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The king tides are back, along with high winds, and they caused some havoc in Boston – leading to a teachable moment by Boston Harbor. A massive ship broke free from dock, and had drifted out – while crewed! They were rescued by tugboats, and the boat is now stationed between Nahant and Winthrop.
This was the perfect opportunity to discuss with students where Boston Harbor was, how tides are created, how to read maps, and maritime geography.
As for those King Tides:
It’s that time of the year again. Sure, the holiday season has returned, but so have — this week, at least — the king tides. The astronomically caused ultra-high tides peaked in Boston just before noon Tuesday, according to the National Oceanic and Atmospheric Administration. Reaching more than two feet higher than average daily high tides, the seasonal occurrence produced minor flooding in low-lying areas along the East Coast.
Let’s see how the motion of the moon creates tides:
News from the Boston National Historical Park Twitter page.
News story from WCVB
A container ship broke free from a terminal in Boston, the Coast Guard confirmed early Wednesday morning. The 1,065-foot ship “Helsinki Bridge” was at the Paul W. Conley Container Terminal when the 12 lines securing the vessel broke.
“They notified us very quickly. The ship’s crew was very quick in getting their engine equipment up and running so that they could drop their anchor and not be drifting around,” Coast Guard Lt. Jennifer Sheehy said.
Terminal workers who were on the ship were able to get off, and no injuries were reported. Two tug boats and a pilot helped to escort the runaway ship out to Broad Sound, between Winthrop and Nahant. State police said the ship hit a dock and did some minor damage when it broke free.
“They’ll take a look at all of the equipment. They’ll talk to the ship’s crew, and a team is at Conley Terminal looking at any damage that might be there,” Sheehy said.
Officials said weather may have played a role in the ship breaking free. “Winds that we had last night, the strength of those winds and a ship this size has a lot of sail area to push against, so it’s not unheard of for a ship this size to part ways because of the wind strength,” Sheehy said. The ship will eventually be towed back to the terminal.
Ocean Literacy Scope and Sequence for Grades K-12
Ocean Literacy Principle #3, The ocean interaction of oceanic and atmospheric processes controls weather and climate by dominating the Earth’s energy, water and carbon systems.
Ocean Literacy Principle #6,
b. The ocean provides foods, medicines, and mineral and energy resources. It supports jobs and national economies, serves as a highway for transportation of goods and people, and plays a role in national security.
f. Much of the worlds population lives in coastal areas. Coastal regions are susceptible to natural hazards (tsunamis, hurricanes, cyclones, sea level change, and storm surges).
By Natalie Wolchover, Senior Writer, Quanta Magazine
October 23, 2017
In 1985, when Carl Sagan was writing the novel Contact, he needed to quickly transport his protagonist Dr. Ellie Arroway from Earth to the star Vega. He had her enter a black hole and exit light-years away, but he didn’t know if this made any sense. The Cornell University astrophysicist and television star consulted his friend Kip Thorne, a black hole expert at the California Institute of Technology (who won a Nobel Prize earlier this month). Thorne knew that Arroway couldn’t get to Vega via a black hole, which is thought to trap and destroy anything that falls in. But it occurred to him that she might make use of another kind of hole consistent with Albert Einstein’s general theory of relativity: a tunnel or “wormhole” connecting distant locations in space-time.
While the simplest theoretical wormholes immediately collapse and disappear before anything can get through, Thorne wondered whether it might be possible for an “infinitely advanced” sci-fi civilization to stabilize a wormhole long enough for something or someone to traverse it.
He figured out that such a civilization could in fact line the throat of a wormhole with “exotic material” that counteracts its tendency to collapse. The material would possess negative energy, which would deflect radiation and repulse space-time apart from itself. Sagan used the trick in Contact, attributing the invention of the exotic material to an earlier, lost civilization to avoid getting into particulars. Meanwhile, those particulars enthralled Thorne, his students and many other physicists, who spent years exploring traversable wormholes and their theoretical implications. They discovered that these wormholes can serve as time machines, invoking time-travel paradoxes — evidence that exotic material is forbidden in nature.
Now, decades later, a new species of traversable wormhole has emerged, free of exotic material and full of potential for helping physicists resolve a baffling paradox about black holes. This paradox is the very problem that plagued the early draft of Contact and led Thorne to contemplate traversable wormholes in the first place; namely, that things that fall into black holes seem to vanish without a trace. This total erasure of information breaks the rules of quantum mechanics, and it so puzzles experts that in recent years, some have argued that black hole interiors don’t really exist — that space and time strangely end at their horizons.
The flurry of findings started last year with a paper that reported the first traversable wormhole that doesn’t require the insertion of exotic material to stay open. Instead, according to Ping Gao and Daniel Jafferis of Harvard University and Aron Wall of Stanford University, the repulsive negative energy in the wormhole’s throat can be generated from the outside by a special quantum connection between the pair of black holes that form the wormhole’s two mouths. When the black holes are connected in the right way, something tossed into one will shimmy along the wormhole and, following certain events in the outside universe, exit the second.
Remarkably, Gao, Jafferis and Wall noticed that their scenario is mathematically equivalent to a process called quantum teleportation, which is key to quantum cryptography and can be demonstrated in laboratory experiments.
John Preskill, a black hole and quantum gravity expert at Caltech, says the new traversable wormhole comes as a surprise, with implications for the black hole information paradox and black hole interiors. “What I really like,” he said, “is that an observer can enter the black hole and then escape to tell about what she saw.” This suggests that black hole interiors really exist, he explained, and that what goes in must come out.
The new wormhole work began in 2013, when Jafferis attended an intriguing talk at the Strings conference in South Korea. The speaker, Juan Maldacena, a professor of physics at the Institute for Advanced Study in Princeton, New Jersey, had recently concluded, based on various hints and arguments, that “ER = EPR.” That is, wormholes between distant points in space-time, the simplest of which are called Einstein-Rosen or “ER” bridges, are equivalent (albeit in some ill-defined way) to entangled quantum particles, also known as Einstein-Podolsky-Rosen or “EPR” pairs. The ER = EPR conjecture, posed by Maldacena and Leonard Susskind of Stanford, was an attempt to solve the modern incarnation of the infamous black hole information paradox by tying space-time geometry, governed by general relativity, to the instantaneous quantum connections between far-apart particles that Einstein called “spooky action at a distance.”
