.

Click here to read Carnival of Space #348.

And if you’re interested in looking back, here’s an archive to all the past Carnivals of Space. If you’ve got a space-related blog, you should really join the carnival. Just email an entry to [email protected], and the next host will link to it. It will help get awareness out there about your writing, help you meet others in the space community – and community is what blogging is all about. And if you really want to help out, sign up to be a host. Send an email to the above address.

Curiosity rover maneuvers around ‘Kimberley’ seeking potential Red Planet Drill Sites

Curiosity maneuvers into ‘Kimbeley’ and scans scientifically intriguing Martian rock outcrops in search of next drilling location exhibiting several shallow hills in foreground and dramatic Gale crater rim backdrop. Rover tracks at right in this colorized Navcam photomosaic assembled from raw images snapped on Sol 589, April 3, 2014. Credit: NASA/JPL/Marco Di Lorenzo /Ken Kremer - kenkremer.com

Curiosity maneuvers into ‘Kimbeley’ and scans scientifically intriguing Martian rock outcrops in search of next drilling location exhibiting several shallow hills in foreground and dramatic Gale crater rim backdrop. Rover tracks at right in this colorized Navcam photomosaic assembled from raw images snapped on Sol 589, April 3, 2014.
Credit: NASA/JPL/Marco Di Lorenzo /Ken Kremer – kenkremer.com[/caption]

NASA’s car sized Curiosity rover has arrived at a scientifically enticing science destination at “The Kimberley Waypoint” where researchers hope to carry out the next drilling operation into alien Martian terrain in search of further clues about ancient Red Planet environments that may have been favorable for life.

“We are officially in ‘The Kimberley’ now,” Curiosity Principal Investigator John Grotzinger, of the California Institute of Technology, Pasadena, told Universe Today.

Since arriving in the Kimberley region, Curiosity’s earth-bound handlers have been maneuvering the 1 ton robot to thoroughly survey the destination dubbed “The Kimberley”.

Why was Kimberley chosen as a science destination?

“The Kimberley” has interesting, complex stratigraphy,” Grotzinger told me.

The team moved the six wheeled robot further this week in search of a suitable location to conduct the next drilling operation. The terrain is replete with diverse rock types and extensive outcrops.

I asked Grotzinger if today’s (April 5) location at ‘The Kimberley’ is the intended drill site?

“It’s a possible drill site,” Grotzinger replied.

“Pending further evaluation,” he noted.

Curiosity scans scientifically intriguing rock outcrops of Martian terrain at ‘The Kimberley’ waypoint in search of next drilling location, beside low hill at right.  Mastcam color photomosaic assembled from raw images snapped on Sol 590, April 4, 2014. Credit: NASA/JPL/MSSS/Ken Kremer - kenkremer.com/Marco Di Lorenzo
Curiosity scans scientifically intriguing rock outcrops of Martian terrain at ‘The Kimberley’ waypoint in search of next drilling location, beside low hill at right. Mastcam color photomosaic assembled from raw images snapped on Sol 590, April 4, 2014. Credit: NASA/JPL/MSSS/Ken Kremer – kenkremer.com/Marco Di Lorenzo

Curiosity drove the final stretch of some 98 feet (30 meters) on Wednesday, April 2, required to arrive at a major stopping waypoint planned since early 2013 for up close study of the Red Planet’s rocks.

Along the recent dune filled path to ‘The Kimberley’, Curiosity snapped breathtaking landscapes around the irresistible ‘Junda’ outcrop, much like a tourist.

See our photomosaics showing the spectacularly inviting terrain around Kimberly and Junda, above and below, by Marco Di Lorenzo and Ken Kremer.

Martian landscape with rows of curved rock outcrops at ‘Kimberly’ in the foreground and spectacular Mount Sharp on the horizon. NASA’s Curiosity Mars rover pulled into Kimberly waypoint dominated by layered rock outcrops as likely drilling site.  This colorized navcam camera photomosaic was assembled from imagery taken on Sol 576 (Mar. 20, 2014).  Credit: NASA/JPL-Caltech/Marco Di Lorenzo/Ken Kremer-kenkremer.com
Martian landscape with rows of curved rock outcrops at ‘Kimberly’ in the foreground and spectacular Mount Sharp on the horizon. NASA’s Curiosity Mars rover pulled into Kimberly waypoint dominated by layered rock outcrops as likely drilling site. This colorized navcam camera photomosaic was assembled from imagery taken on Sol 576 (Mar. 20, 2014). Credit: NASA/JPL-Caltech/Marco Di Lorenzo/Ken Kremer-kenkremer.com

The state-of-the-art robot now sits at a vantage point at “The Kimberley” enabling a detailed photographic survey of the rock exposures and surroundings with the high resolution Mastcam cameras.

The new imagery will be used to select the most scientifically productive drilling locations.

“It is named after a remote region of western Australia,” Grotzinger informed me.

The team chose Kimberley because its lies at the intersection of four different types of rocks, including striated rocks overlain by others and deposited in a decipherable geological relationship to each other.

Researchers directed Curiosity on a pinpoint drive to ‘Kimberley’ after high resolution imagery and mineral mapping spectrometry gathered by NASA’s powerful telescopic cameras aboard the Mars Reconnaissance Orbiter (MRO) circling overhead piqued their interest.

