Origin of the moon
There are a number of models describing how Earth’s moon originated.
A NASA camera aboard the Deep Space Climate Observatory (DSCOVR) satellite captured a unique view of the moon as it moved in front of the sunlit side of Earth last month. The series of test images shows the fully illuminated “dark side” of the moon that is never visible from Earth. The images were captured by NASA’s Earth Polychromatic Imaging Camera (EPIC), a four megapixel CCD camera and telescope on the DSCOVR satellite orbiting 1 million miles from Earth. From its position between the sun and Earth, DSCOVR conducts its primary mission of real-time solar wind monitoring for the National Oceanic and Atmospheric Administration (NOAA). https://www.nasa.gov/feature/goddard/from-a-million-miles-away-nasa-camera-shows-moon-crossing-face-of-earth
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)
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What Made the Moon? New Ideas Try to Rescue a Troubled Theory
Quanta Magazine, Rebecca Boyle, 8/2/17
http://www.quantamagazine.org/what-made-the-moon-new-ideas-try-to-rescue-a-troubled-theory-20170802/
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:
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Perhaps Theia did form the moon, but Theia was made of material that was almost identical to Earth.
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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.
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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.
A synestia would be made of a bagel-like mass of vaporized rock surrounding a rocky planet.
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.
Mike Zeng for Quanta Magazine
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.
Jean Lachat/ University of Chicago (Dauphas portrait); Nicolas Dauphas (enstatite chondrite)
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.
Are LLSVPs the remains of the impact that created the Moon?
Intro TBA
By Olena Shmahalo at Quanta Magazine, source data from Sanne Cottaar.
TBA
Remains of impact that created the Moon may lie deep within Earth, Paul Voosen, Science, 3/23/2021
A remnant of a protoplanet may be hiding inside Earth, Nicoletta Lanese, Live Science, 3/29/2021
Continent-Sized Remnants Of An Alien World May Be Buried Deep Within Earth, Mary Papenfuss, HuffPost Science, 3/29/2021
Giant Impact Origin for the Large Low Shear Velocity Provinces, Q. Yuan , M. M. Li1, S. J. Desch1 and B. Ko, 52nd Lunar and Planetary Science Conference 2021 (LPI Contrib. No. 2548)
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Soundly Proving the Curvature of the Earth at Lake Pontchartrain
Excerpted from an article by Mick West
A classic experiment to demonstrate the curvature of a body of water is to place markers (like flags) a fixed distance above the water in a straight line, and then view them along that line in a telescope. If the water surface is flat then the markers will appear also in a straight line. If the surface of the water is curved (as it is here on Earth) then the markers in the middle will appear higher than the markers at the ends.
Here’s a highly exaggerated diagram of the effect by Alfred Russel Wallace in 1870, superimposed over an actual photograph.
This is a difficult experiment to do as you need a few miles for the curvature to be apparent. You also need the markers to be quite high above the surface of the water, as temperature differences between the water and the air tend to create significant refraction effects close to the water.
However Youtuber Soundly has found a spot where there’s a very long line of markers permanently fixed at constant heights above the water line, clearly demonstrating the curve. It’s a line of power transmission towers at Lake Pontchartrain, near New Orleans, Louisiana.
The line of power lines is straight, and they are all the same size, and the same height above the water. They are also very tall, and form a straight line nearly 16 miles long. Far better than any experiment one could set up on a canal or a lake. You just need to get into a position where you can see along the line of towers, and then use a powerful zoom lense to look along the line to make any curve apparent
One can see quite clearly in the video and photos that there’s a curve. Soundly has gone to great lengths to provide multiple videos and photos of the curve from multiple perspectives. They all show the same thing: a curve.
One objection you might make is that the towers could be curving to the right. However the same curve is apparent from both sides, so it can only be curving over the horizon.
c
People have asked why the curve is so apparent in one direction, but not in the other. The answer is compressed perspective. Here’s a physical example:
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That’s my car, the roof of which is slightly curved both front to back and left to right. I’ve put some equal sized chess pawns on it in two straight lines. If we step back a bit and zoom in we get:
Notice a very distinct curve from the white pieces, but the “horizon” seems to barely curve at all.
Similarly in the front-back direction, where there’s an even greater curve:
There’s a lot more discussion with photos here Soundly Proving the Curvature of the Earth at Lake Pontchartrain
Lord Of The Rings Optics challenge
A great physics problem!
In J. R. R. Tolkien’s The Lord of the Rings (volume 2, p. 32), Legolas the Elf claims to be able to accurately count horsemen and discern their hair color (yellow) 5 leagues away on a bright, sunny day.
“Riders!” cried Aragorn, springing to his feet. “Many riders on swift steeds are coming towards us!”
