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Most recent 19 results returned for keyword: solar eclipse (Search this on MAP) Yoshinori Saito : General relativity The most beautiful theory A century ago Albert Einstein changed the way humans saw...
General relativity
The most beautiful theory

A century ago Albert Einstein changed the way humans saw the universe. His work is still offering new insights today
Nov 28th 2015 | From the print edition

“ALFRED, it’s spinning.” Roy Kerr, a New Zealand-born physicist in his late 20s, had, for half an hour, been chain-smoking his way through some fiendish mathematics. Alfred Schild, his boss at the newly built Centre for Relativity at the University of Texas, had sat and watched. Now, having broken the silence, Kerr put down his pencil. He had been searching for a new solution to Albert Einstein’s equations of general relativity, and at last he could see in his numbers and symbols a precise description of how space-time—the four-dimensional universal fabric those equations describe—could be wrapped into a spinning ball. He had found what he was looking for.

When this happened, in 1962, the general theory of relativity had been around for almost half a century. It was customarily held up as one of the highest intellectual achievements of humanity. And it was also something of an intellectual backwater. It was mathematically taxing and mostly applied to simple models with little resemblance to the real world, and thus not widely worked on. Kerr’s spinning solution changed that. Given that pretty much everything in the universe is part of a system that spins at some rate or other, the new solution had a relevance to real-world possibilities—or, rather, out-of-this-world ones—that previous work in the field had lacked. It provided science with a theoretical basis for understanding a bizarre object that would soon bewitch the public imagination: the black hole.

Related topics
Isaac Newton
Albert Einstein
General relativity was presented to the Prussian Academy of Sciences over the course of four lectures in November 1915; it was published on December 2nd that year. The theory explained, to begin with, remarkably little, and unlike quantum theory, the only comparable revolution in 20th-century physics, it offered no insights into the issues that physicists of the time cared about most. Yet it was quickly and widely accepted, not least thanks to the sheer beauty of its mathematical expression; a hundred years on, no discussion of the role of aesthetics in scientific theory seems complete without its inclusion.

When gravity fails
Today its appeal goes beyond its elegance. It provides a theoretical underpinning to the wonders of modern cosmology, from black holes to the Big Bang itself. Its equations have recently turned out to be useful in describing the physics of earthly stuff too. And it may still have secrets to give up: enormous experiments are under way to see how the theory holds in the most extreme physical environments that the universe has to offer.

The theory built on the insights of Einstein’s first theory of relativity, the “special theory”, one of a trio of breakthroughs that made his reputation in 1905. That theory dramatically abandoned the time-honoured description of the world in terms of absolute space and time in favour of a four dimensional space-time (three spatial dimensions, one temporal one). In this new space-time observers moving at different speeds got different answers when measuring lengths and durations; for example, a clock moving quickly with respect to a stationary observer would tell the time more slowly than one sitting still. The only thing that remained fixed was the speed of light, c, which all observers had to agree on (and which also got a starring role in the signature equation with which the theory related matter to energy, E=mc2).

Special relativity applied only to special cases: those of observers moving at constant speeds in a straight line. Einstein knew that a general theory would need to deal with accelerations. It would also have to be reconciled with Isaac Newton’s theory of gravity, which relied on absolute space, made no explicit mention of time at all, and was believed to act not at the speed of light but instantaneously.

Einstein developed all his ideas about relativity with “thought experiments”: careful imaginary assessments of highly stylised states of affairs. In 1907 one of these provided him with what he would later refer to as his “happiest thought”: that someone falling off a roof would not feel his own weight. Objects in free-fall, he realised, do not experience gravity. But the curved trajectories produced by gravity—be they the courses of golf balls or planets—seemed to imply some sort of pushing or pulling. If golf balls and planets, like people falling off roofs, felt no sort of push or pull, why then did they not fall in straight lines?

The central brilliance of general relativity lay in Einstein’s subsequent assertion that they did. Objects falling free, like rays of light, follow straight lines through space-time. But that space-time itself is curved. And the thing that made it curve was mass. Gravity is not a force; it is a distortion of space-time. As John Wheeler, a physicist given to pithy dictums about tricky physics, put it decades later: “Space-time tells matter how to move; matter tells space-time how to curve.”

The problem was that, in order to build a theory on this insight, Einstein needed to be able to create those descriptions in warped four-dimensional space-time. The Euclidean geometry used by Newton and everyone else was not up to this job; fundamentally different and much more challenging mathematics were required. Max Planck, the physicist who set off the revolution in quantum mechanics, thought this presented Einstein with an insurmountable problem. “I must advise you against it,” he wrote to Einstein in 1913, “for in the first place you will not succeed, and even if you succeed no one will believe you.”

Handily for Einstein, though, an old university chum, Marcel Grossmann, was an expert in Riemannian geometry, a piece of previously pure mathematics created to describe curved multi-dimensional surfaces. By the time of his lectures in 1915 Einstein had, by making use of this unorthodox geometry, boiled his grand idea down to the elegant but taxing equations through which it would become known.

Just before the fourth lecture was to be delivered on November 25th, he realised he might have a bit more to offer than thought experiments and equations. Astronomers had long known that the point in Mercury’s orbit closest to the sun changed over time in a way Newton’s gravity could not explain. In the 1840s oddities in the orbit of Uranus had been explained in terms of the gravity of a more distant planet; the subsequent discovery of that planet, Neptune, had been hailed as a great confirmation of Newton’s law. Attempts to explain Mercury’s misbehaviour in terms of an undiscovered planet, though, had come to naught.

Famous long ago
Einstein found that the curvature of space-time near the sun explained Mercury’s behaviour very nicely. At the time of the lectures it was the only thing he could point to that general relativity explained and previous science did not. Martin Rees, Britain’s Astronomer Royal, is one of those who sees the nugatory role played by evidence in the development of the theory as one of the things “that makes Einstein seem even more remarkable: he wasn’t motivated by any mysterious phenomena he couldn’t explain.” He depended simply on his insight into what sort of thing gravity must be, and the beauty of the mathematics required to describe it.

After the theory was published, Einstein started to look for ways to test it through observation. One of them was to compare the apparent positions of stars that were in the same part of the sky as the sun during a solar eclipse with their apparent positions at other times. Rays of light, like free-falling objects, trace straight lines in space-time. Because the sun’s mass warps that space-time, the positions of the stars would seem to change when the rays skirted the sun (see diagram).

In 1919 Arthur Eddington, a famed British astronomer, announced that observations of an eclipse made on the Atlantic island of Principe showed just the distortion Einstein had predicted (one of his images is pictured). “LIGHTS ALL ASKEW IN THE HEAVENS”, read the New York Times headline, adding helpfully that “Nobody Need Worry”. Einstein, while pleased, had faith enough in his idea not to have been on tenterhooks. When asked what he would have done had Eddington found a different result, he replied, “Then I would feel sorry for the good Lord. The theory is correct.”

As far as the rest of the world was concerned, Eddington’s result put general relativity more or less beyond doubt. But that did not make it mainstream. For one thing it was hard to grasp. At a public event Eddington was momentarily stumped by the suggestion that he “must be one of the three persons in the world who understand general relativity”. When the silence was taken for modesty, he replied “On the contrary, I am trying to think who the third person is!” 

General relativity also seemed somewhat beside the point. The quantum revolution that Planck had begun, and that Einstein had contributed to in one of his other great papers of 1905, was bearing fascinating fruit. Together with a blossoming understanding of the atomic nucleus, it was at the centre of physicists’ attention. Special relativity had a role in the excitement; its most famous expression, E=mc2, gave a measure of the energy stored in those fascinating nuclei. General relativity had none.

What it offered instead was a way to ask questions not about what was in the universe, but about the structure of the universe as a whole. There were solutions to the equations in which the universe was expanding; there were others in which it was contracting. This became a topic of impassioned debate between Einstein and Willem de Sitter, a Dutch physicist who had found one of the expanding-universe solutions. Einstein wanted a static universe. In 1917 he added to his equations a “cosmological constant” which could be used to fix the universe at a given size.

That became an embarrassment when, in 1929, an American astronomer put forward strong evidence that the universe was, indeed, getting bigger. Edwin Hubble had measured the colour of the light from distant galaxies as a way of studying their motion; light from objects approaching the Earth looks bluer than it would otherwise, light from objects receding looks redder. Hubble found that, on average, the more distant the galaxy, the more its light was shifted towards the red; things receded faster the farther away they were. The evidence for an expanding universe these red-shifts provided led Einstein to reject the cosmological constant as the “greatest blunder of my life”.

The theory had other implications at which its architect initially balked. In the 1930s nuclear physicists worked out that stars were powered by nuclear reactions, and that when those reactions ran out of fuel the stars would collapse. Something like the sun would collapse into a “white dwarf” about the size of the Earth. Bigger stars would collapse yet further into “neutron stars” as dense as an atomic nucleus and just 20 kilometres or so across. And the biggest stars would collapse into something with no length, breadth or depth but infinite density: a singularity.

Finding singularities in a theory is highly distasteful to the mathematically minded; they are normally signs of a mistake. Einstein did not want any of them in his universe, and in 1939 he published a paper attempting to show that the collapse of giant stars would be halted before a singularity could be formed. Robert Oppenheimer, a brilliant young physicist at Berkeley, used the same relativistic physics to contradict the great man and suggest that such extreme collapses were possible, warping space-time so much that they would create regions from which neither light nor anything else could ever escape: black holes.

