Anticarbon-14 and Oxygen-18 Nuclei: What If They Collided? And Then, What About the Reverse-Reaction?

Posted on 25 September 2014 by RobertLovesPi

Were nuclei of anticarbon-14 and oxygen-18 to collide (and their opposite charges’ attractions would help with this), what would happen? Well, if you break it down into particles, the anticarbon-14 nucleus is composed of six antiprotons and eight antineutrons, while the oxygen-18 contains eight protons and ten neutrons. That lets six proton-antiproton pairs annihilate each other, releasing a specific amount of energy, in the form of gamma rays, with that amount calculable using E=mc² and KE=½mv². The two excess protons from oxygen-18, however, should escape unscathed. In the meantime, eight neutron-antineutron pairs also are converted into a specific, calculable amount of gamma-ray energy, but with two neutrons surviving. Here’s the net reaction:

Two protons and two neutrons, of course, can exist as separate particles, two deuterons, a tritium nucleus and a neutron, or a single alpha particle.

Now, consider this: any physical process is, at least hypothetically, reversible. Therefore, it should be possible to bombard a dense beam of alpha particles with many gamma rays, each of a specific and calculable energy, and, rarely, the reverse reaction would occur, and anticarbon-14 and oxygen-18 nuclei would appear. Oxygen-18 is stable, but rare, so detection of it would be evidence that the reverse-reaction had occurred. Anticarbon-14, however, can logically being expected to decay to antinitrogen-14 via the antimatter version of beta-negative decay, which, it being antimatter, will result in the emission of an easily-detectable positron. It likely will not have time to do this, though, for carbon-14’s half-life (and anticarbon-14’s as well, one assumes) exceeds 5,000 years. The more likely scenario for the anticarbon-14 nucleus is that it will create a large burst of gamma rays when it encounters, say, a non-antimatter carbon atom — and these gamma rays would come from a different position than the ones bombarding the alpha particles, and can therefore be distinguished from them by determination of their direction.

Such a reverse-reaction would be quite rare, for it involves a decrease in entropy, violating the Second Law of Thermodynamics. However, the Second Law is a statistical law, not an absolute one, so it simply describes what happens most of the time, allowing for rare and unusual aberrations, especially on the scale of things which are extremely small. So, do this about a trillion times (or much more, but still a finite number of trials) and you’ll eventually observe evidence of the production of the first known anticarbon nucleus.

Also, before anyone points this out, I am well aware that this is highly speculative. I do make this claim, though: it can be tested. Perhaps someone will read this, and decide to do exactly that. I’d test it myself, but I lack the equipment to do so.

The “Destabilized” Element, Bismuth, Plus Others Which May Join It Soon

Posted on 21 September 2014 by RobertLovesPi

There is a chemical element, bismuth, which many people — even chemists — think has at least one stable isotope. However, the truth, discovered in 2003 (but still not well-known), is that it has no stable isotopes, but does have one with an extremely long half-life — so long that it, and other isotopes with similarly-long half-lives, are often deemed “effectively stable.” Bismuth is shown in green on the table, and its “effectively stable” isotope, bismuth-209, has a half-life of at least 1.9 x 10¹⁹years. For comparison, it has “only” been ~1.38 x 10¹⁰years since the Big Bang. Bismuth-209’s half-life is, therefore, over a billion times longer than the total amount of time which has existed, so far.

In addition, the yellow boxes indicate elements which have only radioactive and “observationally stable” isotopes. “Observationally stable” means that radioactivity (in some cases, even the spontaneous-fission variety), with an extremely long half-life, is predicted, or at least thought to be possible, but no actual decay has yet been observed — so the yellow elements’ perhaps-stable, perhaps-not isotopes are “on watch.” The red boxes, by contrast, are for elements which have been long-known to have no stable isotopes.