“Yes,” said Legolas,”there are one hundred and five. Yellow is their hair, and bright are their spears.
Their leader is very tall.”
Aragorn smiled. “Keen are the eyes of the Elves,” he said.
“Nay! The riders are little more than five leagues distant,” said Legolas.”
Make appropriate estimates and argue that Legolas must have very strange-looking eyes, have some means of non-visual perception, or have made a lucky guess. (1 league ~ 3.0 mi.)
On land, the league is most commonly defined as three miles, though the length of a mile could vary from place to place and depending on the era. At sea, a league is three nautical miles (3.452 miles; 5.556 kilometres).
Several solutions are possible, depending on the estimating assumptions
When parallel light waves strike a concave lens the waves striking the lens surface at a right angle goes straight through but light waves striking the surface at other angles diverge. In contrast, light waves striking a convex lens converge at a single point called a focal point. The distance from the long axis of the lens to the focal point is the focal length. Both the cornea and the lens of the eye have convex surfaces and help to focus light rays onto the retina. The cornea provides for most of the refraction but the curvature of the lens can be adjusted to adjust for near and far vision.
I. Here is one solution
By Chad Orzel is an Associate Professor in the Department of Physics and Astronomy at Union College in Schenectady, NY
The limiting factor here is the wave nature of light– light passing through any aperture will interfere with itself, and produce a pattern of bright and dark spots.
So even an infinitesimally small point source of light will appear slightly spread out, and two closely spaced point sources will begin to run into one another.
The usual standard for determining whether two nearby sources can be distinguished from one another is the Rayleigh criterion:
The sine of the angular separation between two objects = 1.22 x ratio of the light wavelength to the diameter of the (circular) aperture, through which the light passes.
To get better resolution, you need either a smaller wavelength or a larger aperture.
Legolas says that the riders are “little more than five leagues distant.”
A league is something like three miles, which would be around 5000 meters, so let’s call it 25,000 meters from Legolas to the Riders.
Visible light has an average wavelength of around 500 nm, which is a little more green than the blond hair of the Riders, but close enough for our purposes.
The sine of a small angle can be approximated by the angle itself.
The angle = the size of the separation between objects divided by the distance from the objects to the viewer.
Putting it all together, Legolas’s pupils would need to be 0.015 m in diameter.
That’s a centimeter and a half, which is reasonable, provided he’s an anime character. I don’t think Tolkien’s Elves are described as having eyes the size of teacups, though.
We made some simplifying assumptions to get that answer, but relaxing them only makes things worse. Putting the Riders farther away, and using yellower light would require Legolas’s eyes to be even bigger. And the details he claims to see are almost certainly on scales smaller than one meter, which would bump things up even more.
Any mathematical objections to these assumptions? Sean Barrett writes:
“The sine of a small angle can be approximated by the angle itself, which in turn is given, for this case, by the size of the separation between objects divided by the distance from the objects to the viewer.”
Technically this is not quite right; the separation divided by the distance is not the angle itself, but rather the tangent of the angle. (SOHCAHTOA: sin = opposite/hypotenuse; tangent = opposite/adjacent.)
Because the cos of a very small angle is very nearly 1, however, the tangent is just as nearly equal the angle as is the sine. But that doesn’t mean you can just skip that step.
And there’s really not much need to even mention the angle; with such a very tiny angle, clearly the hypotenuse and the adjacent side have essentially the same length (the distance to either separated point is also essentially 25K meters), and so you can correctly say that the sine itself is in this case approximated by the separation divided by the distance, and never mention the angle at all.
(You could break out a calculator to be on the safe side, but if you’re going to do that you need to know the actual formulation to compute the angle, not compute it as opposite/adjacent! But, yes, both angle (in radians) and the sine are also 1/25000 to about 10 sig figs.)
II. Another solution
Using the Rayleigh Criterion. In order for two things, x distance apart, to be discernible as separate, at an angular distance θ, to an instrument with a circular aperture with diameter a:
θ > arcsin(1.22 λ/a)
5 leagues is approximately 24000 m.
We can sssume that each horse is ~2 m apart from each other
So arctan (1/12000) ≅ θ.
We can use the small-angle approximation (sin(θ) ≅ tan(θ) ≅ θ when θ is small)
So we get 1/12000 ≅ 1.22 λ/a
Yellow light has wavelengths between 570 and 590 nm, so we’ll use 580.
a ≅ 1.22 * (580E-9 m)* 12000 ≅ .0085 m.
8 mm is about as far as a human pupil will dilate, so for Legolas to have pupils this big in broad daylight must be pretty odd-looking.