Oppenheimer’s paper, though, was published on the day Germany invaded Poland, which rather put the debate on hold. Just a month before, Einstein had written to Franklin Roosevelt highlighting the military implications of E=mc2; it would be for realising those implications, rather than for black holes, that Oppenheimer would be remembered.

In part because of Oppenheimer’s government-bewitching success, new sorts of physical research flourished in the post-war years. One such field, radio astronomy, revealed cosmic dramas that observations using light had never hinted at. Among its discoveries were sources of radio waves that seemed at the same time small, spectacularly powerful and, judging by their red-shifts, phenomenally distant. The astronomers dubbed them quasars, and wondered what could possibly produce radio signals with the power of hundreds of billions of stars from a volume little bigger than a solar system.

Roy Kerr’s solution to the equations of general relativity provided the answer: a supermassive spinning black hole. Its rotation would create a region just outside the hole’s “event horizon”—the point of no return for light and everything else—in which matter falling inward would be spun up to enormous speeds. Some of that matter would be squirted out along the axis of rotation, forming the jets seen in radio observations of quasars.

Disappear like smoke
For the first time, general relativity was explaining new phenomena in the world. Bright young minds rushed into the field; wild ideas that had been speculated on in the fallow decades were buffed up and taken further. There was talk of “wormholes” in space-time that could connect seemingly distant parts of the universe. There were “closed time-like curves” that seemed as though they might make possible travel into the past. Less speculatively, but with more profound impact, Stephen Hawking, a physicist (pictured, with a quasar), and Roger Penrose, a mathematician, showed that relativistic descriptions of the singularities in black holes could be used to describe the Big Bang in which the expansion of the universe began—that they were, in fact, the only way to make sense of it. General relativity gave humans their first physical account of the creation.

Dr Hawking went on to bring elements of quantum theory into science’s understanding of the black hole. Quantum mechanics says that if you look at space on the tiniest of scales you will see a constant ferment in which pairs of particles pop into existence and then recombine into nothingness. Dr Hawking argued that when this happens at the event horizon of a black hole, some of the particles will be swallowed up, while some will escape. These escaping particles mean, in Dr Hawking’s words, that “black holes ain’t so black”—they give off what is now called “Hawking radiation”. The energy lost this way comes ultimately from the black hole itself, which gives up mass in the process. Thus, it seems, a black hole must eventually evaporate away to nothingness.

Adding quantum mechanics to the description of black holes was a step towards what has become perhaps the greatest challenge in theoretical physics: reconciling the theory used to describe all the fields and particles within the universe with the one that explains its overall shape. The two theories view reality in very different ways. In quantum theory everything is, at some scale, bitty. The equations of relativity are fundamentally smooth. Quantum mechanics deals exclusively in probabilities—not because of a lack of information, but because that is the way the world actually is. In relativity all is certain. And quantum mechanics is “non-local”; an object’s behaviour in one place can be “entangled” with that of an object kilometres or light-years away. Relativity is proudly local; Einstein was sure that the “spooky action at a distance” implied by quantum mechanics would disappear when a better understanding was reached.

It hasn’t. Experiment after experiment confirms the non-local nature of the physical world. Quantum theory has been stunningly successful in other ways, too. Quantum theories give richly interlinked accounts of electromagnetism and of the strong and weak nuclear forces—the processes that hold most atoms together and split some apart. This unified “standard model” now covers all observable forms of matter and all their interactions—except those due to gravity.

Some people might be satisfied just to let each theory be used for what it is good for and to worry no further. But people like that do not become theoretical physicists. Nor will they ever explain the intricacies of the Big Bang—a crucible to which grandiose theory-unifiers are ceaselessly drawn. In the very early universe space-time itself seems to have been subject to the sort of fluctuations fundamental to the quantum world (like those responsible for Hawking radiation). Getting to the heart of such shenanigans requires a theory that combines the two approaches.

There have been many rich and subtle attempts at this. Dr Penrose has spent decades elaborating an elegant way of looking at all fields and particles as new mathematical entities called “twistors”. Others have pursued a way of adding quantum bittiness to the fabric of space-time under the rubric of “loop quantum gravity”. Then there is the “Exceptionally Simple Theory of Everything”—which isn’t. As Steven Weinberg, one of the unifiers whose work built the standard model, puts it, “There are so many theories and so few observations that we’re not getting very far.”

Dr Weinberg, like many of his colleagues, fancies an approach called superstring theory. It is an outgrowth of an outgrowth of the standard model with various added features that seem as though they would help in the understanding of space-time and which its proponents find mathematically beguiling. Ed Witten of the Institute for Advanced Study (IAS) in Princeton, Einstein’s institutional home for the last 22 years of his life, is one of those who has raised it to its current favoured status. But he warns that much of the theory remains to be discovered, and that no-one knows how much. “We only understand bits and pieces—but the bits and pieces are staggeringly beautiful.”

This piecemeal progress, as Dr Witten tells it, offers a nice counterpoint to the process which led up to November 1915. “Einstein had the conception behind general relativity before he had the theory. That’s in part why it has stood: it was complete when it was formulated,” he says. “String theory is the opposite, with many manifestations discovered by happy accident decades ago.”

Entangled up in blue
And the happy accidents continue. In 1997 Juan Maldacena, an Argentine theoretician who now also works at the IAS, showed that there is a deep connection between formulations of quantum mechanics known as conformal field theories and solutions to the Einstein equations called anti-de Sitter spaces (similar to the expanding-universe solution derived by Willem de Sitter, but static and much favoured by string theorists). Neither provides an account of the real world, but the connection between them lets physicists recast intractable problems in quantum mechanics into the sort of equations found in general relativity, making them easier to crack.

This approach is being gainfully employed solving problems in materials science, superconductivity and quantum computing. It is also “influencing the field in a totally unexpected way,” says Leonard Susskind, of Stanford University. “It’s a shift in our tools and our methodology and our way of thinking about how phenomena are connected.” One possibility Dr Maldacena and Dr Susskind have developed by looking at things this way is that the “wormholes” relativity allows (which can be found in the anti-de Sitter space) may be the same thing as the entanglement between distant particles in quantum mechanics (which is part of the conformal field theory). The irony of Einstein’s spooky quantum bête noire playing such a crucial role has not gone unremarked.

There is more to the future of relativity, though, than its eventual subsumption into some still unforeseeable follow-up theory. As well as offering new ways of understanding the universe, it is also providing new ways of observing it.

This is helpful, because there are bits of the universe that are hard to observe in other ways. Much of the universe consists of “dark matter” which emits no radiation. But it has mass, and so it warps space, distorting the picture of more distant objects just as the eclipse-darkened sun distorted the positions of Eddington’s stars. Studying distortions created by such “gravitational lenses”—both luminous (pictured, with Einstein) and dark—allows astronomers with the precise images of the deep sky today’s best telescopes provide to measure the distribution of mass around the universe in a new way.

Another form of relativity-assisted astronomy uses gravitation directly. Einstein’s equations predict that when masses accelerate around each other they will create ripples in space-time: gravitational waves. As with black holes and the expanding universe, Einstein was not keen on this idea. Again, later work has shown it to be true. A pair of neutron stars discovered spinning round each other in the 1970s are exactly the sort of system that should produce such waves. Because producing gravitational waves requires energy, it was realised that these neutron stars should be losing some. And so they proved to be—at exactly the rate that relativity predicts. This indirect but convincing discovery garnered a Nobel prize in 1993.

As yet, though, no one has seen a wave in action by catching the expansion and contraction of space that should be seen as one goes by, because the effects involved are ludicrously small. But researchers at America’s recently upgraded Laser Interferometer Gravitational-wave Observatory (LIGO) now think they can do it. At LIGO’s two facilities, one in Louisiana and one in Washington state, laser beams bounce up and down 4km-long tubes dozens of times before being combined in a detector to make a pattern. A passing gravitational wave that squashes space-time by a tiny fraction of the radius of an atomic nucleus in one arm but not the other will make a discernible change to that pattern. Comparing measurements at the two sites could give a sense of the wave’s direction.

Step into the light
The aim is not just to detect gravitational waves—though that would be a spectacular achievement—but to learn about the processes that produce them, such as mergers of neutron stars and black holes. The strengths of the warping effects in such cataclysms are unlike anything seen to date; their observation would provide a whole new type of test for the theory.

And history suggests there should be completely unanticipated discoveries, too. Kip Thorne, a specialist in relativity at the California Institute of Technology and co-founder of LIGO, says that “every time we’ve opened a new window on the cosmos with new radiation, there have been unexpected surprises”. For example, the pioneers of radio astronomy had no inkling that they would discover a universe full of quasars—and thus black holes. A future global array of gravitational-wave observatories could open a whole new branch of observational astronomy.

A century ago general relativity answered no-one’s questions except its creator’s. Many theories are hit upon by two or more people at almost the same time; but if Einstein had not devoted years to it, the curvature of space-time which is the essence of gravity might not have been discovered for decades. Now it has changed the way astronomers think about the universe, has challenged them to try and build theories to explain its origin, and even offered them new ways to inspect its contents. And still it retains what most commended it to Einstein: its singular beauty, revealed first to his eyes alone but appreciated today by all who have followed. “The Einstein equations of general relativity are his best epitaph and memorial,” Stephen Hawking has written. “They should last as long as the universe.”