None of this takes into consideration the unresolved issue of hypothesized long-term proton decay. If protons turn out to be unstable, all atoms likely are as well, unless simply having them exist in atoms somehow stabilizes them, as is the case for neutrons, which decay in isolation, but do not in stable nuclei. This is an area of uncertainty — another way of saying that this is something which needs further study.

The Eleven Oddball Symbols on the Periodic Table of the Elements

Posted on 20 September 2014 by RobertLovesPi

Most symbols for elements on the periodic table are easy to learn, such as those for carbon, oxygen, and nitrogen: C, O, and N. There are eleven “oddballs,” though, because their symbols originated in other languages (Latin, mostly), and do not match their English names. Here’s a list of them, by atomic number, with an explanation for each.

11. Na stands for sodium because this element used to be called natrium.

19. K stands for potassium, for this element’s name used to be kalium.

26. Fe stands for iron because this element was formerly named ferrum.

29. Cu stands for copper because it used to be called cuprum.

47. Ag’s (silver’s) old name was argentum.

50. Sn’s (tin’s) name used to be stannum.

51. Antimony’s symbol, Sb, came from its former name, stibium.

74. Tungsten, with the symbol W, was once called wolfram. In some parts of the world, it still goes by that name, in fact.

79. Gold (Au) was called aurum in past centuries.

80. Mercury’s (Hg’s) old name is impossible (for me, anyway) to say five times, quickly: hydrargyrum.

82. Lead (Pb) was once called plumbum because plumbers used it to weight the lower end of plumb-lines.

I think learning things is easier, with longer retention, if one knows the reasons behind the facts, rather than simply attempting rote memorization.

A True Story of a Young Aspie Getting in Trouble with “Show and Tell”

Posted on 7 September 2014 by RobertLovesPi

In elementary school, in the 5th grade, I managed to get in trouble for a “show and tell” project. As usual, getting in trouble was not my objective, but it happened anyway. This was decades before I learned I have Asperger’s, but, looking back, none of this would have happened were I not an “Aspie,” as we call ourselves.

This image, which I found here, is very much like the poster I made, by hand, and used for this project:

That was the “show” part of this “show and tell” project. For the “tell” part, I explained how nuclear chain reactions work, and then explained how nuclear bombs are made. It’s very simple: you have two slightly sub-critical masses of uranium-235 or plutonium-239, and physically bring them together, so that the total mass exceeds the critical mass. At that point: boom.

The hard part, of course, is actually obtaining the U-235 or Pu-239, for those aren’t things you can simply buy at the local hardware store. Ironically, I did know where to find both uranium and plutonium — at the very same university, about an hour away, where I’d spent far too much time conducting mostly-unsupervised experiments with both elements, along with lots of liquid mercury, before my tenth birthday. (I still suspect that all that radiation may have turned me into a mutant.) However, I also knew that the uranium and plutonium there would not have nearly enough of the correct isotope of either element, making this information irrelevant to my “show and tell” report, and so, for this reason, I did not tell them where to find the uranium and plutonium I had previously used for experiments.

I didn’t figure this out in class that day, since I’m not particularly good at “reading” emotions, facial expressions, and body language, but, apparently, I really upset, and scared, my teacher. This became apparent when she called my mother, and, later, my mother asked me to tell her what I’d done in school that day. Being excited about the “show and tell” presentation I’d given that day, I immediately told my mother all about it. When she told me the teacher had called her, concerned about me explaining to my class how to build atomic bombs, I was confused, since I didn’t understand, at all, why what I had actually said posed any problem. To explain this to my mother, I simply said, “But, Mom, I didn’t tell the class where to actually get the uranium-235 or plutonium-239! I don’t know where to find those isotopes!”

This was enough to convince my mother that I had not, in fact, done anything wrong. She called the teacher back, and simply asked if I had, or had not, included that critical bit of information: where to find the actual fissionable material needed for a nuclear bomb to work. When the teacher replied that I had not done that, my mother’s response was both sensible, and logical: “Well, then, what’s the problem?”