Edit: The book is Six Ideas that Shaped Physics: Unit Q, by Thomas Moore
III. Great discussion on the Physics StackExchange
Could Legolas actually see that far? Physics StackExchange discussion
Here, Kyle Oman writes:
The best seeing, achieved from mountaintops in perfect conditions, is about 1 arcsec,
Let’s first substitute the numbers to see what is the required diameter of the pupil according to the simple formula:
θ = 1.220.4 μmD = 2m24 km θ=1.220.4μm D= 2m24km
I’ve substituted the minimal (violet…) wavelength because that color allowed me a better resolution i.e. smaller θθ. The height of the knights is two meters.
Unless I made a mistake, the diameter DD is required to be 0.58 centimeters. That’s completely sensible because the maximally opened human pupil is 4-9 millimeter in diameter.
Just like the video says, the diffraction formula therefore marginally allows to observe not only the presence of the knights – to count them – but marginally their first “internal detailed” properties, perhaps that the pants are darker than the shirt. However, to see whether the leader is 160 cm or 180 cm is clearly impossible because it would require the resolution to be better by another order of magnitude. Just like the video says, it isn’t possible with the visible light and human eyes. One would either need a 10 times greater eye and pupil; or some ultraviolet light with 10 times higher frequency.
It doesn’t help one to make the pupils narrower because the resolution allowed by the diffraction formula would get worse. The significantly more blurrier images are no helpful as additions to the sharpest image. We know that in the real world of humans, too. If someone’s vision is much sharper than the vision of someone else, the second person is pretty much useless in refining the information about some hard-to-see objects.
The atmospheric effects are likely to worsen the resolution relatively to the simple expectation above. Even if we have the cleanest air – it’s not just about the clean air; we need the uniform air with a constant temperature, and so on, and it is never so uniform and static – it still distorts the propagation of light and implies some additional deterioration. All these considerations are of course completely academic for me who could reasonably ponder whether I see people sharply enough from 24 meters to count them. 😉
Even if the atmosphere worsens the resolution by a factor of 5 or so, the knights may still induce the minimal “blurry dots” at the retina, and as long as the distance between knights is greater than the distance from the (worsened) resolution, like 10 meters, one will be able to count them.
In general, the photoreceptor cells are indeed dense enough so that they don’t really worsen the estimated resolution. They’re dense enough so that the eye fully exploits the limits imposed by the diffraction formula, I think. Evolution has probably worked up to the limit because it’s not so hard for Nature to make the retinas dense and Nature would be wasting an opportunity not to give the mammals the sharpest vision they can get.
Concerning the tricks to improve the resolution or to circumvent the diffraction limit, there aren’t almost any. The long-term observations don’t help unless one could observe the location of the dots with the precision better than the distance of the photoreceptor cells. Mammals’ organs just can’t be this static. Image processing using many unavoidably blurry images at fluctuating locations just cannot produce a sharp image.
The trick from the Very Large Array doesn’t work, either. It’s because the Very Large Array only helps for radio (i.e. long) waves so that the individual elements in the array measure the phase of the wave and the information about the relative phase is used to sharpen the information about the source.
The phase of the visible light – unless it’s coming from lasers, and even in that case, it is questionable – is completely uncorrelated in the two eyes because the light is not monochromatic and the distance between the two eyes is vastly greater than the average wavelength.
So the two eyes only have the virtue of doubling the overall intensity; and to give us the 3D stereo vision. The latter is clearly irrelevant at the distance of 24 kilometers, too. The angle at which the two eyes are looking to see the 24 km distant object are measurably different from the parallel directions. But once the muscles adapt into this slightly non-parallel angles, what the two eyes see from the 24 km distance is indistinguishable.
V. This is also analyzed in “How Far Can Legolas See?” by minutephysics (Henry Reich)
Organic food and farming
Organic food
“People got in their head, well, if it’s man-made somehow it’s potentially dangerous, but if it’s natural, it isn’t. That doesn’t really fit with anything we know about toxicology. When we understand how animals are resistant to chemicals, the mechanisms are all independent of whether it’s natural or synthetic. And in fact, when you look at natural chemicals, half of those tested came out positive [for toxicity in humans].” –Bruce Ames
Organic food is food produced by organic farming, a set of techniques that mixes scientific knowledge of soil depletion and enrichment with anti-scientific beliefs and myths about nature and the natural.
A key belief of groups like the International Federation of Organic Agriculture Movements (IFOAM) and the Soil Association, which oppose conventional farming in favor of organic farming, is that pesticides and fertilizers are so harmful that they should be avoided unless they are “natural.”