From the print edition: Science and technology

Announcement 179: Division by zero is clear as z/0=0 and it is fundamental in mathematics

\title{\bf Announcement 179: Division by zero is clear as z/0=0 and it is fundamental in mathematics\\
\author{{\it Institute of Reproducing Kernels}\\
Kawauchi-cho, 5-1648-16,\\
Kiryu 376-0041, Japan\\
{\bf Abstract: } In this announcement, we shall introduce the zero division $z/0=0$. The result is a definite one and it is fundamental in mathematics.
By a natural extension of the fractions
for any complex numbers $a$ and $b$, we, recently, found the surprising result, for any complex number $b$
incidentally in \cite{s} by the Tikhonov regularization for the Hadamard product inversions for matrices, and we discussed their properties and gave several physical interpretations on the general fractions in \cite{kmsy} for the case of real numbers. The result is a very special case for general fractional functions in \cite{cs}. 
The division by zero has a long and mysterious story over the world (see, for example, google site with division by zero) with its physical viewpoints since the document of zero in India on AD 628, however,
Sin-Ei, Takahasi (\cite{taka}) (see also \cite{kmsy}) established a simple and decisive interpretation (1.2) by analyzing some full extensions of fractions and by showing the complete characterization for the property (1.2). His result will show that our mathematics says that the result (1.2) should be accepted as a natural one:
{\bf Proposition. }{\it Let F be a function from ${\bf C }\times {\bf C }$ to ${\bf C }$ such that
F (b, a)F (c, d)= F (bc, ad)
for all
a, b, c, d \in {\bf C }
F (b, a) = \frac {b}{a }, \quad a, b \in {\bf C }, a \ne 0.
Then, we obtain, for any $b \in {\bf C } $
F (b, 0) = 0.
\section{What are the fractions $ b/a$?}
For many mathematicians, the division $b/a$ will be considered as the inverse of product;
that is, the fraction
is defined as the solution of the equation
a\cdot x= b.
The idea and the equation (2.2) show that the division by zero is impossible, with a strong conclusion. Meanwhile, the problem has been a long and old question:
As a typical example of the division by zero, we shall recall the fundamental law by Newton:
F = G \frac{m_1 m_2}{r^2}
for two masses $m_1, m_2$ with a distance $r$ and for a constant $G$. Of course,
\lim_{r \to +0} F =\infty,
however, in our fraction
F = G \frac{m_1 m_2}{0} = 0.

Now, we shall introduce an another approach. The division $b/a$ may be defined {\bf independently of the product}. Indeed, in Japan, the division $b/a$ ; $b$ {\bf raru} $a$ ({\bf jozan}) is defined as how many $a$ exists in $b$, this idea comes from subtraction $a$ repeatedly. (Meanwhile, product comes from addition).
In Japanese language for "division", there exists such a concept independently of product.
H. Michiwaki and his 6 years old girl said for the result $ 100/0=0$ that the result is clear, from the meaning of the fractions independently the concept of product and they said:
$100/0=0$ does not mean that $100= 0 \times 0$. Meanwhile, many mathematicians had a confusion for the result.
Her understanding is reasonable and may be acceptable:
$100/2=50 \quad$ will mean that we divide 100 by 2, then each will have 50.
$100/10=10 \quad$ will mean that we divide 100 by10, then each will have 10.
$100/0=0 \quad$ will mean that we do not divide 100, and then nobody will have at all and so 0.
Furthermore, she said then the rest is 100; that is, mathematically;
100 = 0\cdot 0 + 100.
Now, all the mathematicians may accept the division by zero $100/0=0$ with natural feelings as a trivial one?
For simplicity, we shall consider the numbers on non-negative real numbers. We wish to define the division (or fraction) $b/a$ following the usual procedure for its calculation, however, we have to take care for the division by zero:
The first principle, for example, for $100/2 $ we shall consider it as follows:
How may times can we subtract $2$? At this case, it is 50 times and so, the fraction is $50$.
The second case, for example, for $3/2$ we shall consider it as follows:
3 - 2 = 1
and the rest (remainder) is $1$, and for the rest $1$, we multiple $10$,
then we consider similarly as follows:
Therefore $10/2=5$ and so we define as follows:
\frac{3}{2} =1 + 0.5 = 1.5.
By these procedures, for $a \ne 0$ we can define the fraction $b/a$, usually. Here we do not need the concept of product. Except the zero division, all the results for fractions are valid and accepted.
Now, we shall consider the zero division, for example, $100/0$. Since
100 - 0 = 100,
that is, by the subtraction $100 - 0$, 100 does not decrease, so we can not say we subtract any from $100$. Therefore, the subtract number should be understood as zero; that is,
\frac{100}{0} = 0.
We can understand this: the division by $0$ means that it does not divide $100$ and so, the result is $0$.
Similarly, we can see that
\frac{0}{0} =0.
As a conclusion, we should define the zero divison as, for any $b$
\frac{b}{0} =0.
See \cite{kmsy} for the details.

\section{In complex analysis}
We thus should consider, for any complex number $b$, as (1.2);
that is, for the mapping
w = \frac{1}{z},
the image of $z=0$ is $w=0$. This fact seems to be a curious one in connection with our well-established popular image for the point at infinity on the Riemann sphere.
However, we shall recall the elementary function
W(z) = \exp \frac{1}{z}
= 1 + \frac{1}{1! z} + \frac{1}{2! z^2} + \frac{1}{3! z^3} + \cdot \cdot \cdot .
The function has an essential singularity around the origin. When we consider (1.2), meanwhile, surprisingly enough, we have:
W(0) = 1.
{\bf The point at infinity is not a number} and so we will not be able to consider the function (3.2) at the zero point $z = 0$, meanwhile, we can consider the value $1$ as in (3.3) at the zero point $z = 0$. How do we consider these situations?
In the famous standard textbook on Complex Analysis, L. V. Ahlfors (\cite{ahlfors}) introduced the point at infinity as a number and the Riemann sphere model as well known, however, our interpretation will be suitable as a number. We will not be able to accept the point at infinity as a number.
As a typical result, we can derive the surprising result: {\it At an isolated singular point of an analytic function, it takes a definite value }{\bf with a natural meaning.} As the important applications for this result, the extension formula of functions with analytic parameters may be obtained and singular integrals may be interpretated with the division by zero, naturally (\cite{msty}).
The division by zero $b/0=0$ is possible and the result is naturally determined, uniquely.
The result does not contradict with the present mathematics - however, in complex analysis, we need only to change a little presentation for the pole; not essentially, because we did not consider the division by zero, essentially.
The common understanding that the division by zero is impossible should be changed with many text books and mathematical science books. The definition of the fractions may be introduced by {\it the method of Michiwaki} in the elementary school, even.
Should we teach the beautiful fact, widely?:
For the elementary graph of the fundamental function
y = f(x) = \frac{1}{x},
f(0) = 0.
The result is applicable widely and will give a new understanding for the universe ({\bf Announcement 166}).
If the division by zero $b/0=0$ is not introduced, then it seems that mathematics is incomplete in a sense, and by the intoduction of the division by zero, mathematics will become complete in a sense and perfectly beautiful.

For the procedure of the developing of the division by zero and for some general ideas on the division by zero, we presented the following announcements in Japanese:
{\bf Announcement 148} (2014.2.12):  $100/0=0, 0/0=0$    by a natural extension of fractions - A wish of the God
{\bf Announcement 154} (2014.4.22): A new world: division by zero, a curious world, a new idea
{\bf Announcement 157} (2014.5.8): We wish to know the idea of the God for the division by zero; why the infinity and zero point are coincident?
{\bf Announcement 161} (2014.5.30): Learning from the division by zero, sprits of mathematics and of looking for the truth
{\bf Announcement 163} (2014.6.17): The division by zero, an extremely pleasant mathematics - shall we look for the pleasant division by zero: a proposal for a fun club looking for the division by zero.
{\bf Announcement 166} (2014.6.29): New general ideas for the universe from the viewpoint of the division by zero
{\bf Announcement 171} (2014.7.30): The meanings of product and division -- The division by zero is trivial from the own sense of the division independently of the concept of product
{\bf Announcement 176} (2014.8.9):  Should be changed the education of the division by zero
L. V. Ahlfors, Complex Analysis, McGraw-Hill Book Company, 1966.
L. P. Castro and S.Saitoh, Fractional functions and their representations, Complex Anal. Oper. Theory {\bf7} (2013), no. 4, 1049-1063.
S. Koshiba, H. Michiwaki, S. Saitoh and M. Yamane,
An interpretation of the division by zero z/0=0 without the concept of product
M. Kuroda, H. Michiwaki, S. Saitoh, and M. Yamane,
New meanings of the division by zero and interpretations on $100/0=0$ and on $0/0=0$,
Int. J. Appl. Math. Vol. 27, No 2 (2014), pp. 191-198, DOI: 10.12732/ijam.v27i2.9.
H. Michiwaki, S. Saitoh, M. Takagi and M. Yamada,
A new concept for the point at infinity and the division by zero z/0=0
S. Saitoh, Generalized inversions of Hadamard and tensor products for matrices, Advances in Linear Algebra \& Matrix Theory. Vol.4 No.2 (2014), 87-95.
S.-E. Takahasi,
{On the identities $100/0=0$ and $ 0/0=0$}
S.-E. Takahasi, M. Tsukada and Y. Kobayashi, Classification of continuous fractional binary operators on the real and complex fields. (submitted)
私は数学を信じない。 アルバート・アインシュタイン / I don't believe in mathematics. Albert Einstein→ゼロ除算ができなかったからではないでしょうか。
59 minutes ago - Via Community - View - 평이 : Solar eclipse🌒🌑🌘
Solar eclipse🌒🌑🌘
3 hours ago - Via Reshared Post - View - Dmitry Volkoff : Gold and platinum offer clues about the moon's mysterious tilt A total solar eclipse occurs somewhere...
Gold and platinum offer clues about the moon's mysterious tilt

A total solar eclipse occurs somewhere on Earth about once every year and a half, on average. But imagine if it happened every single month. For this to be the case, the moon would have to orbit Earth in the same plane in which Earth travels around the sun - that way, the new moon would always come directly between us and the sun.