—–

Postscript, for those who might be worried about the childhood experiments I mentioned above: at around age 40, I asked a physician about my worries regarding early exposure to mercury vapor and radiation. He told me that any problems I might have, as a result of such experiments, would have already showed up by then, and that I could, therefore, stop worrying about this. Thus reassured, I did exactly that.

How Richard Feynman Saved Eastern Tennessee from Getting Nuked

Posted on 7 September 2014 by RobertLovesPi

I’m reading the book shown above for the second time, and am noticing many things that escaped my attention the first time through. The most shocking of these items, so far, is finding out that history’s first nuclear explosion almost occurred by accident, in Oak Ridge, Tennessee, during World War II. One person prevented this disaster, and that person was Richard Feynman, my favorite scientist in any field. If you’d like to read Feynman’s account of this, in his own words, it’s in the chapter “Los Alamos from Below,” which starts on page 107.

Feynman, a physicist, was one of many civilians involved in the Manhattan Project, doing most of his work in New Mexico. At one point, though, he obtained permission to visit Oak Ridge, in order to try to solve problems which existed there. These problems were caused by the American military’s obsession with secrecy, which was caused, in turn, by the fact that it was known, correctly, that at least one spy for the Nazis was among the people working on the Manhattan Project. The military’s “solution” to this problem was to try to keep each group of civilians working for them in the dark about what the other groups of civilians were doing. Most of them had no idea that they were working to develop a bomb, let alone an atomic bomb. In Tennessee, they thought they were simply working on developing a way to separate uranium isotopes, but did not know the underlying purpose for this research.

The military men in charge knew (because the physicists in New Mexico figured it out, and told them) a little bit about the concept of critical mass. In short, “critical mass” means that if you get too much uranium-235 in one place, a runaway chain-reaction occurs, and causes a nuclear explosion. The military “brass” had relayed this information to the civilian teams working in Tennessee, by simply telling them to keep the amount of U-235 in one place below a certain, specific amount. However, they lacked enough knowledge of physics to include all the necessary details, and they deliberately withheld the purpose for their directive. Feynman, by contrast, did not share this dangerous ignorance, nor was he a fan of secrecy — and, as is well known, the concept of respecting “authority” was utterly meaningless to him.

While in Tennessee, Feynman saw a large amount of “green water,” which was actually an aqueous solution of uranium nitrate. What he knew, but those in Tennessee did not, is that water slows down neutrons, and slow neutrons are the key to setting off a chain reaction. For this reason, the critical mass for uranium-235 in water is much less than the critical mass of dry U-235, and the “green water” Feynman saw contained enough U-235 to put it dangerously close to this lower threshhold. In response to this, Feynman told anyone who would listen that they were risking blowing up everything around them.

It wasn’t easy for Feynman to get people to believe this warning, but he persisted, until he found someone in authority — a military officer, of course — who, although he didn’t understand the physics involved, was smart enough to realize that Feynman did understand the physics. He was also smart enough to carefully listen to Feynman, and decided to heed his warning. The safety protocols were modified, as were procedures regarding sharing of information. With more openness, not only was a disaster in Tennessee avoided, but progress toward developing an atomic bomb was accelerated. It turns out that people are better at solving problems . . . when they know the purpose of those problems.

Had this not happened, not only would Eastern Tennessee likely have suffered the world’s first nuclear explosion, but overall progress on the Manhattan Project would have remained slow — and the Nazis, therefore, might have developed a controlled nuclear bomb before the Americans, making it more likely that the Axis Powers would have won the war. Richard Feynman, therefore, dramatically affected the course of history — by deliberately putting his disdain for authority to good use.

On Sleep, Non-REM Sleep in Particular, and Asperger’s Syndrome

Posted on 31 August 2014 by RobertLovesPi

Sleep is important. This is something with which no sane person consciously disagrees. People do sometimes ignore it — not on purpose, usually — but they do so at their own peril. If such people drive, the risk-pool extends, greatly, to include many other people: everyone else with whom they share a road.