This belief is contradicted by the vast majority of scientific studies that have been done on these subjects (Morris and Bate 1999; Taverne 2006; NCPA study). The United States Department of Agriculture (USDA) has put in place a set of national standards that food labeled “organic” must meet, whether it is grown in the United States or imported from other countries.
“USDA makes no claims that organically produced food is safer or more nutritious than conventionally produced food. Organic food differs from conventionally produced food in the way it is grown, handled, and processed.”*
Harm from bacterial contamination is a much greater possibility from natural fertilizers (Stossel 2005: 194). (For those of you who hate John Stossel, read the newspaper. The most dangerous bacteria in America’s food supply is E. coli, which is found in abundance in cattle manure, a favorite “natural” fertilizer of organic farming.)
The residues from pesticides on food, natural or synthetic, are not likely to cause harm to consumers because they occur in minute quantities.* (This fact does not make either kind of pesticide safe for those who work with them and are exposed to large quantities on a regular basis. I refer to residues on foods you and I are likely to find on fruits and vegetable we buy at the store or market.)
Using natural biological controls rather than synthetic pesticides is more dangerous to the environment (Morris and Bate 1999). The amounts of pesticide residue produced by plants themselves or introduced by organic farmers are significantly greater than the amounts of synthetic pesticide residues.
Almost all of the pesticides we ingest in food are naturally produced by plants to defend themselves against insects, fungi, and animal predators (Ames and Gold 1997). The bottom line is that fresh fruits and vegetables are good for you and it doesn’t matter whether they’re organic.
Over 30 separate investigations of about 500,000 people have shown that farmers, millers, pesticide-users, and foresters, occupationally exposed to much higher levels of pesticide than the general public, have much lower rates of cancer overall (Taverne 2006: 73.)
Groups like IFOAM refer to synthetic pesticides as “toxic,” even though the amount of pesticides people are likely to ingest through food are always in non-toxic amounts.
Many toxic substances occur naturally in foods, e.g.,arsenic in meat, poultry, dairy products, cereals, fish, and shellfish, but usually in doses so small as not to be worthy of concern. On the IFOAM website you will find the following message:
Although IFOAM has no official position on the quality of organic food, it’s easy to conclude that the overall nutritional and health-promoting value of food is compromised by farming methods that utilize synthetic fertilizers and toxic pesticides.
It’s easy to conclude—as long as you ignore the bulk of the scientific evidence that is available.
the myth of organic superiority
The evidence for the superiority of organic food is mostly anecdotal and based more on irrational assumptions and wishful thinking than on hard scientific evidence. There is no significant difference between a natural molecule and one created in the laboratory. Being natural or organic does not make a substance safe* nor does being synthetic make a substance unsafe.
Organic food does not offer special protection against cancer or any other disease. Organic food is not “healthier” than food produced by conventional farming, using synthetic pesticides and herbicides. Organic farming is not necessarily better for the environment than conventional farming. There is scant scientific evidence that most people can tell the difference in taste between organic and conventional foods. The bottom line is: fresher is better. Organic produce that travels thousands of miles to market is generally inferior to the same produce from local farmers, organic or not.
Is there any difference between organic and conventional fruits and vegetables? According to one scientific paper, there are several differences:
Based on the results of our literature review and experiment we conclude that there are substantial differences between organic and conventional fruits and vegetables. They differ with respect to production method, labeling, marketing, price and potentially other parameters.
You don’t need to do a scientific study to know that organic foods are produced differently from conventionally farmed foods. Anyone who has been to the market knows that you will pay substantially more for food labeled “organic.”
… The aforementioned scientific study did find that the literature provides evidence for one nutritional difference between organic and conventional foods: vitamin C was found to be higher for organic food.
coddling by the media
The way the media treat “green” issues accounts for one reason that the organic-is-better myth is pervasive. Here’s an example from BBC News:
Growing apples organically is not only better for the environment than other methods but makes them taste better than normal apples, US scientists say.
The study is among the first to give scientific credence to the claim that organic farming really is the better option.
The researchers found organic cultivation was more sustainable than either conventional or integrated farming, which cuts the use of chemicals.
The scientists, from Washington State University in Pullman, found the organic apples were rated highest for sweetness by amateur tasting panels.
They reported: “Escalating production costs, heavy reliance on non-renewable resources, reduced biodiversity, water contamination, chemical residues in food, soil degradation and health risks to farm workers handling pesticides all bring into question the sustainability of conventional farming systems.”
The headline for the story reads: Organic apples tickle tastebuds.
Most people might stop reading the story after five paragraphs of nothing but positive statements about organic farming and the mention of a number of problems ahead for conventional farming. For those who persevere, however, the following bits of information are also provided:
…organic farming systems were “less efficient, pose greater health risks and produce half the yields of conventional farming”.