Read more :

Gravitational interactions of small bodies with the Earth-Moon system shortly after its formation. Credit: Laetitia Lalila
3 hours ago - Via Reshared Post - View - Omar Loisel : Gold and platinum offer clues about the moon's mysterious tilt A total solar eclipse occurs somewhere...
Gold and platinum offer clues about the moon's mysterious tilt

A total solar eclipse occurs somewhere on Earth about once every year and a half, on average. But imagine if it happened every single month. For this to be the case, the moon would have to orbit Earth in the same plane in which Earth travels around the sun - that way, the new moon would always come directly between us and the sun.

Read more :

Gravitational interactions of small bodies with the Earth-Moon system shortly after its formation. Credit: Laetitia Lalila
3 hours ago - Via Google+ - View - Mozaffar Javed : Garbage powers a bright idea A German company promises to turn Howrah’s mountain of garbage  into a ...
Garbage powers a bright idea
A German company promises to turn Howrah’s mountain
of garbage  into a fountain of energy.
Nov 27. In several
previous posts [1][2][3][4] we showed examples of how the last solar eclipse
Garbage powers a bright idea

3 hours ago - Via Google+ - View - Hassnain Ali : As seen from the Earth, a solar eclipse is a type of eclipse that occurs when the Moon passes between...
As seen from the Earth, a solar eclipse is a type of eclipse that occurs when the Moon passes between the Sun and Earth, and the Moon fully or partially blocks ("occults") the Sun. This can happen only at new moon, when the Sun and the Moon are in conjunction as seen from Earth in an alignment referred to as syzygy. In a total eclipse, the disk of the Sun is fully obscured by the Moon. In partial and annular eclipses, only part of the Sun is obscured.

If the Moon were in a perfectly circular orbit, a little closer to the Earth, and in the same orbital plane, there would be total solar eclipses every month. However, the Moon's orbit is inclined (tilted) at more than 5 degrees to the Earth's orbit around the Sun (see ecliptic), so its shadow at new moon usually misses Earth. Earth's orbit is called the ecliptic plane as the Moon's orbit must cross this plane in order for an eclipse (both solar as well as lunar) to occur. In addition, the Moon's actual orbit is elliptical, often taking it far enough away from Earth that its apparent size is not large enough to block the Sun totally. The orbital planes cross each other at a line of nodes resulting in at least two, and up to five, solar eclipses occurring each year; no more than two of which can be total eclipses.

A solar eclipse occurs when the moon gets between Earth and the sun, and the moon casts a shadow over Earth. A solar eclipse can only take place at the phase of new moon, when the moon passes directly between the sun and Earth and its shadows fall upon Earth’s surface. But whether the alignment produces a total solar eclipse, a partial solar eclipse or an annular solar eclipse depends on several factors, all explained below.
The fact that an eclipse can occur at all is a fluke of celestial mechanics and time. Since the moon formed about 4.5 billion years ago, it has been gradually moving away from Earth (by about 1.6 inches, or 4 centimeters per year). Right now the moon is at the perfect distance to appear in our sky exactly the same size as the sun, and therefore block it out. But this is not always true.
The last solar eclipse was a total eclipse on March 20, 2015.

Here is a schedule of upcoming solar eclipses:
Sept. 13, 2015: Partial eclipse. Time of greatest eclipse: 6:54 UT. Visible from southern Africa, south Indian Ocean and Antarctica.
March 9, 2016: Total eclipse. Time of greatest eclipse: 1:58 UT. Visible from Australia, Sumatra, Borneo.
Sept. 1, 2016: Annular eclipse. Time of greatest eclipse: 9:08 UT. Visible from Atlantic Ocean, central Africa, Madagasgar, Indian Ocean.

There are four types of solar eclipses: total, annular, partial and hybrid. Here’s what causes each type:
Total solar eclipses
These are a happy accident of nature. The sun's 864,000-mile diameter is fully 400 times greater than that of our puny moon, which measures just about 2,160 miles. But the moon also happens to be about 400 times closer to Earth than the sun (the ratio varies as both orbits are elliptical), and as a result, when the orbital planes intersect and the distances align favorably, the new moon can appear to completely blot out the disk of the sun. On the average a total eclipse occurs somewhere on Earth about every 18 months.
There are actually two types of shadows: the umbra is that part of the shadow where all sunlight is blocked out. The umbra takes the shape of a dark, slender cone. It is surrounded by the penumbra, a lighter, funnel-shaped shadow from which sunlight is partially obscured.
During a total solar eclipse, the moon casts its umbra upon Earth's surface; that shadow can sweep a third of the way around the planet in just a few hours. Those who are fortunate enough to be positioned in the direct path of the umbra will see the sun's disk diminish into a crescent as the moon's dark shadow rushes toward them across the landscape.
During the brief period of totality, when the sun is completely covered, the beautiful corona — the tenuous outer atmosphere of the sun — is revealed.
Totality may last as long as 7 minutes 31 seconds, though
most total eclipses are usually much shorter.

If you want to see a solar eclipse, you must be in the path of the Moon's shadow, which has 3 distinct parts:
Umbra: The innermost and darkest part of the Moon's shadow. The Sun's light is blocked in places on Earth where the umbra falls. The Sun's disc is not visible anymore.
Penumbra: The outermost and the lightest part of the Moon's shadow. Only part of the Sun's light is blocked in places on Earth where the Moon's penumbra falls. The Sun's disc is partly visible.
Antumbra: The Moon's antumbra lies beyond the umbra. It appears with the growing distance from the Moon. From Earth, the Moon appears smaller and cannot completely block the Sun, so the Sun's outer rim is still seen.
A partial solar eclipse occurs when only the penumbra (the partial shadow) passes over you. In these cases, a part of the sun always remains in view during the eclipse. How much of the sun remains in view depends on the specific circumstances.
Usually the penumbra gives just a glancing blow to our planet over the polar regions; in such cases, places far away from the poles but still within the zone of the penumbra might not see much more than a small scallop of the sun hidden by the moon. In a different scenario, those who are positioned within a couple of thousand miles of the path of a total eclipse will see a partial eclipse.
The closer you are to the path of totality, the greater the solar obscuration. If, for instance, you are positioned just outside of the path of the total eclipse, you will see the sun wane to a narrow crescent, then thicken up again as the shadow passes by.

Eclipses in 2015
March 20: Total solar eclipse
April 4: Total lunar eclipse
September 13: Partial solar eclipse
September 28: Total lunar eclipse
Eclipses in 2016
March 9: Total solar eclipse
March 23: Penumbral lunar eclipse
September 1: Annular solar eclipse
September 16: Penumbral lunar eclipse

There are 4 types of solar eclipses and they are determined by what part of the Moon's shadow falls on the Earth:
Total: A total solar eclipse takes place when the Moon completely covers the Sun and casts its umbra and penumbra on Earth. A total eclipse of the Sun can only take place when the Moon is at perigee. You can experience a total solar eclipse if you're in the path of the Moon's umbra. You can see a partial eclipse at a place where the Sun's penumbra falls.
Partial: Partial solar eclipses happen when the Moon does not completely cover the Sun's disc and casts only its penumbra on Earth.
Annular: Annular solar eclipses occur when the Moon's antumbra falls on Earth. The Moon's disc covers the center of the Sun's disc, leaving the Sun's outer edges uncovered. An annular eclipse of the Sun can only take place when the Moon is at apogee.
Hybrid: Hybrid eclipses are rare. They happen when an annular eclipse turns into a total solar eclipse.