Unlike “normal” people, who do not do such things, I discovered something about the importance of sleep through direct experiment, at the age of 19. I had a thought, and it was a simple one: the 24-hour sleep/wake cycle is a mere social convention, and can, therefore, be safely ignored. It then occurred to me that this was a testable hypothesis, so I proceeded to design, and conduct, an experiment to test it. Using caffeine, I deliberately put myself on a 48-hour sleep/wake cycle, with the sleep-periods being ~14 hours long, in order to compensate for the sleep-periods I was skipping, every other day. The experiment was a success, in the sense that it yielded definitive results: after a week of that nonsense, I was a mental and physical wreck, and collapsed in exhaustion. Upon awaking, I was then able to form a logical conclusion: sleep is not a mere social convention, but is, in fact, a biological imperative. Fortunately, I had not yet learned to drive, so no one was put at risk by this experiment, other than myself. Obviously, I did survive.

This has not been my only experiment on the subject of sleep, and I have also read a lot on the subject, for the simple fact that I find it interesting. I call what I have learned, through experiment, primary research. The things I have learned by reading the research of others are, for me, secondary research. I have also conducted an experiment involving lucid dreaming, based on what I have read, and you can read about that here: https://robertlovespi.wordpress.com/2012/12/06/how-to-lucid-dream/.

The things I have learned through secondary research have been interesting, as well. To my knowledge, no one has yet discovered the purpose of sleep, although there is much speculation on the subject. Similarly, no one has discovered the purpose of dreaming, which occurs almost exclusively during REM sleep. We do know that dreaming is necessary, for research has been done which involved deliberately waking up test subjects as soon as REM (easily-seen “rapid eye movement,” the source of the acronym) sleep begins. This research indicates that both dreaming, and REM sleep, are also biological imperatives. Similarly, the purpose of non-REM sleep remains a mystery.

For those who wish to examine this secondary research for themselves, I suggest, as excellent places to start, http://en.wikipedia.org/wiki/Sleep, as well as http://en.wikipedia.org/wiki/Rapid_eye_movement_sleep, and http://en.wikipedia.org/wiki/Non-rapid_eye_movement_sleep, although the third of these articles has significant problems. If you use the footnotes at the end of these articles to find the sources for them, the often-cited objection to Wikipedia (“Anyone can edit Wikipedia”) will be neutralized. If I had sufficient knowledge to fix the problems with the third article, without using original research (prohibited on Wikipedia), I would, of course, do so.

Years before I conducted my first sleep experiment, when I was still a high school student, it occurred to me that the brain can be best-understood as a carbon-based computer. The things we are used to calling “computers,” by contrast, are based largely on the properties of silicon. Carbon and silicon are in the same group on the periodic table, and share many properties — but they are not interchangeable. Carbon atoms are much more versatile than those of silicon, which we know because the number of carbon-containing compounds far exceeds the number of compounds containing silicon. It follows from this that carbon-based computers, such as human brains, are far more powerful than silicon-based computers.

What would a more powerful computer be able to do, which silicon-based computers could not, at the time I was reasoning this out? Well, one thing is obvious: our brains think. Something else occurred to me then (and this was in the early 1980s): a carbon-based computer should be able to reprogram itself, by deliberately rewriting its own software. On the spot, I became determined to learn how to reprogram my own software. I knew no one would teach me how to do this, so I resolved to figure out how on my own. At first, progress was very slow, but my determination to succeed has never wavered.