The paradox has loomed since 1974, when the British physicist Stephen Hawking determined that black holes evaporate — slowly giving off heat in the form of particles now known as “Hawking radiation.” Hawking calculated that this heat is completely random; it contains no information about the black hole’s contents. As the black hole blinks out of existence, so does the universe’s record of everything that went inside. This violates a principle called “unitarity,” the backbone of quantum theory, which holds that as particles interact, information about them is never lost, only scrambled, so that if you reversed the arrow of time in the universe’s quantum evolution, you’d see things unscramble into an exact re-creation of the past.
Almost everyone believes in unitarity, which means information must escape black holes — but how? In the last five years, some theorists, most notably Joseph Polchinski of the University of California, Santa Barbara, have argued that black holes are empty shells with no interiors at all — that Ellie Arroway, upon hitting a black hole’s event horizon, would fizzle on a “firewall” and radiate out again.
Many theorists believe in black hole interiors (and gentler transitions across their horizons), but in order to understand them, they must discover the fate of information that falls inside. This is critical to building a working quantum theory of gravity, the long-sought union of the quantum and space-time descriptions of nature that comes into sharpest relief in black hole interiors, where extreme gravity acts on a quantum scale.
The quantum gravity connection is what drew Maldacena, and later Jafferis, to the ER = EPR idea, and to wormholes. The implied relationship between tunnels in space-time and quantum entanglement posed by ER = EPR resonated with a popular recent belief that space is essentially stitched into existence by quantum entanglement. It seemed that wormholes had a role to play in stitching together space-time and in letting black hole information worm its way out of black holes — but how might this work? When Jafferis heard Maldacena talk about his cryptic equation and the evidence for it, he was aware that a standard ER wormhole is unstable and non-traversable. But he wondered what Maldacena’s duality would mean for a traversable wormhole like the ones Thorne and others played around with decades ago. Three years after the South Korea talk, Jafferis and his collaborators Gao and Wall presented their answer. The work extends the ER = EPR idea by equating, not a standard wormhole and a pair of entangled particles, but a traversable wormhole and quantum teleportation: a protocol discovered in 1993 that allows a quantum system to disappear and reappear unscathed somewhere else.
When Maldacena read Gao, Jafferis and Wall’s paper, “I viewed it as a really nice idea, one of these ideas that after someone tells you, it’s obvious,” he said. Maldacena and two collaborators, Douglas Stanford and Zhenbin Yang, immediately began exploring the new wormhole’s ramifications for the black hole information paradox; their paper appeared in April. Susskind and Ying Zhao of Stanford followed this with a paper about wormhole teleportation in July. The wormhole “gives an interesting geometric picture for how teleportation happens,” Maldacena said. “The message actually goes through the wormhole.”
In their paper, “Diving Into Traversable Wormholes,” published in Fortschritte der Physik, Maldacena, Stanford and Yang consider a wormhole of the new kind that connects two black holes: a parent black hole and a daughter one formed from half of the Hawking radiation given off by the parent as it evaporates. The two systems are as entangled as they can be. Here, the fate of the older black hole’s information is clear: It worms its way out of the daughter black hole.
During an interview this month in his tranquil office at the IAS, Maldacena, a reserved Argentinian-American with a track record of influential insights, described his radical musings. On the right side of a chalk-dusty blackboard, Maldacena drew a faint picture of two black holes connected by the new traversable wormhole.
On the left, he sketched a quantum teleportation experiment, performed by the famous fictional experimenters Alice and Bob, who are in possession of entangled quantum particles a and b, respectively.
Say Alice wants to teleport a qubit q to Bob. She prepares a combined state of q and a, measures that combined state (reducing it to a pair of classical bits, 1 or 0), and sends the result of this measurement to Bob. He can then use this as a key for operating on b in a way that re-creates the state q. Voila, a unit of quantum information has teleported from one place to the other.
Maldacena turned to the right side of the blackboard. “You can do operations with a pair of black holes that are morally equivalent to what I discussed [about quantum teleportation]. And in that picture, this message really goes through the wormhole.”
Say Alice throws qubit q into black hole A. She then measures a particle of its Hawking radiation, a, and transmits the result of the measurement through the external universe to Bob, who can use this knowledge to operate on b, a Hawking particle coming out of black hole B. Bob’s operation reconstructs q, which appears to pop out of B, a perfect match for the particle that fell into A. This is why some physicists are excited: Gao, Jafferis and Wall’s wormhole allows information to be recovered from black holes. In their paper, they set up their wormhole in a negatively curved space-time geometry that often serves as a useful, if unrealistic, playground for quantum gravity theorists. However, their wormhole idea seems to extend to the real world as long as two black holes are coupled in the right way: “They have to be causally connected and then the nature of the interaction that we took is the simplest thing you can imagine,” Jafferis explained. If you allow the Hawking radiation from one of the black holes to fall into the other, the two black holes become entangled, and the quantum information that falls into one can exit the other.
The quantum-teleportation format precludes using these traversable wormholes as time machines. Anything that goes through the wormhole has to wait for Alice’s message to travel to Bob in the outside universe before it can exit Bob’s black hole, so the wormhole doesn’t offer any superluminal boost that could be exploited for time travel. It seems traversable wormholes might be permitted in nature as long as they offer no speed advantage. “Traversable wormholes are like getting a bank loan,” Gao, Jafferis and Wall wrote in their paper: “You can only get one if you are rich enough not to need it.”
A Naive Octopus
While traversable wormholes won’t revolutionize space travel, according to Preskill the new wormhole discovery provides “a promising resolution” to the black hole firewall question by suggesting that there is no firewall at black hole horizons. Preskill said the discovery rescues “what we call ‘black hole complementarity,’ which means that the interior and exterior of the black hole are not really two different systems but rather two very different, complementary ways of looking at the same system.” If complementarity holds, as is widely assumed, then in passing across a black hole horizon from one realm to the other, Contact’s Ellie Arroway wouldn’t notice anything strange. This seems more likely if, under certain conditions, she could even slide all the way through a Gao-Jafferis-Wall wormhole.
The wormhole also safeguards unitarity — the principle that information is never lost — at least for the entangled black holes being studied. Whatever falls into one black hole eventually exits the other as Hawking radiation, Preskill said, which “can be thought of as in some sense a very scrambled copy of the black hole interior.”