Fortnight (approximate two-week) separation between solar and lunar eclipses. A solar eclipse always takes place within one fortnight of any lunar eclipse. For instance, in 2015, the total solar eclipse on March 20 comes one fortnight before the Blood Moon total lunar eclipse of April 4. The partial solar eclipse on September 13 occurs one fortnight before the Blood Moon total lunar eclipse of September 28. In 2016, the total solar eclipse of March 9 happens one fortnight before the penumbral lunar eclipse of March 23; and the September 1 annular solar eclipse takes place one fortnight before the September 16 penumbral lunar eclipse.
Somewhat rarely, a solar eclipse can occur one fortnight before and after a lunar eclipse. This will next happen in the year 2018:
July 13: Partial solar eclipse
July 27: Total lunar eclipse
August 11: Partial solar eclipse
Somewhat rarely, a lunar eclipse can come one fortnight before and after a solar eclipse. This will next happen in the year 2020:
June 5: Penumbral lunar eclipse
June 21: Annular solar eclipse
July 5: Penumbral lunar eclipse

An annular eclipse, though a rare and amazing sight, is far different from a total one. The sky will darken ... somewhat; a sort of weird “counterfeit twilight” since so much of the sun still shows. The annular eclipse is a subspecies of a partial eclipse, not total. The maximum duration for an annular eclipse is 12 minutes 30 seconds.
However, an annular solar eclipse is similar to a total eclipse in that the moon appears to pass centrally across the sun. The difference is, the moon is too small to cover the disk of the sun completely. Because the moon circles Earth in an elliptical orbit, its distance from Earth can vary from 221,457 miles to 252,712 miles. But the dark shadow cone of the moon’s umbra can extend out for no longer than 235,700 miles; that’s less than the moon’s average distance from Earth.
So if the moon is at some greater distance, the tip of the umbra does not reach Earth. During such an eclipse, the antumbra, a theoretical continuation of the umbra, reaches the ground, and anyone situated within it can look up past either side of the umbra and see an annulus, or “ring of fire” around the moon. A good analogy is putting a penny atop a nickel, the penny being the moon, the nickel being the sun.

Since looking directly at the Sun can lead to permanent eye damage or blindness, special eye protection or indirect viewing techniques are used when viewing a solar eclipse. It is technically safe to view only the total phase of a total solar eclipse with the unaided eye and without protection; however, this is a dangerous practice, as most people are not trained to recognize the phases of an eclipse, which can span over two hours while the total phase can only last up to 7.5 minutes for any one location. People referred to as eclipse chasers or umbraphiles will travel to remote locations to observe or witness predicted central solar eclipses.

The magnitude of an eclipse is the ratio of the apparent size of the Moon to the apparent size of the Sun during an eclipse. An eclipse that occurs when the Moon is near its closest distance to Earth (i.e., near its perigee) can be a total eclipse because the Moon will appear to be large enough to completely cover the Sun's bright disk, or photosphere; a total eclipse has a magnitude greater than 1. Conversely, an eclipse that occurs when the Moon is near its farthest distance from Earth (i.e., near its apogee) can only be an annular eclipse because the Moon will appear to be slightly smaller than the Sun; the magnitude of an annular eclipse is less than 1. Slightly more solar eclipses are annular than total because, on average, the Moon lies too far from Earth to cover the Sun completely. A hybrid eclipse occurs when the magnitude of an eclipse changes during the event from less to greater than one, so the eclipse appears to be total at some locations on Earth and annular at other locations.

Hybrid solar eclipses
These are also called annular-total (“A-T”) eclipses. This special type of eclipse occurs when the moon’s distance is near its limit for the umbra to reach Earth. In most cases, an A-T eclipse starts as an annular eclipse because the tip of the umbra falls just short of making contact with Earth; then it becomes total, because the roundness of the planet reaches up and intercepts the shadow tip near the middle of the path, then finally it returns to annular toward the end of the path.
Because the moon appears to pass directly in front of the sun, total, annular and hybrid eclipses are also called “central” eclipses to distinguish them from eclipses that are merely partial.
Of all solar eclipses, about 28 percent are total; 35 percent are partial; 32 percent annular; and just 5 percent are hybrids.

Predictions of solar eclipses
Eclipses do not happen at every new moon, of course. This is because the moon’s orbit is tilted just over 5 degrees relative to Earth’s orbit around the sun. For this reason, the moon’s shadow usually passes either above or below Earth, so a solar eclipse doesn’t occur.
But as a rule, at least twice each year (and sometimes as many as five times in a year), a new moon will align itself in just such a way to eclipse the sun. That alignment point is called a node. Depending on how closely the new moon approaches a node will determine whether a particular eclipse is central or partial. And of course, the moon’s distance from the Earth — and to a lesser degree, Earth’s distance from the sun — will ultimately determine whether a central eclipse is total, annular or a hybrid.
And these alignments don’t happen haphazardly, for after a specific interval of time, an eclipse will repeat itself or return. This interval is known as the Saros cycle and was known as far back as the days of the early Chaldean astronomers some 28 centuries ago. The word Saros means “repetition” and is equal to 18 years, 11⅓ days (or a day less or more depending on the number of leap years that have intervened). After this interval, the relative positions of the sun and moon relative to a node are nearly the same as before. That third of a day in the interval causes the path of each eclipse of a series to be displaced in longitude a third of the way around Earth to the west with respect to its predecessor.
For example, on March 29, 2006, a total eclipse swept across parts of western and northern Africa and then across southern Asia. One Saros later, on April 8, 2024, this eclipse will recur, except instead of Africa and Asia, it will track across northern Mexico, the central and eastern United States and the Maritime provinces of Canada.

As a solar eclipse approaches, the mainstream media often will provide a variety of warnings and advisories against looking at the sun with bare eyes, as blindness could ensue. This has given most people the idea that eclipses are dangerous.
Not so!
It’s the sun that is dangerous — all the time! The sun constantly emits invisible infrared rays that can damage your eyes. Ordinarily, we have no reason to gaze at the sun. An eclipse gives us a reason, but we shouldn’t.
There are safe ways, however . . .
By far, the safest way to view a solar eclipse is to construct a “pinhole camera.” A pinhole or small opening is used to form an image of the sun on a screen placed about 3 feet (or about 1 meter) behind the opening. Binoculars or a small telescope mounted on a tripod can also be used to project a magnified image of the sun onto a white card. The farther away the card, the larger you can focus the image. Look for sunspots. Notice that the sun appears somewhat darker around its limb or edge. This method of solar viewing is safe so long as you remember not to look through the binoculars or telescope when they are pointed toward the sun; put another way, never look directly at the sun when any part of its blindingly bright surface is visible.
A variation on the pinhole theme is the “pinhole mirror.” Cover a pocket-mirror with a piece of paper that has a ¼-inch hole punched in it. Open a sun-facing window and place the covered mirror on the sunlit sill so it reflects a disk of light onto the far wall inside. The disk of light is an image of the sun’s face. The farther away from the wall is the better; the image will be only 1 inch across for every 9 feet (or 3 centimeters for every 3 meters) from the mirror. Modeling clay works well to hold the mirror in place. Experiment with different-sized holes in the paper. Again, a large hole makes the image bright, but fuzzy, and a small one makes it dim but sharp. Darken the room as much as possible. Be sure to try this out beforehand to make sure the mirror’s optical quality is good enough to project a clean, round image. Of course, don’t let anyone look at the sun in the mirror.
If you’re around leafy trees, look at the shadow cast by them during the partial phases. What do you see? Is it worth a photograph? You will see scores of partially eclipsed suns projected through pinhole gaps between the leaves. This is caused by diffraction, a property of light. According to Vince Huegele, an optical physicist at the NASA Marshall Space Flight Center, the light rays do not shoot straight by the rim of the gaps, or a pinhole, but bend around the edge. This wave effect creates a pattern of rings that resembles a bull's eye.
Acceptable filters for unaided visual solar observations include aluminized Mylar. Some astronomy dealers carry Mylar filter material specially designed for solar observing. Also acceptable is shade 14 arc-welder’s glass, available for just a few dollars at welding supply shops. Of course, it is always a good idea to test your filters and/or observing techniques before eclipse day.
Unacceptable filters include sunglasses, old color film negatives, black-and-white film that contains no silver, photographic neutral-density filters and polarizing filters. Although these materials have very low visible-light transmittance levels, they transmit an unacceptably high level of near-infrared radiation that can cause a thermal retinal burn. The fact that the sun appears dim, or that you feel no discomfort when looking at the sun through these types of filters, is no guarantee that your eyes are safe.
There is one time when you can safely look directly at the sun: during a total eclipse, when the sun's disk is entirely covered. During those few precious seconds or minutes, the magnificent corona shines forth in all its glory surrounding the darkened sun; a marvelous fringe of pearly white light. It differs in size, in tints and patterns from eclipse to eclipse. It is always faint and delicate, with a sheen like a pale aurora. It has a variable appearance. Sometimes it has a soft continuous look; at other times, long rays of it shoot out in three or four directions. It may stand out from the disk in filmy petals and streamers. But when the sun begins to again emerge into view, the corona quickly disappears and you’ll need to protect your eyes once again.

First contact—when the Moon's limb (edge) is exactly tangential to the Sun's limb.
Second contact—starting with Baily's Beads (caused by light shining through valleys on the Moon's surface) and the diamond ring effect. Almost the entire disk is covered.
Totality—the Moon obscures the entire disk of the Sun and only the solar corona is visible.
Third contact—when the first bright light becomes visible and the Moon's shadow is moving away from the observer. Again a diamond ring may be observed.
Fourth contact—when the trailing edge of the Moon ceases to overlap with the solar disk and the eclipse ends.