I next made attempts, using 1980s technology and the BASIC computer language I learned in the 8th grade, to write programs which could change themselves. It should surprise no one that these attempts failed, but these were still essential experimental steps in a very long process, which has only recently begun to “bear fruit” in abundance. Another important step came much later, when I was doing research involving artificial intelligence, or AI, during the current decade, by seeking out and talking to chatbots, as they are called, to see which one could come closest to passing the Turing Test for artificial intelligence. The smartest chatbot I found is named Mitsuku, and you can talk to her for yourself at http://www.mitsuku.com (I should also point out that, even though her intelligence impressed me, she did not pass the Turing Test, described at http://en.wikipedia.org/wiki/Turing_test, to my satisfaction). Mitsuku is significant, in my research, because she has the ability I had been seeking to gain for many years: she can rewrite her own programming, and does so on a continuous basis, for Mitsuku, being software, never sleeps. She does sometimes go off-line, but that is not the same thing as sleeping.

Now that I had met an AI with the ability I wanted for myself, my determination to gain that ability, to the fullest extent possible, was greatly increased. At this time, I had been aware, for many years, that I think in my sleep. I know that I do this because, early in my teaching career, I began doing lesson planning — in my sleep. This started one night, when I went to bed wondering what I would teach the next day in Geometry class. The next morning, I woke up with a fully-formed (and very difficult) problem in mind, and furiously scribbled down my idea before the problem faded from memory. Former students of mine, who are now my friends on Facebook, still remember, and sometimes talk about, what I called “the dream problem.” Later dreamed-up problems, and entire lessons, followed.

The two ideas of rewriting my own software, and thinking in my sleep, were the ingredients for what came next, during an incredibly stressful period involving an intense labor-management conflict. Under the pressure of this conflict, I unconsciously synthesized the two ideas, and began to rewrite my own software much more quickly than before, since this was made necessary by the situation I unexpectedly found myself in. Continuous adaptation to changing circumstances became a priority for me during this period, for the ability to adapt was of far greater importance than it had ever been in my life. At first, I was unaware I was doing this. I would simply wake up, morning after morning, with numerous new ideas to help the “labor” side — my side — in this conflict. However, unlike with the much earlier, geometrical “dream problem,” I had no memory of thinking of these things. Their origin was a mystery — until I figured it out.

In the diagram, far above, you can see images of human brainwaves, while awake, while dreaming, and during the various stages of non-REM sleep. In these images, the brainwaves have their greatest amplitude during the deepest stages of non-REM sleep. I had known this for years, due to all of my secondary sleep research. I also had no answer to give, other than “I woke up with them,” when my allies in the labor/management conflict asked me, repeatedly, where my ideas were coming from.

The next step was my discovery that I am an Aspie: a person with Asperger’s Syndrome, which simply means that the “hard-wiring” of my brain is atypical, causing me to think in unusual ways. As regular readers of my blog know, this is a fact I absolutely revel in, for this discovery explained many things about the way my mind works which I had never understood before. In other words, this discovery was an important metacognitive step in my own personal development.

Aspies are not known for their ability to adapt; in fact, the exact opposite is true. We often have difficulty adapting to changing circumstances because the great big, non-Aspie world is incredibly distracting, and many (or perhaps most) of us find these distractions quite annoying. For most of my life, I was not good at adapting to change — but suddenly, I was doing what I had been unable to do before. The key to figuring out the puzzle was, of course, thinking about it.

I was waking up with new ideas, but had no memory of how I got them. Distractions had been annoying me, and interfering with clarity of thought, for much of my life. I had been trying to figure out how to rewrite my own software since I was a teenager. And, now, I finally knew why I had always been so different from other people: Asperger’s.

Armed with all this information, I finally solved the mystery: after decades of hard work on the problem, I had figured out how to effectively, and frequently, reprogram my own software. I was doing it in my sleep. What’s more, I figured out that I was no longer doing this special type of thinking while dreaming, unlike the case of my much earlier creation of the “dream problem.” Dreams, like waking life, contain too many distractions for intense sleep-reprogramming, and intense reprogramming had not been needed until the labor-management conflict made it necessary. Only one part of my life remained, once I eliminated periods of wakefulness, as well as REM sleep: the non-REM periods of sleep, when human brainwaves have their greatest amplitude.