Taking the findings to their logical conclusion, Preskill thinks it ought to be possible (at least for an infinitely advanced civilization) to influence the interior of one of these black holes by manipulating its radiation. This “sounds crazy,” he wrote in an email, but it “might make sense if we can think of the radiation, which is entangled with the black hole — EPR — as being connected to the black hole interior by wormholes — ER. Then tickling the radiation can send a message which can be read from inside the black hole!” He added, “We still have a ways to go, though, before we can flesh out this picture in more detail.”
Indeed, obstacles remain in the quest to generalize the new wormhole findings to a statement about the fate of all quantum information, or the meaning of ER = EPR.
In Maldacena and Susskind’s paper proposing ER = EPR, they included a sketch that’s become known as the “octopus”: a black hole with tentacle-like wormholes leading to distant Hawking particles that have evaporated out of it.
The authors explained that the sketch illustrates “the entanglement pattern between the black hole and the Hawking radiation. We expect that this entanglement leads to the interior geometry of the black hole.”
But according to Matt Visser, a mathematician and general-relativity expert at Victoria University of Wellington in New Zealand who has studied wormholes since the 1990s, the most literal reading of the octopus picture doesn’t work. The throats of wormholes formed from single Hawking particles would be so thin that qubits could never fit through. “A traversable wormhole throat is ‘transparent’ only to wave packets with size smaller than the throat radius,” Visser explained. “Big wave packets will simply bounce off any small wormhole throat without crossing to the other side.”
Stanford, who co-wrote the recent paper with Maldacena and Yang, acknowledged that this is a problem with the simplest interpretation of the ER = EPR idea, in which each particle of Hawking radiation has its own tentacle-like wormhole.
However, a more speculative interpretation of ER = EPR that he and others have in mind does not suffer from this failing. “The idea is that in order to recover the information from the Hawking radiation using this traversable wormhole,” Stanford said, one has to “gather the Hawking radiation together and act on it in a complicated way.”
This complicated collective measurement reveals information about the particles that fell in; it has the effect, he said, of “creating a large, traversable wormhole out of the small and unhelpful octopus tentacles. The information would then propagate through this large wormhole.” Maldacena added that, simply put, the theory of quantum gravity might have a new, generalized notion of geometry for which ER equals EPR. “We think quantum gravity should obey this principle,” he said. “We view it more as a guide to the theory.”
In his 1994 popular science book, Black Holes and Time Warps, Kip Thorne celebrated the style of reasoning involved in wormhole research. “No type of thought experiment pushes the laws of physics harder than the type triggered by Carl Sagan’s phone call to me,” he wrote; “thought experiments that ask, ‘What things do the laws of physics permit an infinitely advanced civilization to do, and what things do the laws forbid?’”
Learning standards for astronomy, and related parts of Earth Science.
6.MS-ESS1-1a. Develop and use a model of the Earth-Sun-Moon system to explain the causes of lunar phases and eclipses of the Sun and Moon.
6.MS-ESS1-5(MA). Use graphical displays to illustrate that Earth and its solar system are one of many in the Milky Way galaxy, which is one of billions of galaxies in the universe.
8.MS-ESS1-1b. Develop and use a model of the Earth-Sun system to explain the cyclical pattern of seasons, which includes Earth’s tilt and differential intensity of sunlight on
different areas of Earth across the year
8.MS-ESS1-2. Explain the role of gravity in ocean tides, the orbital motions of planets, their moons, and asteroids in the solar system
HS-ESS1-1. Use informational text to explain that the life span of the Sun over approximately 10 billion years is a function of nuclear fusion in its core. Communicate that stars, through nuclear fusion over their life cycle, produce elements from helium to iron and release energy that eventually reaches Earth in the form of radiation.
HS-ESS1-2. Describe the astronomical evidence for the Big Bang theory, including the red shift of light from the motion of distant galaxies as an indication that the universe is currently expanding, the cosmic microwave background as the remnant radiation from the Big Bang, and the observed composition of ordinary matter of the universe, primarily found in stars and interstellar gases, which matches that predicted by the Big Bang theory (3/4 hydrogen and 1/4 helium).
HS-ESS1-4. Use Kepler’s laws to predict the motion of orbiting objects in the solar system.
Describe how orbits may change due to the gravitational effects from, or collisions
with, other objects in the solar system. Kepler’s laws apply to human-made satellites as well as planets, moons, and other objects.
Stars’ radiation of visible light and other forms of energy can be measured and studied to develop explanations about the formation, age, and composition of the universe. Stars go through a sequence of developmental stages—they are formed; evolve in size, mass, and brightness; and eventually burn out. Material from earlier stars that exploded as supernovas is recycled to form younger stars and their planetary systems. The sun is a medium-sized star about halfway through its predicted life span of about 10 billion years.
Grade Band Endpoints for ESS1.A
By the end of grade 2. Patterns of the motion of the sun, moon, and stars in the sky can be observed, described, and predicted. At night one can see the light coming from many stars with the naked eye, but telescopes make it possible to see many more and to observe them and the moon and planets in greater detail.
By the end of grade 5. The sun is a star that appears larger and brighter than other stars because it is closer. Stars range greatly in their size and distance from Earth.
By the end of grade 8. Patterns of the apparent motion of the sun, the moon, and stars in the sky can be observed, described, predicted, and explained with models. The universe began with a period of extreme and rapid expansion known as the Big Bang. Earth and its solar system are part of the Milky Way galaxy, which is one of many galaxies in the universe.
By the end of grade 12. The star called the sun is changing and will burn out over a life span of approximately 10 billion years. The sun is just one of more than 200 billion stars in the Milky Way galaxy, and the Milky Way is just one of hundreds of billions of galaxies in the universe. The study of stars’ light spectra and brightness is used to identify compositional elements of stars, their movements, and their distances from Earth.
Grade Band Endpoints for ESS1.B
By the end of grade 2. Seasonal patterns of sunrise and sunset can be observed, described, and predicted.
By the end of grade 5. The orbits of Earth around the sun and of the moon around Earth, together with the rotation of Earth about an axis between its North and South poles, cause observable patterns. These include day and night; daily and seasonal changes in the length and direction of shadows; phases of the moon; and different positions of the sun, moon, and stars at different times of the day, month, and year.
Some objects in the solar system can be seen with the naked eye. Planets in the night sky change positions and are not always visible from Earth as they orbit the sun. Stars appear in patterns called constellations, which can be used for navigation and appear to move together across the sky because of Earth’s rotation.