As best as we can determine, the earliest record of a solar eclipse occurred over four millennia ago. In China, it was believed that the gradual blotting out of the sun was caused by a dragon who was attempting to devour the sun, and it was the duty of the court astronomers to shoot arrows, beat drums and raise whatever cacophony they could to frighten the dragon away.
In the ancient Chinese classic Shujing (or Book of Documents) is the account of Hsi and Ho, two court astronomers who were caught completely unaware by a solar eclipse, having gotten drunk just before the event began. In the aftermath, Zhong Kang, the fourth emperor of the Xia dynasty ordered that Hsi and Ho be punished by having their heads chopped off. The eclipse in question was that of Oct. 22 in the year 2134 B.C.
In the Bible, in the book of Amos 8:9, are the words, “I will cause the sun to go down at noon, and I will darken the Earth in the clear day.” Biblical scholars believe this is a reference to a celebrated eclipse observed at Nineveh in ancient Assyria on June 15, 763 B.C. An Assyrian tablet also attests to the event.
A solar eclipse even stopped a war.
According to the historian Herodotus, there was a five-year war that raged between the Lydians and the Medes. As the war was about to move into its sixth year, a Greek sage, Thales of Miletus foretold to the Ionians that the time was soon approaching when day would turn to night. On May 17, 603 B.C. the sun faded away just as Thales had alluded that it would. So believing that it was a sign from above, the combatants called a truce, which was cemented by a double marriage, for, as Herodotus wrote: “Without some strong bond, there is little of security to be found in men’s covenants.”
And giving new meaning to the term, “Scared to death,” is the timid emperor Louis of Bavaria, the son of Charlemagne, who witnessed an unusually long total eclipse of the sun on May 5, A.D. 840, which lasted for over five minutes.  But no sooner had the sun begun to emerge back into view, Louis was so overwhelmed by what he had just seen that he died of fright!

Astronomers have learned much by studying eclipses and by the 18th century, observations of solar eclipses were recognized as providing veritable treasure troves of astronomical information, though sometimes getting that information wasn’t easy.
Samuel Williams, a professor at Harvard, led an expedition to Penobscot Bay, Maine, to observe the total solar eclipse of Oct. 27, 1780. As it turned out, this eclipse took place during the Revolutionary War, and Penobscot Bay lay behind enemy lines. Fortunately, the British granted the expedition safe passage, citing the interest of science above political differences.
And yet in the end, it was all for naught.
Williams apparently made a crucial error in his computations and inadvertently positioned his men at Islesboro — just outside the path of totality — likely finding this out with a heavy heart when the narrowing crescent of sunlight slid completely around the dark edge of the moon and then started to thicken!
During a total solar eclipse, a few ruby-red spots may seem to hover around the jet-black disk of the moon. Those are solar prominences, tongues of incandescent hydrogen gas rising above the surface of the sun. During the total eclipse of Aug. 18, 1868, the French astronomer Pierre Janssen trained his spectroscope on the prominences and discovered a new chemical element. Two English astronomers, J. Norman Lockyer and Edward Frankland, later named it “helium,” from the Greek helios (the sun). The gas was not identified on Earth until 1895.
And because sunlight is blocked during a total eclipse, some of the brighter stars and planets can be observed in the darkened sky. Under such conditions astronomers were able to test part of Einstein’s now-celebrated general theory of relativity. That theory predicted that light from stars beyond the sun would bend from a straight path in a certain way as it passed the sun. The positions of stars photographed near the sun’s edge during a total eclipse on May 29, 1919, were compared with photographs of the same region of the sky taken at night; the results strongly supported Einstein’s theory.
4 hours ago - Via Google+ - View - Eric Templeton : Solar Eclipse From the International Space Station Expedition 43 Flight Engineer Samantha Cristoforetti...
Solar Eclipse From the International Space Station

Expedition 43 Flight Engineer Samantha Cristoforetti took a series of photographs of the March 20, 2015 solar eclipse from the International Space Station. Cristoforetti wrote, "Orbital sunrise and the #SolarEclipse... could it go any better?"

A solar eclipse occurs when the moon passes between Earth and the sun, casting a shadow over Earth. The moon’s shadow masks the solar surface and blocks sunlight from reaching Earth directly – but the amount of sunlight blocked depends on location.

Image Credit: ESA/NASA

+European Space Agency, ESA
10 hours ago - Via Reshared Post - View - The Solar Eclipse :
14 hours ago - Via Reshared Post - View - The Solar Eclipse :
14 hours ago - Via Reshared Post - View - Projekt [Solar Eclipse] : ...doom death metal: Swallow the Sun, Wolfheart & Adimiron.... #doomdeath #k17 #berlin
...doom death metal: Swallow the Sun, Wolfheart & Adimiron....

#doomdeath #k17 #berlin
15 hours ago - Via Google+ - View - Jeremia Mutig : Two children are seen gazing at a beautiful, unique sunset caused by a partial solar eclipse. Beautiful...
Two children are seen gazing at a beautiful, unique sunset caused by a partial solar eclipse. Beautiful. 

Please Follow: +Interesting Things
16 hours ago - Via Reshared Post - View - BetterPhotography : Spectacular Solar Eclipse View Wins Astronomy Photographer of the Year Prize #photography #photo http...
Spectacular Solar Eclipse View Wins Astronomy Photographer of the Year Prize #photography #photo
Spectacular Solar Eclipse View Wins Astronomy Photographer of the Year Prize
The winning images from the Insight Astronomy Photographer of the Year competition were announced last week, and the list is an awe-inspiring collection of celestial awesomeness.
17 hours ago - Via - View - Solar Market India : SunEdison's Solar Eclipse Brightens Indian Power Prospects
SunEdison's Solar Eclipse Brightens Indian Power Prospects
Andy Mukherjee

17 hours ago - Via - View - Tatjana Glušac :

GLOBAL ASTROLOGY: A New Solar Year: The Vernal Equinox Of 2015 > A Total Solar Eclipse & Supermoon Over Europe > Also, April's 'Blood Moon' Total Lunar Eclipse > Uranus-Pluto World Squares: Generational War In A Transitional Decade? > The Mutable Middle Years: 2015, 2016 & 2017 > Global Cooling Forecast - 2017-2053: Climate Change Of Historic Proportions?
17 hours ago - Via Google+ - View - Hassnain Ali : A lunar eclipse occurs when the Moon passes directly behind the Earth into its umbra (shadow). This ...
A lunar eclipse occurs when the Moon passes directly behind the Earth into its umbra (shadow). This can occur only when the sun, Earth and moon are aligned (in "syzygy") exactly, or very closely so, with the Earth in the middle. Hence, a lunar eclipse can occur only the night of a full moon.

A total lunar eclipse has the direct sunlight completely blocked by the earth's shadow. The only light seen is refracted through the earth's shadow. This light looks red for the same reason that the sunset looks red, due to rayleigh scattering of the more blue light. Because of its reddish color, a total lunar eclipse is sometimes called a blood moon.

There is a total eclipse of the moon on the night of September 27-28, 2015. It happens to be the closest supermoon of 2015. It’s the Northern Hemisphere’s Harvest Moon, or full moon nearest the September equinox. It’s the Southern Hemisphere’s first full moon of spring. This September full moon is also called a Blood Moon, because it presents the fourth and final eclipse of a lunar tetrad: four straight total eclipses of the moon, spaced at six lunar months (full moons) apart. Phew!
The total lunar eclipse is visible from the most of North America and all of South America after sunset September 27. From eastern South America and Greenland, the greatest eclipse happens around midnight September 27-28. In Europe, Africa and the Middle East, the total eclipse takes place in the wee hours of the morning, after midnight and before sunrise September 28. A partial lunar eclipse can be seen after sunset September 27 from western Alaska, or before sunrise September 28 in far-western Asia. Photo top of post shows a partial phase of the April 14-15, 2014 total lunar eclipse by Fred Espenak. Follow the links below to learn more about the 2015 Harvest Moon and the September 27-28 total lunar eclipse.
                                                                         In the US, Canada, and Central and South America, this rare Total Lunar Eclipse of a Supermoon will begin on the evening of September 27, 2015. In Europe, South/East Asia, Africa, the Arctic, and in the Pacific, Atlantic, and Indian Oceans it starts after midnight on September 28, 2015.
Also called a Blood Moon this eclipse will last for about 1 hour and 12 minutes.

Unlike a solar eclipse, which can be viewed only from a certain relatively small area of the world, a lunar eclipse may be viewed from anywhere on the night side of the Earth. A lunar eclipse lasts for a few hours, whereas a total solar eclipse lasts for only a few minutes at any given place, due to the smaller size of the Moon's shadow. Also unlike solar eclipses, lunar eclipses are safe to view without any eye protection or special precautions, as they are dimmer than the full moon.

                      Lunar eclipses occur when Earth's shadow blocks the sun’s light, which otherwise reflects off the moon. There are three types — total, partial and penumbral — with the most dramatic being a total lunar eclipse, in which Earth’s shadow completely covers the moon.
Throughout history, eclipses have inspired awe and even fear, especially when total lunar eclipses turned the moon blood-red, an effect that terrified people who had no understanding of what causes an eclipse and therefore blamed the events on this god or that. Below, you’ll find the science and history of lunar eclipses, learn how they work, and see a list of the next ones on tap. [See also our guide to Solar Eclipses.]