…the tests “found no differences among organic, conventional and integrated apples in texture or overall acceptance”.
…Growers of more sustainable systems may be unable to maintain profitable enterprises without economic incentives, such as price premiums or subsidies for organic and integrated products.
Apparently, the measure used to determine that organic farming was “better for the environment” was based on physical, chemical, and biological soil properties. The scientists created their own index and found that organic was better mainly because of the addition of compost and mulch.
Certainly, there are going to be some organic farms that use methods of composting and mulching that improve growing conditions. But there are also methods conventional farmers can use to accomplish the same thing.
Finally, there are some organic farmers who used methods of composting and mulching that don’t improve anything except the chances of bacterial infection. Only a “green” journalist or scientist could turn being less efficient, posing greater health risks, no different in texture or appearance, and producing half the yields of conventional farming into “better than conventional farming.”
I’ll provide just one more example of how the media and scientists with agendas distort the results of scientific studies that compare organic with conventional agricultural practices. In 2003, Alyson Mitchell, Ph.D., a food scientist at the University of California, Davis, co-authored a paper with the formidable title of “Comparison of the Total Phenolic and Ascorbic Acid Content of Freeze-Dried and Air-Dried Marionberry, Strawberry, and Corn Grown Using Conventional, Organic, and Sustainable Agricultural Practices.”
The article was published in the Journal of Agricultural and Food Chemistry, a peer-reviewed journal of the American Chemical Society. The article got some good press from “green” journalists, who proclaimed that the study showed that organic foods have significantly higher levels of antioxidants than conventional foods.
(Examples of glowing press reports can be found here and here.) There is a strong belief among promoters of organic foods that there is good scientific support for the claim that diets rich in antioxidants contribute to significantly lower cancer rates.
The data, however, do not support this belief. “Study after study has shown no benefit of antioxidants for heart disease, cancer, Parkinson’s disease, Alzheimer’s disease, or longevity” (Hall 2011).
The study compared total phenolic metabolites and ascorbic acid in only two crops, marionberries and corn. Both crops were grown organically and conventionally on different farms. The organic berries were grown on land that had been used for growing berries for four years; the conventional berries were grown on land that had been used to grow conventional berries for 21-22 years.
The crops were grown on different soil types: the organic soil was “sandy, clay, loam”; the conventional was “sandy, Ritzville loam.” The soil for the conventional corn had been used before for wheat; the soil for the organic corn had been used for green beans. The conventional farm used well water; the organic farm used a combination of well and creek water. (I don’t mention the strawberry listed in the title of the article because no organic strawberries were tested.)
As you can tell from the title of the article, the metabolites measured were not taken from fresh berries or corn but from samples that had been freeze-dried and air-dried. Though not mentioned in the title, the scientists also compared samples that were simply frozen.
The data provided by the authors in their published study shows clearly that there was not enough measurable ascorbic acid (AA) in either of the marionberry samples to compare the organic to the conventional. As already noted, no organic strawberries were studied. There was not enough measurable AA for the freeze-dried or air-dried corn to be compared.
So, the only data on AA is for the frozen corn: organic had a value of 3.2 and conventional had a value of 2.1. You can read the study yourself to find out what these numbers represent, but whatever they represent they do not merit the conclusion drawn by the authors of the study: “Levels of AA in organically grown … samples were consistently higher than the levels for the conventionally grown crops.”
The study also compared what it calls “sustainable agricultural practices” to organic and conventional practices. Sustainable practices in this study included the use of synthetic fertilizers.
“Our results indicate,” the authors write, “that TPs [total phenolics] were highest in the crops grown by sustainable agricultural methods as compared to organic methods.” Dr. Mitchell is quoted in the press as saying that their study “helps explain why the level of antioxidants is so much higher in organically grown food.” Yet, her study clearly states that the evidence for this claim is anecdotal. In fact, the authors write of the comparative studies that have been done:
These data demonstrate inconsistent differences in the nutritional quality of conventionally and organically produced vegetables with the exception of nitrate and ascorbic acid (AA) in vegetables.
distortion of evidence by scientists
One thing these “green” advocates are good at is distorting data to make lead appear to be gold. Another study led by Mitchell claims that organic tomatoes have “statistically higher levels (P < 0.05) of quercetin and kaempferol aglycones” than conventional tomatoes. The increase of these flavonoids corresponds “with reduced manure application rates once soils in the organic systems had reached equilibrium levels of organic matter.”
In fact, the study suggests that it is the nitrogen “in the organic and conventional systems that most strongly influence these differences.” The authors suggest that “overfertilization (conventional or organic) might reduce health benefits from tomatoes.” The argument is that the flavonoids are a protective response by the plants and one of the things they respond to is the amount of nitrogen in the soil.