By the end of grade 8. The solar system consists of the sun and a collection of objects, including planets, their moons, and asteroids that are held in orbit around the sun by its gravitational pull on them. This model of the solar system can explain tides, eclipses of the sun and the moon, and the motion of the planets in the sky relative to the stars. Earth’s spin axis is fixed in direction over the short term but tilted relative to its orbit around the sun. The seasons are a result of that tilt and are caused by the differential intensity of sunlight on different areas of Earth across the year.
By the end of grade 12. Kepler’s laws describe common features of the motions of orbiting objects, including their elliptical paths around the sun. Orbits may change due to the gravitational effects from, or collisions with, other objects in the solar system. Cyclical changes in the shape of Earth’s orbit around the sun, together with changes in the orientation of the planet’s axis of rotation, both occurring over tens to hundreds of thousands of years, have altered the intensity and distribution of sunlight falling on Earth. These phenomena cause cycles of ice ages and other gradual climate changes.
Earth exchanges mass and energy with the rest of the solar system. It gains or loses energy through incoming solar radiation, thermal radiation to space, and gravitational forces exerted by the sun, moon, and planets. Earth gains mass from the impacts of meteoroids and comets and loses mass from the escape of gases into space. (p.180)
By the end of the 8th grade, students should know that
Because every object is moving relative to some other object, no object has a unique claim to be at rest. Therefore, the idea of absolute motion or rest is misleading. 10A/M1*
Telescopes reveal that there are many more stars in the night sky than are evident to the unaided eye, the surface of the moon has many craters and mountains, the sun has dark spots, and Jupiter and some other planets have their own moons. 10A/M2
By the end of the 12th grade, students should know that
To someone standing on the earth, it seems as if it is large and stationary and that all other objects in the sky orbit around it. That perception was the basis for theories of how the universe is organized that prevailed for over 2,000 years. 10A/H1*
Ptolemy, an Egyptian astronomer living in the second century A.D., devised a powerful mathematical model of the universe based on continuous motion in perfect circles, and in circles on circles. With the model, he was able to predict the motions of the sun, moon, and stars, and even of the irregular “wandering stars” now called planets. 10A/H2*
In the 1500s, a Polish astronomer named Copernicus suggested that all those same motions could be explained by imagining that the earth was turning around once a day and orbiting around the sun once a year. This explanation was rejected by nearly everyone because it violated common sense and required the universe to be unbelievably large. Worse, it flew in the face of the belief, universally held at the time, that the earth was at the center of the universe. 10A/H3*
Johannes Kepler, a German astronomer, worked with Tycho Brahe for a short time. After Brahe’s death, Kepler used his data to show mathematically that Copernicus’ idea of a sun-centered system worked well if uniform circular motion was replaced with uneven (but predictable) motion along off-center ellipses. 10A/H4*
Using the newly invented telescope to study the sky, Galileo made many discoveries that supported the ideas of Copernicus. It was Galileo who found the moons of Jupiter, sunspots, craters and mountains on the moon, and many more stars than were visible to the unaided eye. 10A/H5
Writing in Italian rather than in Latin (the language of scholars at the time), Galileo presented arguments for and against the two main views of the universe in a way that favored the newer view. His descriptions of how things move provided an explanation for why people might notice the motion of the earth. Galileo’s writings made educated people of the time aware of these competing views and created political, religious, and scientific controversy. 10A/H6*
Tycho Brahe, a Danish astronomer, proposed a model of the universe that was popular for a while because it was somewhat of a compromise of Ptolemy’s and Copernicus’ models. Brahe made very precise measurements of the positions of the planets and stars in an attempt to validate his model. 10A/H7**
The work of Copernicus, Galileo, Brahe, and Kepler eventually changed people’s perception of their place in the universe. 10A/H8** (SFAA)
By the end of the 12th grade, students should know that
Isaac Newton, building on earlier descriptions of motion by Galileo, Kepler, and others, created a unified view of force and motion in which motion everywhere in the universe can be explained by the same few rules. Newton’s system was based on the concepts of mass, force, and acceleration; his three laws of motion relating them; and a physical law stating that the force of gravity between any two objects in the universe depends only upon their masses and the distance between them. 10B/H1*
Newton’s mathematical analysis of gravitational force and motion showed that planetary orbits had to be the very ellipses that Kepler had proposed two generations earlier. 10B/H2*
The Newtonian system made it possible to account for such diverse phenomena as tides, the orbits of planets and moons, the motion of falling objects, and the earth’s equatorial bulge. 10B/H3*
For several centuries, Newton’s science was accepted without major changes because it explained so many different phenomena, could be used to predict many physical events (such as the appearance of Halley’s comet), was mathematically sound, and had many practical applications. 10B/H4
Although overtaken in the 1900s by Einstein’s relativity theory, Newton’s ideas persist and are widely used. Moreover, his influence has extended far beyond physics and astronomy, serving as a model for other sciences and even raising philosophical questions about free will and the organization of social systems. 10B/H5*
By the end of the 12th grade, students should know that
Prior to the 1700s, many considered the earth to be just a few thousand years old. By the 1800s, scientists were starting to realize that the earth was much older even though they could not determine its exact age. 10D/H1*
In the early 1800s, Charles Lyell argued in Principles of Geology that the earth was vastly older than most people believed. He supported his claim with a wealth of observations of the patterns of rock layers in mountains and the locations of various kinds of fossils. 10D/H2*
In formulating and presenting his theory of biological evolution, British naturalist Charles Darwin adopted Lyell’s claims about the age of the earth and his assumption that the processes that occurred in the past are the same as the processes that occur today. 10D/H3*
By the end of the 5th grade, students should know that
The patterns of stars in the sky stay the same, although they appear to move across the sky nightly, and different stars can be seen in different seasons. 4A/E1
Telescopes magnify the appearance of some distant objects in the sky, including the moon and the planets. The number of stars that can be seen through telescopes is dramatically greater than can be seen by the unaided eye. 4A/E2
Planets change their positions against the background of stars. 4A/E3
The earth is one of several planets that orbit the sun, and the moon orbits around the earth. 4A/E4
Stars are like the sun, some being smaller and some larger, but so far away that they look like points of light. 4A/E5
A large light source at a great distance looks like a small light source that is much closer. 4A/E6** (BSL)
By the end of the 8th grade, students should know that