A lunar eclipse can occur only at full moon. A total lunar eclipse can happen only when the sun, Earth and moon are perfectly lined up — anything less than perfection creates a partial lunar eclipse or no eclipse at all. Some understanding of simple celestial mechanics explains how lunar eclipses work. [Infographic: Total Eclipse of the Moon]
Because the moon’s orbit around Earth lies in a slightly different plane than Earth’s orbit around the sun, perfect alignment for an eclipse doesn’t occur at every full moon. A total lunar eclipse develops over time, typically a couple hours for the whole event. Here’s how it works: Earth casts two shadows that fall on the moon during a lunar eclipse: The umbra is a full, dark shadow. The penumbra is a partial outer shadow. The moon passes through these shadows in stages. The initial and final stages — when the moon is in the penumbral shadow — are not so noticeable, so the best part of an eclipse is during the middle of the event, when the moon is in the umbral shadow.
Total eclipses are a freak of cosmic happenstance. Ever since the moon formed, about 4.5 billion years ago, it has been inching away from our planet (by about 1.6 inches, or 4 centimeters per year). The setup right now is perfect: the moon is at the perfect distance for Earth’s shadow to cover the moon totally, but just barely. Billions of years from now, that won’t be the case.

Total lunar eclipse: Earth’s full (umbral) shadow falls on the moon. The moon won’t completely disappear, but it will be cast in an eerie darkness that makes it easy to miss if you were not looking for the eclipse. Some sunlight passing through Earth’s atmosphere is scattered and refracted, or bent, and refocused on the moon, giving it a dim glow even during totality. If you were standing on the moon, looking back at the sun, you’d see the black disk of Earth blocking the entire sun, but you’d also see a ring of reflected light glowing around the edges of Earth — that’s the light that falls on the moon during a total lunar eclipse.
Partial lunar eclipse: Some eclipses are only partial. But even a total lunar eclipse goes through a partial phase on either side of totality. During the partial phase, the sun, Earth and moon are not quite perfectly aligned, and Earth’s shadow appears to take a bite out of the moon.
Penumbral lunar eclipse: This is the least interesting type of eclipse, because the moon is in Earth’s faint outer (penumbral) shadow. Unless you’re a seasoned skywatcher, you likely won’t notice the effect.
The blood-red moon
The moon may turn red or coppery colored during the total portion of an eclipse. The red moon is possible because while the moon is in total shadow, some light from the sun passes through Earth's atmosphere and is bent toward the moon. While other colors in the spectrum are blocked and scattered by Earth’s atmosphere, red light tends to make it through easier. The effect is to cast all the planet's sunrises and sunsets on the moon.

The shadow of the Earth can be divided into two distinctive parts: the umbra and penumbra. Within the umbra, there is no direct solar radiation. However, as a result of the Sun's large angular size, solar illumination is only partially blocked in the outer portion of the Earth's shadow, which is given the name penumbra.

A penumbral eclipse occurs when the moon passes through the Earth's penumbra. The penumbra causes a subtle darkening of the moon's surface. A special type of penumbral eclipse is a total penumbral eclipse, during which the Moon lies exclusively within the Earth's penumbra. Total penumbral eclipses are rare, and when these occur, that portion of the moon which is closest to the umbra can appear somewhat darker than the rest of the moon.
A partial lunar eclipse occurs when only a portion of the moon enters the umbra. When the moon travels completely into the Earth's umbra, one observes a total lunar eclipse. The moon's speed through the shadow is about one kilometer per second (2,300 mph), and totality may last up to nearly 107 minutes. Nevertheless, the total time between the moon's first and last contact with the shadow is much longer, and could last up to four hours.[1] The relative distance of the moon from the Earth at the time of an eclipse can affect the eclipse's duration. In particular, when the moon is near its apogee, the farthest point from the Earth in its orbit, its orbital speed is the slowest. The diameter of the umbra does not decrease appreciably within the changes in the orbital distance of the moon. Thus, a totally eclipsed moon occurring near apogee will lengthen the duration of totality.

"The exact color that the moon appears depends on the amount of dust and clouds in the atmosphere," according to NASA scientists. "If there are extra particles in the atmosphere, from say a recent volcanic eruption, the moon will appear a darker shade of red."
Christopher Columbus leveraged a blood-red eclipse in 1504 to frighten natives on Jamaica into feeding him and his crew. It was on Columbus’ fourth and final voyage to the New World. An epidemic of shipworms ate holes in the ships of his fleet; Columbus' was forced to abandon two ships. He then beached his last two on Jamaica on June 25, 1503. The natives welcomed the castaways and fed them. But after six months, Columbus’ crew mutinied, and robbed and murdered some of the Jamaicans, who had grown weary of feeding the crew.
Columbus had an almanac that foretold a lunar eclipse on Feb. 29, 1504. He met the local chief, and told him the Christian god was angry with his people for no longer supplying food. Columbus said to expect a sign of God’s displeasure three nights later, when he would make the full moon appear "inflamed with wrath." When the blood-red moon came to pass, the natives were terrified and “with great howling and lamentation came running from every direction to the ships laden with provisions,” according to an account by Columbus’ son.
Just before the total phase of the eclipse was about to end, Columbus said God had pardoned the natives and would bring the moon back. The crew was well fed until help arrived in November and Columbus and his men sailed back to Spain.

Lunar eclipses are among the easiest skywatching events to observe. Simply go out, look up and enjoy. You don’t need a telescope or any other special equipment. However, binoculars or a small telescope will bring out details in the lunar surface — moonwatching is as interesting during an eclipse as anytime. If the eclipse occurs during winter, bundle up if you plan to be out for the duration — an eclipse can take a couple hours to unfold. Bring warm drinks and blankets or chairs for comfort.
                       A selenelion or selenehelion occurs when both the Sun and the eclipsed Moon can be observed at the same time. This can happen only just before sunset or just after sunrise, and both bodies will appear just above the horizon at nearly opposite points in the sky. This arrangement has led to the phenomenon being referred to as a horizontal eclipse. There are typically a number of high ridges undergoing sunrise or sunset that can see it. Although the moon is in the Earth’s umbra, the Sun and the eclipsed Moon can both be seen at the same time because the refraction of light through the Earth’s atmosphere causes each of them to appear higher in the sky than their true geometric position.

When is the September 2015 moon exactly full? Generally speaking, we can say the moon stays full all night on September 27-28.
But, to astronomers, the moon turns full at a well-defined instant: when it’s opposite the sun in ecliptic longitude.
That instant happens on September 28, 2015 at 2:51 UTC. At our U.S. time zones, that places the precise time of full moon on September 27 at 10:51 p.m. EDT, 9:51 p.m CDT, 8:51 p.m. MDT or 7:51 p.m. PDT. At that time, because there’s an eclipse happening, the moon will be totally submerged in the Earth’s dark umbral shadow.
Meanwhile, because of the difference in time zones, this same full moon happens around local midnight (September 27-28) for Brazil and Greenland. It’s sunset (September 27) for far northeastern North America and it’s sunrise (September 28) in far-eastern Africa, the Middle East and European Russia.
Watch the full-looking moon on the night of September 27-28 to rise in the east as the sun goes down. Like any full moon, the Northern Hemisphere’s Harvest Moon will shine all night long. It’ll soar highest in the sky around midnight and will set in the west around sunrise.

Who will see the September 27-28 total lunar eclipse? The September 2015 full moon passes directly through Earth’s dark (umbral) shadow. The total part of this eclipse lasts for 72 minutes. A partial umbral eclipse precedes totality by some 64 minutes, and follows totality by about the same period of time, so the moon takes about 3 and 1/3 hours to completely sweep through the Earth’s dark shadow.
North America, South America, the Atlantic Ocean, Greenland, Europe, Africa and the Middle East are in a good position worldwide to watch the total eclipse of the moon. If you live in the Americas, the total eclipse happens after sunset September 27. In the world’s eastern hemisphere, the total eclipse happens after midnight and before sunrise September 28.
A very light penumbral eclipse comes before and after the dark (umbral) stage of the lunar eclipse. But this sort of eclipse is so faint that many people won’t even notice it. The penumbral eclipse would be more fun to watch from the moon, where it would be seen as a partial eclipse of the sun.
Who will see the partial lunar eclipse on September 27? A partial lunar eclipse may be visible in the haze of evening dusk on September 27 from the extreme northwestern portion of North America (western Alaska). A partial lunar eclipse might also be observed in the haze of morning dawn (September 28) from far-western Asia (Pakistan, Afghanistan, eastern Iran).