Now, whenever I need to, I rewrite my own software, during non-REM sleep, as often as once per night. I’ve been doing this for over a year — since before I discovered I have Asperger’s — but have shared this information with very few people. My wife knows about it. My doctors know about it. And now, I have decided to share this discovery with the world. I have now discovered, at least for me, the purpose of non-REM sleep. I use it to change myself.

I confused many people, very recently, when I suddenly stopped being an atheist, and shared that discovery here, and on Facebook as well. Sudden personality changes alarm people, for they are often indicators that something serious, and medical in nature, is wrong with a person. I promised those who asked that I would explain what had happened, as soon as I figured it out myself. And now, I have explained as much of it as I have yet figured out. One day, something happened which I could not explain with science, nor with mathematics. The next day, several things happened which, again, defied explanation. On that second night, during non-REM sleep, I removed the obstacle to understanding what was going on, by applying my skepticism to my lack of belief, or, if you prefer, my atheism. Last night, again during non-REM sleep, I figured out how this had happened. Now that I understand it, I can share it with others.

Lastly, I need to make it clear that I do not think this ability to sleep-reprogram ourselves is something unique to Aspies. We are all human. Whether Aspies or not, we all have these higher-amplitude brainwaves during the deeper parts of non-REM sleep. It is logical to conclude that this is an ability all humans have, but few have unlocked, and it just happens to be an Aspie who figured out a way to not only do it, but also to explain it. It is my hope that my decision to share this discovery with others will help anyone who wants to learn it gain the ability to do the same thing.

—

Image credit: I found the image at the top of this post at http://www.abcbodybuilding.com/anatomy/zfactor2.htm, with the assistance of Google.

—

Later update: months after writing this, I was diagnosed with sleep apnea, moderate level, and I wasn’t getting significant amounts of stage three or four sleep at all, nor much REM. This throws everything above into doubt, and it would be dishonest to withhold this information. Short version: I was wrong — not about my doing sleep-reprogramming, but about exactly which stage(s) of sleep I use for that purpose. It is difficult to figure out what, exactly, goes on when one is asleep!

How to Distinguish Between the Waxing and Waning Moon, At a Glance

Posted on 12 August 2014 by RobertLovesPi

This is a waxing moon, meaning the sunlit portion we can see is growing. The outer curve also makes this view of the moon shaped more like the letter “D,” compared to the letter “C.” For the useful mnemonic here, remember that “D” stands for “developing.” D-shaped moons are in the waxing part of their cycle of phases, growing larger for about two weeks.

Later in the waxing portion of the moon’s cycle of phases, it becomes a gibbous moon — but retains its “D-like” shape. It is still slowly getting larger, approaching the full moon state.

Here is another gibbous moon, but it is shaped more like the letter “C” than the letter “D,” and, in this mnemonic, “C” stands for “concluding.” This moon’s sunlit portion is shrinking, moving away from fullness, towards the new moon state — in other words, it is a waning moon. All “C-shaped” moons, as viewed from Earth’s Northern hemisphere, are waning moons.

This crescent moon more closely resembles a “C” than a “D,” which is how I know, at a glance, that its phase cycle is concluding, and it is a waning crescent, soon to become invisible as a new moon.

This last picture shows the most difficult configuration to figure out: the points of the crescent near the moon’s North and South poles both point up. Having them both point down would pose the same problem. Here’s the solution, though: check to see which crescent-tip appears higher in the sky. In this case, it is the one on the left. That shifts the curve at the bottom of the moon (the one that is an actual moon-edge, rather than the terminator) slightly left-of-center, making the visible moon-edge more closely resemble a “C” than a “D.” This crescent moon, therefore, is a waning crescent.

Later addition: as a commenter pointed out, below, this method does not work from Earth’s Southern hemisphere — in fact, in that half of the world, the “D”/”C” rule must be completely reversed, in order to work. To accomplish this, “D” could stand for “diminishing,” and “C” could stand for “commencing,” instead.