The sun is a medium-sized star located near the edge of a disc-shaped galaxy of stars, part of which can be seen as a glowing band of light that spans the sky on a very clear night. 4A/M1a
The universe contains many billions of galaxies, and each galaxy contains many billions of stars. To the naked eye, even the closest of these galaxies is no more than a dim, fuzzy spot. 4A/M1bc
The sun is many thousands of times closer to the earth than any other star. Light from the sun takes a few minutes to reach the earth, but light from the next nearest star takes a few years to arrive. The trip to that star would take the fastest rocket thousands of years. 4A/M2abc
Some distant galaxies are so far away that their light takes several billion years to reach the earth. People on earth, therefore, see them as they were that long ago in the past. 4A/M2de
Nine planets of very different size, composition, and surface features move around the sun in nearly circular orbits. Some planets have a variety of moons and even flat rings of rock and ice particles orbiting around them. Some of these planets and moons show evidence of geologic activity. The earth is orbited by one moon, many artificial satellites, and debris. 4A/M3
Many chunks of rock orbit the sun. Those that meet the earth glow and disintegrate from friction as they plunge through the atmosphere—and sometimes impact the ground. Other chunks of rock mixed with ice have long, off-center orbits that carry them close to the sun, where the sun’s radiation (of light and particles) boils off frozen materials from their surfaces and pushes it into a long, illuminated tail. 4A/M4*
By the end of the 12th grade, students should know that
The stars differ from each other in size, temperature, and age, but they appear to be made up of the same elements found on earth and behave according to the same physical principles. 4A/H1a
Unlike the sun, most stars are in systems of two or more stars orbiting around one another. 4A/H1b
On the basis of scientific evidence, the universe is estimated to be over ten billion years old. The current theory is that its entire contents expanded explosively from a hot, dense, chaotic mass. 4A/H2ab
Stars condensed by gravity out of clouds of molecules of the lightest elements until nuclear fusion of the light elements into heavier ones began to occur. Fusion released great amounts of energy over millions of years. 4A/H2cd
Eventually, some stars exploded, producing clouds containing heavy elements from which other stars and planets orbiting them could later condense. The process of star formation and destruction continues. 4A/H2ef
Increasingly sophisticated technology is used to learn about the universe. Visual, radio, and X-ray telescopes collect information from across the entire spectrum of electromagnetic waves; computers handle data and complicated computations to interpret them; space probes send back data and materials from remote parts of the solar system; and accelerators give subatomic particles energies that simulate conditions in the stars and in the early history of the universe before stars formed. 4A/H3
Mathematical models and computer simulations are used in studying evidence from many sources in order to form a scientific account of the universe. 4A/H4
As the earth and other planets formed, the heavier elements fell to their centers. On planets close to the sun (Mercury, Venus, Earth, and Mars), the lightest elements were mostly blown or boiled away by radiation from the newly formed sun; on the outer planets (Jupiter, Saturn, Uranus, Neptune, and Pluto) the lighter elements still surround them as deep atmospheres of gas or as frozen solid layers. 4A/H5** (SFAA)
Our solar system coalesced out of a giant cloud of gas and debris left in the wake of exploding stars about five billion years ago. Everything in and on the earth, including living organisms, is made of this material. 4A/H6** (SFAA)
There are a number of models describing how Earth’s moon originated.
These models are together called the giant-impact hypothesis. It proposes that a Mars-sized body, called Theia, impacted Earth, creating a large debris ring around Earth, which then accreted to form the Moon. This collision also resulted in the 23.5° tilted axis of the earth, thus causing the seasons. (adapted loosely from Wikipedia)
What Made the Moon? New Ideas Try to Rescue a Troubled Theory
Quanta Magazine, Rebecca Boyle, 8/2/17
In the past five years, a bombardment of studies has exposed a problem: The canonical giant impact hypothesis rests on assumptions that do not match the evidence. If Theia hit Earth and later formed the moon, the moon should be made of Theia-type material. But the moon does not look like Theia — or like Mars, for that matter. Down to its atoms, it looks almost exactly like Earth.
Confronted with this discrepancy, lunar researchers have sought new ideas for understanding how the moon came to be. The most obvious solution may also be the simplest, though it creates other challenges with understanding the early solar system:
- Perhaps Theia did form the moon, but Theia was made of material that was almost identical to Earth.
- The second possibility is that the impact process thoroughly mixed everything, homogenizing disparate clumps and liquids the way pancake batter comes together. This could have taken place in an extraordinarily high-energy impact, or a series of impacts that produced a series of moons that later combined.
- The third explanation challenges what we know about planets. It’s possible that the Earth and moon we have today underwent strange metamorphoses and wild orbital dances that dramatically changed their rotations and their futures.
Bad News for Theia
To understand what may have happened on Earth’s most momentous day, it helps to understand the solar system’s youth. Four and a half billion years ago, the sun was surrounded by a hot, doughnut-shaped cloud of debris. Star-forged elements swirled around our newborn sun, cooling and, after eons, combining — in a process we don’t fully understand — into clumps, then planetesimals, then increasingly larger planets. These rocky bodies violently, frequently collided and vaporized one another anew. It was in this unspeakably brutal, billiard-ball hellscape that the Earth and the moon were forged.
To get to the moon we have now, with its size, spin and the rate at which it is receding from Earth, our best computer models say that whatever collided with Earth must have been the size of Mars. Anything bigger or much smaller would produce a system with a much greater angular momentum than we see. A bigger projectile would also throw too much iron into Earth’s orbit, creating a more iron-rich moon than the one we have today.
Early geochemical studies of troctolite 76536 and other rocks bolstered this story. They showed that lunar rocks would have originated in a lunar magma ocean, the likes of which could only be generated by a giant impact. The troctolite would have bobbed in a molten sea like an iceberg floating off Antarctica. On the basis of these physical constraints, scientists have argued that the moon was made from the remnants of Theia. But there is a problem.
Back to the early solar system. As rocky worlds collided and vaporized, their contents mixed, eventually settling into distinct regions. Closer to the sun, where it was hotter, lighter elements would be likelier to heat up and escape, leaving an excess of heavy isotopes (variants of elements with additional neutrons). Farther from the sun, rocks were able to keep more of their water, and lighter isotopes persisted. Because of this, a scientist can examine an object’s isotopic mix to identify where in the solar system it came from, like accented speech giving away a person’s homeland.
These differences are so pronounced that they’re used to classify planets and meteorite types. Mars is so chemically distinct from Earth, for instance, that its meteorites can be identified simply by measuring ratios of three different oxygen isotopes.