Newfoundland Daylight Time (September 27, 2015)
Partial umbral eclipse begins: 10:37 p.m. NDT on September 27
Total eclipse begins: 11:41 p.m. NDT
Greatest eclipse: 12:17 a.m. NDT on September 28
Total eclipse ends: 12:53 a.m. NDT on September 28
Partial eclipse ends: 1:57 a.m. NDT on September 28
Atlantic Daylight Time (September 27, 2015)
Partial umbral eclipse begins: 10:07 p.m. ADT on September 27
Total eclipse begins: 11:11 p.m. ADT
Greatest eclipse: 11:47 p.m. ADT
Total eclipse ends: 12:23 a.m. ADT on September 28
Partial eclipse ends: 1:27 a.m. ADT on September 28
Eastern Daylight Time (September 27, 2015)
Partial umbral eclipse begins: 9:07 p.m. EDT on September 27
Total eclipse begins: 10:11 p.m. EDT
Greatest eclipse: 10:47 p.m. EDT
Total eclipse ends: 11:23 p.m. EDT
Partial eclipse ends: 12:27 a.m. EDT on September 28
Central Daylight Time (September 27, 2015)
Partial umbral eclipse begins: 8:07 p.m. CDT on September 27
Total eclipse begins: 9:11 p.m. CDT
Greatest eclipse: 9:47 p.m. CDT
Total eclipse ends: 10:23 p.m. CDT
Partial eclipse ends: 11:27 p.m. CDT
Mountain Daylight Time (September 27, 2015)
Partial umbral eclipse begins: 7:07 p.m. MDT on September 27
Total eclipse begins: 8:11 p.m. MDT
Greatest eclipse: 8:47 p.m. MDT
Total eclipse ends: 9:23 p.m. MDT
Partial eclipse ends: 10:27 p.m. MDT
Pacific Daylight Time (September 27, 2015)
Partial umbral eclipse begins: 6:07 p.m. PDT on September 27
Total eclipse begins: 7:11 p.m. PDT
Greatest eclipse: 7:47 p.m. PDT
Total eclipse ends: 8:23 p.m. PDT
Partial eclipse ends: 9:27 p.m. PDT
Alaskan Daylight Time (September 27, 2015)
Partial umbral eclipse begins before sunset September 27
Total eclipse begins before sunset
Greatest eclipse: 6:47 p.m. ADT
Total eclipse ends: 7:23 p.m. ADT
Partial eclipse ends: 8:27 p.m. ADT
22 hours ago - Via Google+ - View - Gatherer314 : How the moon got its tilt—and Earth got its gold "Miniplanets zooming through our early solar system...
How the moon got its tilt—and Earth got its gold

"Miniplanets zooming through our early solar system passed close to our moon and tugged it into the strange, tilted orbit it has today, according to a new study. The findings solve a longstanding mystery and may also explain why Earth’s crust is unexpectedly rich in gold and platinum: When some of these small planets slammed into Earth, they delivered a payload of precious metals.

Scientists have long debated the origin of the moon. The prevailing idea, first proposed decades ago, is that a Mars-sized planet collided with Earth, flinging material into space that then coalesced into our only natural satellite. According to current models of that collision, the ring of debris that eventually became the moon should have ended up in a plane tilted no more than 1° from the ecliptic, the plane in which Earth orbits the sun, says Kaveh Pahlevan, a planetary scientist at Université Côte d’Azur in Nice, France. But in fact, the moon’s orbital inclination today is 5°. And the tilt would have been more pronounced, 10° or so, immediately after the moon formed 4.5 billion years ago, before Earth started to smooth the moon’s orbit out a bit. This significant discrepancy between prediction and reality has been dubbed “the lunar inclination problem.”

Scientists have proposed a few solutions to this conundrum. Other large objects may have slammed into the moon and jostled its orbit, they say, or perhaps the strange orbit was caused by repeated tugging from the sun.

But Pahlevan and university colleague Alessandro Morbidelli, also a planetary scientist, realized that for every cosmic collision, there would likely have been dozens of close calls—and the closer the encounter, the more the moon’s orbit would have been influenced. In their new study, the pair used thousands of computer simulations to estimate the cumulative effects of such close encounters on the lunar orbit.

In their models, the researchers began with a common view of the early solar system: one populated with lots of mini-planets that had coalesced from dust, ranging in size from 1 lunar mass down to 0.1 lunar mass. Each simulation started just after the moon formed and ended when all of the mini-planets orbiting near Earth either fell into the sun, crashed into another planet or was ejected from the solar system entirely—an interval that typically lasted about 100 million years in simulated time.

In a substantial fraction of the team’s simulations, the moon’s orbital tilt ended up being 10° or more, the amount that planetary scientists estimate the nascent moon would have had based on today’s orbital tilt. What’s more, says Pahlevan, some of the mini-planets crashed into Earth at some point in those simulations—impacts that would have delivered iridium, gold and platinum, among other elements. The proportions of those metals are unusually high in Earth’s crust, which many scientists have tried to explain with models of an impact-delivered “late veneer” that came after Earth’s formation. According to some models of planetary formation, the metals would have sunk to Earth’s core when much of the planet’s iron did, which means that new supplies had to come later in order for them to be found in the crust in such relatively high abundances.

Those impacts were small individually, but together the objects would have totaled between 60% and 120% the mass of the moon, the researchers report online today in Nature. Based on the known average cosmic abundance of various elements, that’s plenty enough material to explain the anomalous concentrations of the metals now present in Earth’s crust, they say.

The findings are compelling, says Robin Canup, a planetary scientist at the Southwest Research Institute in Boulder, Colorado: “They provide a simple and elegant solution to the lunar inclination problem.”

If all of the mini-planets whizzing through the early solar system hadn’t existed—or if the moon-generating impact had occurred much later than it did, after those objects had been cleared from the inner solar system—the moon’s orbital plane would be very close to Earth’s, Canup says. That would cause our satellite to block the sun each time it orbited Earth, thus providing a total solar eclipse every month, Canup notes in an accompanying News & Views perspective in Nature. The trade-off might be unappealing jewelry, however: Rather than platinum and gold, we’d be adorning ourselves with tin and copper."


How the moon got its tilt—and Earth got its gold
Blame the gravitational tugs of many close calls in a crowded young solar system
1 day ago - Via Google+ - View - J CELTICMATCHWORN : Solar eclipse and rainbow straight after .daer resovior scottish borders. #scotland
Solar eclipse and rainbow straight after .daer resovior scottish borders.
1 day ago - Via Google+ - View - Helen Driscoll : Solar Eclipse From the International Space Station Expedition 43 Flight Engineer Samantha Cristoforetti...
Solar Eclipse From the International Space Station

Expedition 43 Flight Engineer Samantha Cristoforetti took a series of photographs of the March 20, 2015 solar eclipse from the International Space Station. Cristoforetti wrote, "Orbital sunrise and the #SolarEclipse... could it go any better?"

A solar eclipse occurs when the moon passes between Earth and the sun, casting a shadow over Earth. The moon’s shadow masks the solar surface and blocks sunlight from reaching Earth directly – but the amount of sunlight blocked depends on location.

Image Credit: ESA/NASA

+European Space Agency, ESA
1 day ago - Via Reshared Post - View - Chatty Cathy : The importance of 72 is obviously a given considering the number of events attributed to it. Like everything...
The importance of 72 is obviously a given considering the number of events attributed to it. Like everything in this world and above, the dark side counterfeits it…so with that being said….

In the story of Genesis, chapter 11, GOD punishes humanity for building the Tower of Babel, therefore they are dispersed accordingly which creates 72 different languages.
In the tuning of frequencies, Ley Lines are a popular phenomena which produce energy that cross the grids of Earth forming 72 nodal points. This energy of electromagnetic attractions are consistent with many ancient structures. Steve Quayle in a Coast to Coast AM, noted that there are 72 ionospheric heaters similar to the HAARP facility in Gokona, Alaska and this number corresponds with the 72 nations of Genesis 10, as being under the influence (powers) of the 72 regents of the fallen hierarchy and the 72 quinaries of the degrees of the zodiac in Kabbalistic teachings.
Seems 72 is also:

a natural number
The axis of the earth moves of one degree every 72 years compared to stars and to the vault of heaven.

Messier object M72, a magnitude 10.0 globular cluster in the constellation Aquarius.
The New General Catalogue object NGC 72, a magnitude 13.5 barred spiral galaxy in the constellation Andromeda.
The Saros number of the solar eclipse series which began on -727 August 16 and ended on 752 January. The duration of Saros series 72 was 1478.1 years, and it contained 83 solar eclipses.
The Saros number of the lunar eclipse series which began on -407 June 5 and ended on 891 July. The duration of Saros series 72 was 1298.1 years, and it contained 73 lunar eclipses.
The precession of equinoxes traces out a pair of cones joined at their apices in a cycle of approximately 26,000 years, that is 1 degree every 72 years (approximation to the near most integer).
The conventional number of scholars translating the Septuagint, according to the legendary account in the “Letter of Aristeas”.
The conventional number of disciples sent forth by Jesus in Luke 10 in some manuscripts (seventy in others).
The number of names of God, according to Kabbalah.

The name of God is composed of 72 letters according to the cabalistic tradition. It comes from the mystical text (called Schemamphorash) of the Exodus, chapter 14 verses 19, 20 and 21 of which each one is composed of 72 letters in the original Hebraic text. It is this ineffable name of God whom murmured the great priest in the middle of the shouts of the crowd. It was replaced later by the sacred named, YHWH, than cabalists pronounce by spelling them one after the other: Yod, He, Waw, He. It is also by extraction and transposition of the three verses of the Schemamphorash that cabalists deduce the names of the 72 spirits (or angels) of the Cabal which they call the “explained divine name”.
The total number of books in the Holy Bible in the Catholic version if the Book of Lamentations is considered part of the Book of Jeremiah.
The current distribution of the Revelation book is 22 chapters, adopted since the 13th century. But such was not always the case. The oldest known division of the text is that the Greek commentator Andrew of Cesary (6th century) in 72 chapters. Although made with enough accuracy, this structuring could be easily reduced to 70, while putting in the same chapter, the numbers 60, 61 and 62 which constitute a whole, the millennial Reign. Andrew had wanted moreover group these 72 chapters three by three, in order to obtain 24 sections, corresponding to the 24 elders. These 24 sections were completely arbitrary, and divided the texts at the wrong moment. Let us mention that the Codex Amiatinus and the Codex Fuldensis share the book of the Revelation in 25 chapters, and that some Latin handwritten find some from 22 to 44.
The importance of 72 is obviously a given considering the number of events attributed to it. Like everything in this world and above, the dark side counterfeits it…so with that being said…. In the ...
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