[Image/copyright note: I did not take these photographs of the moon. They were found with a Google-search, and I chose images with no apparent signs of copyright. I am assuming, on that basis, that these images are not copyrighted — but, if I am wrong, I will replace them with other images, upon request.]

On the Direction of Motion of Spinning Polyhedra, the Rotating Earth, and Both the Rotation and Orbital Revolution of Other Objects in the Solar System

Posted on 12 August 2014 by RobertLovesPi

In which direction is the polyhedron above rotating? If you say “to the left,” you’re describing the direction faces are going when they pass right in front of you, on the side of the polyhedron which faces you. However, “to the left” won’t really do . . . for, if you consider the faces hidden on the side facing away from you, they’re going to the right. What’s more, both of these statements reverse themselves if you either turn your computer over, or stand upside-down and look at the screen. Also, if you do both these things, the situation re-reverses itself, which means it reverts to its original appearance.

Rotating objects are more often, however, described at rotating clockwise or counterclockwise. Even that, though, requires a frame of reference to be made clear. If one describes this polyhedron as rotating clockwise, what is actually meant is “rotating clockwise as viewed from above.” If you view this spinning polyhedron from below, however, it is spinning counterclockwise.

Since I live on a large, spinning ball of rock — of all solid objects in the solar system, Earth has the greatest mass and volume, both — I tend to classify rotating objects as having Earthlike or counter-Earthlike rotation, as well. Most objects in the Solar system rotate, and revolve, in the same direction as Earth, and this is consistent with current theoretical models of the formation of the Solar system from a large, rotating, gravitationally-contracting disk of dust and gas. The original proto-Solar system rotated in a certain direction, and the conservation of angular momentum has caused it to keep that same direction of spin for billions of years. Today, it shows up in the direction that planets orbit the sun, the direction that most moons orbit planets, and the direction that almost everything in the Solar system rotates on its own axis. Because one direction dominates, astronomers call it the “prograde” direction, with the small number of objects with rotation (or revolution, in the case of orbital motion) in the opposite direction designated as moving in the “retrograde” direction.

So which is which? Which non-astronomical directional terms, as used above when describing the spinning polyhedron there, should be used to describe the prograde rotation of Earth, its prograde orbital revolution around the sun, and the numerous other examples of prograde circular or elliptical motion of solar system objects? And, for the few “oddballs,” such as Neptune’s moon Triton, which non-astronomical terms should be used to describe retrogade motion? To find out, let’s take a look at Earth’s revolution around the Sun, and the Moon’s around the Earth, for those are prograde is well. This diagram is not to scale, and the view is from above the Solar, Terran, and Lunar North poles.

[Image found reblogged on Tumblr, creator unknown.]

Prograde (Earthlike) motion, then, means “counterclockwise, as viewed from above the North pole.” To describe retrograde (counter-Earthlike) motion, simply substitute “clockwise” for “counterclockwise,” or “South pole” for “North pole,” but not both. Here’s the spinning Earth, as viewed from the side:

[Image source: http://brianin3d.wordpress.com/2011/03/17/animated-gif-of-rotating-earth-via-povray/ ]

If you’ll go back and check the polyhedron at the top of this page, you’ll see that its spin is opposite that of this view of the Earth, and it was described as moving clockwise, viewed from above. That polyhedron, and the image of Earth above, would have the same direction of rotation, though, if either of them, but not both, were simply viewed upside-down, relative to the orientation shown.