In any case, the thrust of these and similar studies is that both organic and conventional crops can be manipulated to yield higher levels of antioxidants. At least one study has found “organic food products have a higher total antioxidant activity and bioactivity than the conventional foods.”* That study, however, involved only ten Italian men, aged 30-65 years.
I have to say that I am underwhelmed by the studies I have reviewed that claim to have found organic foods are more nourishing or healthy than conventional fruits and vegetables. At present, there is no strong body of scientific evidence that supports the contention that organic fruits and vegetables are superior to conventional produce.
A best case scenario for the organic folks would be that to achieve the recommended nutrients from five helpings a day of fruits or vegetables you might have to eat four or five more conventionally grown strawberries or two or three more baby carrots to get the same amount of vitamins, minerals, or antioxidants as provided by organic fruits and vegetables. But I’m not sure the evidence supports even that weak position.
History of the term “organic”
The term ‘organic’ as a descriptor for certain sustainable agriculture systems appears to have been used first by Lord Northbourn in his book Look to the Land (1940).
“Northbourn used the term to describe farming systems that focused on the farm as a dynamic, living, balanced, organic whole, or an organism.”* T
he term ‘organic’ was first widely used in the U.S. by J. I. Rodale, founder of Rodale Press, in the 1950s. “Rodale failed to convince scientists of the validity of his approach because of his reliance on what were perceived to be outrageous unscientific claims of organic farming’s benefits.”*
The USDA standards for organic food state:
Organic food is produced without using most conventional pesticides; fertilizers made with synthetic ingredients or sewage sludge; bioengineering; or ionizing radiation.
These standards capture the essence of the organic mythology:
-
Conventional pesticides should be avoided.
-
Synthetic fertilizers should be avoided.
-
Food should not be genetically altered.
-
Food should not be subjected to ionizing radiation.
The bit about sewage sludge is there because some organic farmers follow the “law of return” as proposed by Sir Albert Howard (1873-1947), a founder and pioneer of the organic movement. He advocated recycling all organic waste materials, including sewage sludge, in farmland compost. The practice of adding human and animal feces to the soil is an ancient practice found in many cultures even today.
The fact that these cultures developed their practices without benefit of modern knowledge of such things as bacteria or heavy metals is trumped by the romantic notion that farm life was idyllic in those times and places when life expectancy was half that of today.
Rudolf Steiner, the founder of a set of superstitious agricultural practices known as biodynamics, also advocated using manure as fertilizer but it had to be prepared according to a magical formula based on his belief that cosmic forces entered animals through their horns. Steiner also romanticized farming. Commenting on some peasants stirring up manure, he said:
“I have always had the opinion … that [the peasants’] alleged stupidity or foolishness is wisdom before God [sic], that is to say, before the Spirit. I have always considered what the peasants and farmers thought about their things far wiser than what the scientists were thinking.”*
Steiner gave lectures on farming, but did no scientific research to test his ideas.
A central concept of these lectures was to “individualize” the farm by bringing no or few outside materials onto the farm, but producing all needed materials such as manure and animal feed from within what he called the “farm organism.”
Other aspects of biodynamic farming inspired by Steiner’s lectures include timing activities such as planting in relation to the movement patterns of the moon and planets and applying “preparations,” which consist of natural materials which have been processed in specific ways, to soil, compost piles, and plants with the intention of engaging non-physical beings and elemental forces. Steiner, in his lectures, encouraged his listeners to verify his suggestions scientifically, as he had not yet done.*
Steiner opposed the use of synthetic fertilizers and pesticides, not on scientific grounds but on spiritual grounds. He claimed there were “spiritual shortcomings in the whole chemical approach to farming.”* He had a mystical idea of the farm as an organism, “a closed self-nourishing system.”*
This article has been excerpted from The Skeptic’s Dictionary, http://skepdic.com/organic.html
Crystals in metals
Why do metals have the properties that they have?
Background knowledge: We first need to know what crystals are.
Solid / Liquid / Gas
Metal is a type of solid
Metal is usually an imperfect crystal
At any temperature above absolute zero, atoms vibrate, so even in solids the atoms are always somewhat in motion
Iron atoms, like many other metals, take on this shape
Body-Centered Cubic (BCC) Structure:
there are 8 atoms at the 8 corners, and one atom in the centre of the unit cell.
This structure is then repeated over and over.
“The structure of iron atoms isn’t continuous throughout the entire paper clip. When a metal cools and is transitioning from liquid to solid, its atoms come together to form tiny grains, or crystals.”