Curiosity looks back at Martian sand dunes and rover tracks after passing by Junda outcrop (right) on Sol 548 (Feb. 19, 2014) with Gale Crater rim and Mount Sharp on the distant horizon. Navcam colorized photomosaic. Credit: NASA/JPL-Caltech/Ken Kremer- kenkremer.com/Marco Di Lorenzo
Curiosity looks back at Martian sand dunes and rover tracks after passing by Junda outcrop (right) on Sol 548 (Feb. 19, 2014) with Gale Crater rim and Mount Sharp on the distant horizon. Navcam colorized photomosaic. Credit: NASA/JPL-Caltech/Ken Kremer- kenkremer.com/Marco Di Lorenzo

“This is the spot on the map we’ve been headed for, on a little rise that gives us a great view for context imaging of the outcrops at the Kimberley,” said Melissa Rice, Curiosity science planning lead, of Caltech.

The team expects Curiosity to investigate Kimberley for several weeks of observations, including sample-drilling and onboard laboratory analysis of the area’s rocks with the CheMin and SAM miniaturized chemistry labs.

If drilling is warranted, Kimberley would be the site of Curiosity’s first drilling operation since boring into the ‘John Klein’ and ‘Cumberland’ outcrop targets during the spring of 2013 at Yellowknife Bay.

The robot has conducted cleaning activities of SAM, CheMin and the CHIMRA sample handling mechanism in anticipation of boring into the Martian outcrops and delivering powdery, pulverized samples of cored Martian rocks to SAM and CheMin – waiting patiently inside the robots belly to eat something exciting from the Red Planet.

Curiosity departed the Yellowknife Bay region in July 2013 where she discovered a habitable zone and thereby accomplished the primary goal of the mission.

To date, Curiosity’s odometer totals 3.8 miles (6.1 kilometers) since landing inside Gale Crater on Mars in August 2012. She has taken over 137,000 images.

The sedimentary foothills of Mount Sharp, which reaches 3.4 miles (5.5 km) into the Martian sky, is the 1 ton robots ultimate destination inside Gale Crater because it holds caches of water altered minerals. Such minerals could possibly indicate locations that sustained potential Martian life forms, past or present, if they ever existed.

Curiosity has some 4 kilometers to go to reach the base of Mount Sharp.

She may arrive at the lower reaches of Mount Sharp sometime in the latter half of 2014, but must first pass through a potentially treacherous dune field.

Meanwhile, NASA’s sister Opportunity rover is exploring clay mineral outcrops by the summit of Solander Point on the opposite side of Mars at the start of her 2nd Decade investigating the Red Planet’s mysteries.

A pair of new orbiters are streaking to the Red Planet to fortify Earth’s invasion fleet- NASA’s MAVEN and India’s MOM.

Stay tuned here for Ken’s continuing Curiosity, Opportunity, Chang’e-3, SpaceX, Orbital Sciences, LADEE, MAVEN, MOM, Mars and more planetary and human spaceflight news.

Learn more at Ken’s upcoming presentations at the NEAF convention on April 12/13 and at Washington Crossing State Park, NJ on April 6.

Ken Kremer

Map of Curiosity Mars Rover's Drives to 'the Kimberley' Waypoint. This map shows the route driven by NASA's Curiosity Mars rover during March and April 2014 in its approach to and arrival at a waypoint called "the Kimberley," which rover team scientists chose in 2013 as the location for the mission's next major investigations. Credit: NASA/JPL-Caltech/Univ. of Arizona
Map of Curiosity Mars Rover’s Drives to ‘the Kimberley’ Waypoint. This map shows the route driven by NASA’s Curiosity Mars rover during March and April 2014 in its approach to and arrival at a waypoint called “the Kimberley,” which rover team scientists chose in 2013 as the location for the mission’s next major investigations. Credit: NASA/JPL-Caltech/Univ. of Arizona

Weekly Space Hangout – April 4, 2014: Space Politics, Skydiving Meteor, and Enceladus Ocean

We record the Weekly Space Hangout every Friday at 12:00 pm Pacific / 3:00 pm Eastern. You can watch us live on Google+, Universe Today, or the Universe Today YouTube page.

Host: Nicole Gugliucci (cosmoquest.org / @noisyastronomer)
Guests: Morgan Rehnberg, Scott Lewis, Nancy Atkinson, Dave Dickinson

This Week’s Stories:
Morgan Rehnberg (cosmicchatter.org / @cosmic_chatter):
NASA lowballs Europa mission
Enceladus ocean confirmed?

Scott Lewis (@ScientificScott):
NASA cutting ties w/ Russia except ISS

Nancy Atkinson (@Nancy_A):
Skydiver Almost Hit By Meteor

Dave Dickinson (@astroguyz):
Mars Opposition
Lunar Eclipse

We record the Weekly Space Hangout every Friday at 12:00 pm Pacific / 3:00 pm Eastern. You can watch us live on Google+, Universe Today, or the Universe Today YouTube page.

Stunning Aurora at Mount Kirkjufell in Iceland

Aurora and starry skies at Mount Kirkjufell, Iceland on April 2, 2014. Credit and copyright: Nanut Bovorn.

Wow! Mount Kirkjufell is a well-known and often-photographed landmark, and there are many who say it is the most beautiful mountain in Iceland. Photographer Nanut Bovorn captured Kirkjufell in all its glory on April 2, 2014, surrounded by starry skies and an incredible aurora. Simply stunning.

Below is another image taken the same night which also shows the beautiful landscape that surrounds Kirkjufell, with a stream and waterfalls, all under the beautiful nights skies in Iceland.

Mount Kirkjufell sits on a little peninsula and is 463 meters high.

Mount Kirkjufell in Iceland surrounded by the aurora on April 2, 2014. Credit and copyright: Nanut Bovorn.
Mount Kirkjufell in Iceland surrounded by the aurora on April 2, 2014. Credit and copyright: Nanut Bovorn.

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