In 2001, using advanced mass spectrometry techniques, Swiss researchers remeasured troctolite 76536 and 30 other lunar samples. They found that its oxygen isotopes were indistinguishable from those on Earth. Geochemists have since studied titanium, tungsten, chromium, rubidium, potassium and other obscure metals from Earth and the moon, and everything looks pretty much the same.
This is bad news for Theia. If Mars is so obviously different from Earth, Theia — and thus, the moon — ought to be different, too. If they’re the same, that means the moon must have formed from melted bits of Earth. The Apollo rocks are then in direct conflict with what the physics insist must be true.
“The canonical model is in serious crisis,” said Sarah Stewart, a planetary scientist at the University of California, Davis. “It has not been killed yet, but its current status is that it doesn’t work.”
Stewart has been trying to reconcile the physical constraints of the problem — the need for an impactor of a certain size, going a certain speed — with the new geochemical evidence. In 2012, she and Matija Ćuk, now at the SETI Institute, proposed a new physical model for the moon’s formation. They argued that the early Earth was a whirling dervish, rotating through one day every two to three hours, when Theia collided with it. The collision would produce a disk around the Earth, much like the rings of Saturn — but it would only persist for about 24 hours. Ultimately, this disk would cool and solidify to form the moon.
Supercomputers are not powerful enough to model this process completely, but they showed that a projectile slamming into such a fast-spinning world could shear away enough of Earth, obliterate enough of Theia and scramble enough of both to build a moon and Earth with similar isotopic ratios. Think of smacking a wet lump of clay on a fast-spinning potter’s wheel.
For the fast-spinning-Earth explanation to be right, however, something else would have to come along to slow down Earth’s rotation rate to what it is now. In their 2012 work, Stewart and Ćuk argued that under certain orbital-resonance interactions, Earth could have transferred angular momentum to the sun. Later, Jack Wisdom of the Massachusetts Institute of Technology suggested several alternate scenarios for draining angular momentum away from the Earth-moon system.
But none of the explanations was entirely satisfactory. The 2012 models still couldn’t explain the moon’s orbit or the moon’s chemistry, Stewart said. Then last year, Simon Lock, a graduate student at Harvard University and Stewart’s student at the time, came up with an updated model that proposes a previously unrecognized planetary structure.
In this story, every bit of Earth and Theia vaporized and formed a bloated, swollen cloud shaped like a thick bagel. The cloud spun so quickly that it reached a point called the co-rotation limit. At that outer edge of the cloud, vaporized rock circled so fast that the cloud took on a new structure, with a fat disk circling an inner region. Crucially, the disk was not separated from the central region the way Saturn’s rings are — nor the way previous models of giant-impact moon formation were, either.
Conditions in this structure are indescribably hellish; there is no surface, but instead clouds of molten rock, with every region of the cloud forming molten-rock raindrops. The moon grew inside this vapor, Lock said, before the vapor eventually cooled and left in its wake the Earth-moon system.
Given the structure’s unusual characteristics, Lock and Stewart thought it deserved a new name. They tried several versions before coining synestia, which uses the Greek prefix syn-, meaning together, and the goddess Hestia, who represents the home, hearth and architecture. The word means “connected structure,” Stewart said.
“These bodies aren’t what you think they are. They don’t look like what you thought they did,” she said.
In May, Lock and Stewart published a paper on the physics of synestias; their paper arguing for a synestia lunar origin is still in review. They presented the work at planetary science conferences in the winter and spring and say their fellow researchers were intrigued but hardly sold on the idea. That may be because synestias are still just an idea; unlike ringed planets, which are common in our solar system, and protoplanetary disks, which are common across the universe, no one has ever seen one.
“But this is certainly an interesting pathway that could explain the features of our moon and get us over this hump that we’re in, where we have this model that doesn’t seem to work,” Lock said.
Let a Dozen Moons Bloom
Among natural satellites in the solar system, Earth’s moon may be most striking for its solitude. Mercury and Venus lack natural satellites, in part because of their nearness to the sun, whose gravitational interactions would make their moons’ orbits unstable. Mars has tiny Phobos and Deimos, which some argue are captured asteroids and others argue formed from Martian impacts. And the gas giants are chockablock with moons, some rocky, some watery, some both.
In contrast to these moons, Earth’s satellite also stands out for its size and the physical burden it carries. The moon is about 1 percent the mass of Earth, while the combined mass of the outer planets’ satellites is less than one-tenth of 1 percent of their parents. Even more important, the moon contains 80 percent of the angular momentum of the Earth-moon system. That is to say, the moon is responsible for 80 percent of the motion of the system as a whole. For the outer planets, this value is less than 1 percent.
The moon may not have carried all this weight the whole time, however. The face of the moon bears witness to its lifelong bombardment; why should we assume that just one rock was responsible for carving it out of Earth? It’s possible that multiple impacts made the moon, said Raluca Rufu, a planetary scientist at the Weizmann Institute of Science in Rehovot, Israel.
In a paper published last winter, she argued that Earth’s moon is not the original moon. It is instead a compendium of creation by a thousand cuts — or at the very least, a dozen, according to her simulations. Projectiles coming in from multiple angles and at multiple speeds would hit Earth and form disks, which coalesce into “moonlets,” essentially crumbs that are smaller than Earth’s current moon. Interactions between moonlets of different ages cause them to merge, eventually forming the moon we know today.
Planetary scientists were receptive when her paper was published last year; Robin Canup, a lunar scientist at the Southwest Research Institute and a dean of moon-formation theories, said it was worth considering. More testing remains, however. Rufu is not sure whether the moonlets would have been locked in their orbital positions, similar to how Earth’s moon constantly faces the same direction; if so, she is not sure how they could have merged. “That’s what we are trying to figure out next,” Rufu said.
Meanwhile, others have turned to another explanation for the similarity of Earth and the moon, one that might have a very simple answer. From synestias to moonlets, new physical models — and new physics — may be moot. It’s possible that the moon looks just like Earth because Theia did, too.
All the Same Stuff
The moon is not the only Earth-like thing in the solar system. Rocks like troctolite 76536 share an oxygen isotope ratio with Earth rocks as well as a group of asteroids called enstatite chondrites. These asteroids’ oxygen isotope composition is very similar to Earth’s, said Myriam Telus, a cosmochemist who studies meteorites at the Carnegie Institution in Washington, D.C. “One of the arguments is that they formed in hotter regions of the disk, which would be closer to the sun,” she said. They probably formed near where Earth did.