“Even though the crystalline structure does not continue from crystal to crystal, the crystals are bound to one another. In this diagram, each square represents an individual atom.”
tba
atoms held together with metallic bonds
(add pics here)
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Defects break the bonds
“When a metal crystal forms, the atoms try to assemble themselves into a regular pattern. But sometimes there isn’t an atom available to fill in a space, and sometimes a growing layer is halted by other growing layers.”
“There are many imperfections within each crystal, and these flaws produce weak points in the bonds between atoms. It is at these points, called slip planes, that layers of atoms are prone to move relative to adjacent layers if an outside force is applied.”
“Adding other elements to a metal can counteract the effects of the imperfections and make the metal harder and stronger. Carbon, for example, is added to iron to make steel, and tin is added to copper to make bronze.”
Atoms can slip into a new position
Slipping
Metal atoms can bend
Heat can loosen the fixed positions of metal atoms
PBS NOVA: Building on Ground Zero – The Structure of Metals
PBS NOVA: Interactive Structure of Metals
PBS NOVA: Engineering Ground Zero
Learning Standards
Massachusetts Science and Technology/Engineering Curriculum Framework
High School Chemistry
HS-PS2-6. Communicate scientific and technical information about the molecular-level structures of polymers, ionic compounds, acids and bases, and metals to justify why these are useful in the functioning of designed materials.*
PS1.A Structure of matter. That matter is composed of atoms and molecules can be used to explain the properties of substances, diversity of materials, how mixtures will interact, states of matter, phase changes, and conservation of matter. States of matter can be modeled in terms of spatial arrangement, movement, and strength of interactions between particles.
PS2.B Types of interactions. Electrical forces between electrons and the nucleus of atoms explain chemical patterns. Intermolecular forces determine atomic composition, molecular geometry and polarity, and, therefore, structure and properties of substances.
MCAS Open Response questions
Content Objectives: SWBAT construct answers to open-response questions on the physics MCAS.
2015, High School Intro Physics: sample open response question
2011 sample open response questions
2012 sample open response questions
2013 sample open response questions
2014 sample open response questions
2015 sample open response questions
2016 sample open response questions
- Learning Standards:
- For answering open-response questions – ELA Core Curriculum
- CCRA.R.1 – Read closely to determine what the text says explicitly and to make logical inferences from it; cite
- specific textual evidence when writing or speaking to support conclusions drawn from the text.
- For answering problems involving equations: Massachusetts Curriculum Framework for Mathematics
- Functions: Connections to Expressions, Equations, Modeling, and Coordinates.
- Determining an output value for a particular input involves evaluating an expression; finding inputs that yield a
- given output involves solving an equation.
Fuses
Fuses
You can use adapters to turn one outlet into two… two outlets into four, and so on. What happens if you turn on all the devices connected to all these cords at once? They draw a lot of current through the wires to that outlet – and those wires can overheat, and start an electrical fire.
Electrical fire
This is why we need something in the house which can detect abnormally high electrical currents – and cut them off.
Circuit breakers and fuse boxes.
Here we see what could be a potentially fatal accident – a wet electrical appliance could conduct enough electricity to kill a person. How can we avoid this?
“A ground fault circuit interrupter (GFCI) or Residual Current Device (RCD) is a device that shuts off an electric power circuit when it detects that current is flowing along an unintended path, such as through water or a person.”- Simple Wikipedia
A GFCI on a hair dryer.
Lab Measuring Voltage Current DC circuits
- Learn how to build a simple circuit, measure voltage, and current
- Build a DC series circuit and DC parallel circuit
==========================
The fuse
The fuse breaks the circuit if a fault in an appliance causes too much current flow. This protects the wiring and the appliance if something goes wrong. The fuse contains a piece of wire that melts easily. If the current going through the fuse is too great, the wire heats up until it melts and breaks the circuit.
Fuses in plugs are made in standard ratings. The most common are 3A, 5A and 13A. The fuse should be rated at a slightly higher current than the device needs:
- if the device works at 3A, use a 5A fuse
- if the device works at 10A, use a 13A fuse
A 13A fuse with a low melting point wire
Cars also have fuses. An electrical fault in a car could start a fire, so all the circuits have to be protected by fuses.
The circuit breaker
The circuit breaker does the same job as the fuse, but it works in a different way. A spring-loaded push switch is held in the closed position by a spring-loaded soft iron bolt. An electromagnet is arranged so that it can pull the bolt away from the switch. If the current increases beyond a set limit, the electromagnet pulls the bolt towards itself, which releases the push switch into the open position.
from http://www.bbc.co.uk/schools/gcsebitesize/science/edexcel_pre_2011/electricityworld/mainselectricityrev3.shtml
======================
Additional resources
How does a Residual Current Circuit Breaker Work?