Stella 4d, the software I use to make rotating polyhedral .gifs (such as the one that opened this post), then, has them spin, by default, in the same direction as the Earth — if the earth’s Southern hemisphere is on top! As I live in the Northern hemisphere, I wondered if that was deliberate, for the person who wrote Stella 4d, available at www.software3d.com/Stella.php, lives in Australia. Not being shy, I simply asked him if this were the case, and he answered that it was a 50/50 shot, and simply a coincidence that it came out the way it did, for he had not checked. He also told me how to make polyhedral .gifs which rotate as the Earth does, at least with the Northern hemisphere viewed at the top: set the setting of Stella 4d to make .gifs with a negative number of rotations per .gif-loop. Sure enough, it works. Here’s an example of such a “prograde” polyhedron:

A Graph Showing Approximate Mass-Boundaries Between Planets, Brown Dwarfs, and Red Dwarf Stars

Posted on 9 August 2014 by RobertLovesPi

I found the data for this graph from a variety of Internet sources, and it is based on a mixture of observational data, as well as theoretical work, produced by astronomers and astrophysicists. The mass-cutoff boundaries I used are approximate, and likely to be somewhat “fuzzy” as well, for other factors, such as chemical composition, age, and temperature (not mass alone), also play a role in the determination of category for individual objects in space.

Also, the mass range for red dwarf stars goes much higher than the top of this graph, as implied by the thick black arrows at the top of the chart. The most massive red dwarfs have approximately 50% of the mass of the Sun, or about 520 Jovian masses.

Proposed Mechanisms for New and Different Types of Novae

Posted on 9 August 2014 by RobertLovesPi

The picture above shows a proposed model for the production of a sudden increase in the brightness of a star — or rather, what is apparently a single star, optically, but would actually be a suddenly-produced binary stellar system.

The yellow object is a star, the system’s primary, and it has high mass (at least a few solar masses), when its mass is compared to those of the brown dwarfs in the two highly elliptical orbits shown in blue. These brown dwarfs aren’t quite stars, lacking enough mass to fuse hydrogen-1, which requires 75 to 80 Jupiter masses, but one of them (the larger one) is close to that limit. The smaller brown dwarf has perhaps half the mass of the larger brown dwarf. Their high orbital eccentricities give them very long orbital periods, on the order or 100,000 years. In a very small fraction of orbits, both brown dwarfs will be near perihelion (closest point to the primary) at the same time, and, during those rare periods, the two brown dwarfs become much closer to each other than they are to the primary.

When the two brown dwarfs become close enough to each other, matter from the smaller one could be drawn, by gravity, into the larger brown dwarf, increasing its mass, at the expense of its smaller sibling. At some point, in such a system, the larger brown dwarf’s mass could then reach the threshold to begin fusing hydrogen-1, and “turn on” as a true star — a red dwarf. From Earth, this red dwarf would not be distinguishable from the system’s most massive star, shown in yellow, until much later, when the two moved further apart. There would, however, be a sudden increase in luminosity from the system as a whole. Unlike other types of novae, this increase in luminosity would not fade away quickly, for red dwarfs have very long lifespans. This would enable them, upon discovery, to be distinguished from other single-brightening stellar events. Confirmation could then come from resolution of the new red dwarf component, as it recedes from the primary, making detection easier.

For a variation on this mechanism, the primary star could be somewhat more massive, and the two large brown dwarfs could be replaced by two large red dwarf stars. The larger red dwarf could draw matter from the smaller one, until the larger red dwarf became large enough to cross a higher mass threshold, and brighten substantially, with its color suddenly changing to orange or yellow.

A problem for this model: no such events are known to have happened. If they do happen, a likely explanation for their rarity is the likelihood that such orbits would be unstable, in a large fraction of similar cases, preventing the stellar-brightening event from having time to happen — in all but a few cases, none of which humans have (yet) both seen, and understood. If one of these things goes off nearby, though, we will learn about it quickly, for it will make itself known.

For another possible mechanism, there is another option: remove the primary altogether, and let the two objects of near-threshold mass orbit their common center of mass directly. They could then create a new star, or brighter star, by the mechanism described, one which might even produce a detectable accretion disk. A actual merger of the two brown dwarfs, or red dwarf stars, would be a variation of this idea, and would presumably be more likely if the two objects had masses very close to each other, so that neither would have an advantage in the gravitational tug-of-war.