Some of these rocks came together to form Earth; others would have combined to form Theia. The enstatite chondrites are the detritus, remnant rocks that never combined and grew large enough to form mantles, cores and fully fledged planets.
In January, Nicolas Dauphas, a geophysicist at the University of Chicago, argued that a majority of the rocks that became Earth were enstatite-type meteorites. He argued that anything formed in the same region would be made from them, too. Planet-building was taking place using the same premixed materials that we now find in both the moon and Earth; they look the same because they are the same. “The giant impactor that formed the moon probably had an isotopic composition similar to that of the Earth,” Dauphas wrote.
David Stevenson, a planetary scientist at the California Institute of Technology who has studied lunar origins since the Theia hypothesis was first presented in 1974, said he considers this paper the most important contribution to the debate in the past year, saying it addresses an issue geochemists have grappled with for decades.
“He has put together a story which is quantitative; it’s a clever story, about how to look at the various elements that go into the Earth,” Stevenson said. “From that, he can back out a story of the particular sequence of Earth’s formation, and in that sequence, the enstatite chondrites play an important role.”
Not everyone is convinced, however. There are still questions about the isotopic ratio of elements like tungsten, Stewart points out. Tungsten-182 is a daughter of hafnium-182, so the ratio of tungsten to hafnium acts as a clock, setting the age of a particular rock. If one rock has more tungsten-182 than another, you can safely say the tungsten-filled rock formed earlier. But the most precise measurements available show that Earth’s and moon’s tungsten-halfnium ratios are the same. “It would take special coincidences for the two bodies to end up with matching compositions,” Dauphas concedes.
Clues on Other Worlds
Understanding the moon — our constant companion, our silvery sister, target of dreamers and explorers since time immemorial — is a worthy cause on its own. But its origin story, and the story of rocks like troctolite 76536, may be just one chapter in a much bigger epic.
“I see it as a window into a more general question: What happened when terrestrial planets formed?” Stevenson said. “Everybody is coming up short at present.”
Understanding synestias might help answer that; Lock and Stewart argue that synestias would have formed apace in the early solar system as protoplanets whacked into each other and melted. Many rocky bodies might have started out as puffy vapor halos, so figuring out how synestias evolve could help scientists figure out how the moon and other terrestrial worlds evolved.
More samples from the moon and Earth would help, too, especially from each mantle, because geochemists would have more data to sift through. They would be able to tell whether oxygen stored deep within Earth is the same throughout, or if three common oxygen isotopes preferentially hang out in different areas.
“When we say that Earth and the moon are very close to being identical in the three oxygen isotopes, we are making an assumption that we actually know what the Earth is, and we actually know what the moon is,” Stevenson points out.
New tweaks to solar system origin theories, which are often based on complex computer simulations, are also illuminating where planets were born and where they migrated. Scientists increasingly suggest we can’t count on Mars to tell this story, because it may have formed in a different area of the solar system than Earth, the enstatites and Theia. Stevenson said Mars should no longer be used as a barometer for rocky planets.
Ultimately, lunar scientists agree that the best answers may be found on Venus, the planet most like Earth. It may have had a moon in its youth, and lost it; it may be very similar to Earth, or not. “If we can get a lump of rock from Venus, we can answer this question [of the moon’s origins] very simply. But sadly, that is not on anyone’s priority list right now,” Lock said.
Absent samples from Venus, and without laboratories that can test the unfathomable pressures and temperatures at the heart of giant impacts, lunar scientists will have to keep devising new models — and revising the moon’s origin story.
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– This graphic illustrates how Cassini scientists think water interacts with rock at the bottom of the ocean of Saturn’s icy moon Enceladus, producing hydrogen gas. Credit: NASA/JPL-Caltech
Two veteran NASA missions are providing new details about icy, ocean-bearing moons of Jupiter and Saturn, further heightening the scientific interest of these and other “ocean worlds” in our solar system and beyond. The findings are presented in papers published Thursday by researchers with NASA’s Cassini mission to Saturn and Hubble Space Telescope.
In the papers, Cassini scientists announce that a form of chemical energy that life can feed on appears to exist on Saturn’s moon Enceladus, and Hubble researchers report additional evidence of plumes erupting from Jupiter’s moon Europa.
“This is the closest we’ve come, so far, to identifying a place with some of the ingredients needed for a habitable environment,” said Thomas Zurbuchen, associate administrator for NASA’s Science Mission Directorate at Headquarters in Washington. ”These results demonstrate the interconnected nature of NASA’s science missions that are getting us closer to answering whether we are indeed alone or not.”
The paper from researchers with the Cassini mission, published in the journal Science, indicates hydrogen gas, which could potentially provide a chemical energy source for life, is pouring into the subsurface ocean of Enceladus from hydrothermal activity on the seafloor.
The presence of ample hydrogen in the moon’s ocean means that microbes – if any exist there – could use it to obtain energy by combining the hydrogen with carbon dioxide dissolved in the water. This chemical reaction, known as “methanogenesis” because it produces methane as a byproduct, is at the root of the tree of life on Earth, and could even have been critical to the origin of life on our planet.
Life as we know it requires three primary ingredients: liquid water; a source of energy for metabolism; and the right chemical ingredients, primarily carbon, hydrogen, nitrogen, oxygen, phosphorus and sulfur.
With this finding, Cassini has shown that Enceladus – a small, icy moon a billion miles farther from the sun than Earth – has nearly all of these ingredients for habitability. Cassini has not yet shown phosphorus and sulfur are present in the ocean, but scientists suspect them to be, since the rocky core of Enceladus is thought to be chemically similar to meteorites that contain the two elements.
“Confirmation that the chemical energy for life exists within the ocean of a small moon of Saturn is an important milestone in our search for habitable worlds beyond Earth,” said Linda Spilker, Cassini project scientist at NASA’s Jet Propulsion Laboratory in Pasadena, California.
The Cassini spacecraft detected the hydrogen in the plume of gas and icy material spraying from Enceladus during its last, and deepest, dive through the plume on Oct. 28, 2015. Cassini also sampled the plume’s composition during flybys earlier in the mission. From these observations scientists have determined that nearly 98 percent of the gas in the plume is water, about 1 percent is hydrogen and the rest is a mixture of other molecules including carbon dioxide, methane and ammonia.