External resources
http://www.electronicsteacher.com/direct-current/physics-conductors-insulators/fuses.php
https://www.allaboutcircuits.com/textbook/direct-current/chpt-12/fuses/
https://en.wikipedia.org/wiki/Thermal_management_(electronics)
https://www.howequipmentworks.com/electrical_safety/
https://www.howequipmentworks.com/electricity_basics/
===========================================
Learning Standards
Massachusetts 2016 Science and Technology/Engineering (STE) Standards
HS-PS2-9(MA). Evaluate simple series and parallel circuits to predict changes to voltage, current, or resistance when simple changes are made to a circuit
HS-PS3-1. Use algebraic expressions and the principle of energy conservation to calculate the change in energy of one component of a system… Identify any transformations from one form of energy to another, including thermal, kinetic, gravitational, magnetic, or electrical energy. {voltage drops shown as an analogy to water pressure drops.}
HS-PS3-2. Develop and use a model to illustrate that energy at the macroscopic scale can be accounted for as either motions of particles and objects or energy stored in fields [e.g. electric fields.]
HS-PS3-3. Design and evaluate a device that works within given constraints to convert one form of energy into another form of energy.{e.g. chemical energy in battery used to create KE of electrons flowing in a circuit, used to create light and heat from a bulb, or charging a capacitor.}
Emmy Noether
Amalie Emmy Noether (1882 – 1935) was a German mathematician known for her landmark contributions to abstract algebra and theoretical physics. She was described by Pavel Alexandrov, Albert Einstein, Hermann Weyl, and Norbert Wiener as the most important woman in the history of mathematics. In physics, Noether’s theorem explains the connection between symmetry and conservation laws.
Our related articles
https://kaiserscience.wordpress.com/physics/mathematics/symmetry/
External articles
In her short life, mathematician Emmy Noether changed the face of physics. ScienceNews.Org
http://www.thephysicsmill.com/2014/03/09/international-womens-day-spotlight-emmy-noether/
Magnetism MCAS topics
See the lesson here Kaiserscience -> Physics -> Electromagnetism -> “Magnetism-and-electricity”
text
MCAS Open Response: sample questions with full solutions
MCAS questions
Which of the following forces allow a battery-powered motor to generate mechanical energy? (2014)
A. magnetic and static B. electric and magnetic
C. static and gravitational D. electric and gravitational
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Which of the following statements describes an electric generator? (2013)
A. A magnet is rotated through a coil of wire to produce an electric current.
B. Electric potential in a rotating coil of wire creates a permanent magnet.
C. An electrical current causes a coil of wire to rotate in a magnetic field.
D. Forces from a permanent magnet allow a coil of wire to rotate.
———————————————————
———————————————————
This next one is from 2010
———————————————————
Which of the following would cause the galvanometer needle to move?
A. wrapping additional wire around the tube
B. uncoiling the wire wrapped around the tube
C. moving a magnet back and forth inside the tube
D. moving an aluminum block up and down inside the tube
———————————————————
This next one is from 2009
Precise measuring instruments require shock absorbers to eliminate small vibrations that can affect the results of an experiment. One type of shock absorber that can be used is an electromagnet that repels a magnetic platform placed above it. Which of the following setups would provide the greatest lift to the platform?
Scientific calculators < $10
This might seem amazing, but today one can purchase scientific calculators for less than $10.
http://budgetlightforum.com/node/34682
Learning Standards
MASSACHUSETTS CURRICULUM FRAMEWORK FOR MATHEMATICS
CONCEPTUAL CATEGORY: Number and Quantity
Calculators, spreadsheets, and computer algebra systems can provide ways for students to become better acquainted with these new number systems and their notation. They can be used to generate data for numerical experiments, to help understand the workings of matrix, vector, and complex number algebra, and to experiment with non-integer exponents.
Guiding Principle 3: Technology Technology is an essential tool that should be used strategically in mathematics education. Technology enhances the mathematics curriculum in many ways. Tools such as measuring instruments, manipulatives (such as base ten blocks and fraction pieces), scientific and graphing calculators, and computers with appropriate software, if properly used, contribute to a rich learning environment for developing and applying mathematical concepts. However, appropriate use of calculators is essential; calculators should not be used as a replacement for basic understanding and skills. Elementary students should learn how to perform the basic arithmetic operations independent of the use of a calculator.4 Although the use of a graphing calculator can help middle and secondary students to visualize properties of functions and their graphs, graphing calculators should be used to enhance their understanding and skills rather than replace them. Teachers and students should consider the available tools when presenting or solving a problem. Students should be familiar with tools appropriate for their grade level to be able to make sound decisions about which of these tools would be helpful.
Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.
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