The measurement was made using Cassini’s Ion and Neutral Mass Spectrometer (INMS) instrument, which sniffs gases to determine their composition. INMS was designed to sample the upper atmosphere of Saturn’s moon Titan. After Cassini’s surprising discovery of a towering plume of icy spray in 2005, emanating from hot cracks near the south pole, scientists turned its detectors toward the small moon.
Cassini wasn’t designed to detect signs of life in the Enceladus plume – indeed, scientists didn’t know the plume existed until after the spacecraft arrived at Saturn.
“Although we can’t detect life, we’ve found that there’s a food source there for it. It would be like a candy store for microbes,” said Hunter Waite, lead author of the Cassini study.
The new findings are an independent line of evidence that hydrothermal activity is taking place in the Enceladus ocean. Previous results, published in March 2015, suggested hot water is interacting with rock beneath the sea; the new findings support that conclusion and add that the rock appears to be reacting chemically to produce the hydrogen.
This is what we see on a night without clouds, if there was no light pollution:
Some camera filters can filter out some of the glare
Here are the various levels of polluted vs dark skies:
This video from Sunchaser Pictures shows what LA night skies could look like without light pollution.
“An experimental timelapse created for SKYGLOWPROJECT.COM, a crowdfunded quest to explore the effects and dangers of urban light pollution in contrast with some of the most incredible Dark Sky Preserves in North America. Visit the site for more!
Inspired by the “Darkened Cities” stills project by Thierry Cohen, this short film imagines the galaxy over the glowing metropolis of Los Angeles through composited timelapse and star trail astrophotography. Shot by Gavin Heffernan (SunchaserPictures.com) and Harun Mehmedinovic (Bloodhoney.com). SKYGLOW is endorsed by the International Dark Sky Association”
This lesson is from http://darksky.org/light-pollution/
Less than 100 years ago, everyone could look up and see a spectacular starry night sky. Now, millions of children across the globe will never experience the Milky Way where they live. The increased and widespread use of artificial light at night is not only impairing our view of the universe, it is adversely affecting our environment, our safety, our energy consumption and our health.
What is Light Pollution?
Most of us are familiar with air, water, and land pollution, but did you know that light can also be a pollutant?
The inappropriate or excessive use of artificial light – known as light pollution – can have serious environmental consequences for humans, wildlife, and our climate. Components of light pollution include:
- Glare – excessive brightness that causes visual discomfort
- Skyglow – brightening of the night sky over inhabited areas
- Light trespass – light falling where it is not intended or needed
- Clutter – bright, confusing and excessive groupings of light sources
Light pollution is a side effect of industrial civilization. Its sources include building exterior and interior lighting, advertising, commercial properties, offices, factories, streetlights, and illuminated sporting venues.
The fact is that much outdoor lighting used at night is inefficient, overly bright, poorly targeted, improperly shielded, and, in many cases, completely unnecessary. This light, and the electricity used to create it, is being wasted by spilling it into the sky, rather than focusing it on to the actual objects and areas that people want illuminated.
How Bad is Light Pollution?
With much of the Earth’s population living under light-polluted skies, over lighting is an international concern. If you live in an urban or suburban area all you have to do to see this type of pollution is go outside at night and look up at the sky.
According to the 2016 groundbreaking “World Atlas of Artificial Night Sky Brightness,” 80 percent of the world’s population lives under skyglow.
In the United States and Europe 99 percent of the public can’t experience a natural night!
If you want to find out how bad light pollution is where you live, use this interactive map created from the”World Atlas” data or the NASA Blue Marble Navigator for a bird’s eye view of the lights in your town. Google Earth users can download an overlay also created from the “World Atlas” data. And don’t forget to check out the Globe at Night interactive light pollution map data created with eight years of data collected by citizen scientists.
Effects of Light Pollution
For three billion years, life on Earth existed in a rhythm of light and dark that was created solely by the illumination of the Sun, Moon and stars. Now, artificial lights overpower the darkness and our cities glow at night, disrupting the natural day-night pattern and shifting the delicate balance of our environment. The negative effects of the loss of this inspirational natural resource might seem intangible. But a growing body of evidence links the brightening night sky directly to measurable negative impacts including
- Increasing energy consumption
- Disrupting the ecosystem and wildlife
- Harming human health
- Effecting crime and safety
Light pollution affects every citizen. Fortunately, concern about light pollution is rising dramatically. A growing number of scientists, homeowners, environmental groups and civic leaders are taking action to restore the natural night. Each of us can implement practical solutions to combat light pollution locally, nationally and internationally.
You Can Help!
The good news is that light pollution, unlike many other forms of pollution, is reversible and each one of us can make a difference! Just being aware that light pollution is a problem is not enough; the need is for action. You can start by minimizing the light from your own home at night. You can do this by following these simple steps.
- Learn more. Check out our Light Pollution blog posts
- Only use lighting when and where it’s needed
- If safety is concern, install motion detector lights and timers
- Properly shield all outdoor lights
- Keep your blinds drawn to keep light inside
- Become a citizen scientist and helping to measure light pollution
Then spread the word to your family and friends and tell them to pass it on. Many people either don’t know or don’t understand a lot about light pollution and the negative impacts of artificial light at night. By being an ambassador and explaining the issues to others you will help bring awareness to this growing problem and inspire more people to take the necessary steps to protect our natural night sky. IDA has many valuable resources to help you including Public Outreach Materials, How to Talk to Your Neighbor, Lighting Ordinances and Residential and Business Lighting.
Want to do more? Get Involved Now
Eclipses and the path of light: Geometric optics
How do we get a solar eclipse?
Details about this, and the Earth-moon system in general, are here: Kaiserscience Earth-moon system.
But here are the basics:
How do we get a lunar eclipse?
First we need to know about the three types of shadows.
umbra (Latin “shadow”) is the innermost, darkest part of a shadow.
Where the light source is completely blocked.
penumbra (Latin paene “nearly”) is where only a portion of the light is obscured.
An observer in the penumbra experiences a partial eclipse.
antumbra (Latin ante, “before”) is where the occluding body appears entirely contained within the disc of the light source.
An observer here sees an annular eclipse, in which a bright ring is visible around the eclipsing body.
Here we see rays of light from the Sun, hitting the Earth. This happens 24-7.
Behind the Earth the three types of shadows always exist, 24-7.
If the moon passes through one of these regions, then we get one of these types of eclipses.
What are the conditions for a lunar eclipse?