Re: Stonehenge Aotearoa
In einer eMail vom 16.2.2005 02:33:07 Westeuropäische Normalzeit schreibt [EMAIL PROTECTED]: It isn't quite a sundial, but it has an analemma (see pic half way down webpage), solstice markers and equinox markers, and stuff to do with polynesianstar navigation. Neat. But the analemma is out of place in a stone-age installation. --Art Dr. Arthur Carlson * Gabriel-Max-Str. 31, 81545 München Tel. (089) 32 03 892 * Mobil (0171) 41 57 304 * Fax (089) 15 92 34 61 Email [EMAIL PROTECTED]
Re: Touching Time
In einer eMail vom 2.7.2004 18:38:46 Westeuropäische Sommerzeit schreibt [EMAIL PROTECTED]: So, you don't need the magnifying effects of a glass spherein order to feel thetemperature difference. The sun alone is strong enough. In Tucson. --Art Carlson
Re: Historical determination of the astronomical unit (again)
Thanks for the replies, but ... The geometry and the calculations are not hard, but I question the possibility of a significant observation. Aristarchus of Samos claims 18D20. That implies an astounding ability to determine when the Moon is exactly halved. If you draw a line between the poles of the Moon, then the shadow cannot depart from this line by more than 1/800th of its length!* Does anyone out there believe that Aristarchus was capable of observations with this kind of accuracy? (By daylight, I might add.) To distinguish the true value of 1/400within a factor of tworequires the same accuracy. Maybe the observation was misreported and was intended to be a lower limit, 19 D, but then we still have the question of how Copernicusand Halley did so well. Still unhappy, Art Carlson * The mathematical details: The method assumes that the angle Earth-Moon-Sun is 90 deg. An error in this angle translates directly into an error in the angle Moon-Sun-Earth, reported to be between 1/18 and 1/20 (radians), that is, 1/19 +/- 1/400. If the angle Earth-Moon-Sun is off by 1/400, then the center of the shadow line is 1/400th of a Moon radius to the left or right of the straight line.
Re: Historical determination of the astronomical unit (again)
In einer eMail vom 13.6.2004 20:50:17 Westeuropäische Sommerzeit schreibt [EMAIL PROTECTED]: 1. How does it solve for the astronomical unit, the absolute distance from the earth to the sun? I understand that it solves for the ratio of the distances earth to sun and earth to moon, but not the absolute distance. There is no base line to triangulate for actual distance. Right. You still need to factor in the distance to the Moon. There is a baseline for that, namely the diameter of the Earth. I have to admit I'm not clear on the details, though, and it might prove as difficult in practice as the other problem, once you start thinking about it. 2. How does it demonstrate heliocentricity? The moon rotates around the earth but are not the trianglesthe same if the sun revolves around the earth or the earth resolves around the sun? It doesn't really, except very indirectly. If you argue (with Aristotle?) that the Earth is too big to move, then, if the sun is umpteen times bigger, then it must really not move. (Which is not such a bad argument, when you get down to it.) --Art Carlson
Historical determination of the astronomical unit (again)
Aristarchus of Samos (?310-230BC) used the shadow line of the moon to estimate the distance to the sun. According tohttp://www-astronomy.mps.ohio-state.edu/~pogge/Ast161/Unit3/greek.html, he "Showed geometrically that the Sun was at least 20x further than the Moon. Really 400x further: sound method, poor data." According tohttp://www-astronomy.mps.ohio-state.edu/~pogge/Ast161/Unit4/venussun.html, this corresponds to8 million kilometers, compared to the true value of 150 million. The second web site above also refers to an estimate of87 million km by Copernicus in 1543 and one of 111 million km by Edmund Halley in 1716. All of this before measurements of the transit of Venus. And as far as I can figure out, the transit of Mercury was too difficult to be of any use. Did Copernicus and Halley use the method of Aristarchus, but with more careful observations, or is there some other method that can be applied without a telescope but which is more accurate? --Art Carlson
Transit of Venus: and another thing I don't understand ...
Why was the transit of Venus - really - so important in the determination of the size of the solar system? Although a transit of Mercury has a less favorable geometry, i.e., all other things being equal the accuracy is less, it happens all the time. Wasn't it used? Coulnd't the frequency of measurements make up for the accuracy? And what about measurements of Mars? I would expect that precise measurements of Mars relative to background stars would be easier than Venus relative to the Sun. Or is the decisive trick converting a measurement of angle to a measurement of time? And what was the first ever method used? That using the Moon? (Trangulate from different points on the Earth to the Moon and then triangulate to the Sun by observing the edge of the shadow line on the Moon.) Thanks. --Art Carlson
Re: calendar
BTW, I have the formula for working out Easter if anyone's interested. *The* formula? The Catholic and Orthodox churches celebrate Easter on different dates because they use different formulas. At least they both use formulas (I believe). Astronomical definitions are also possible, which would be more complex still. --Art Carlson
Re: Birthday Challenge
You write, Foucault's Pendulum may be a good demonstration of rotation but can we call it a proof? I have yet to see one provide consistent long term information? It is too subject to minor perturbations to show anything other than the latitude effect. The solar/sidereal difference noted by David Bell would be very hard enough to detect. Precession determination with such an instrument would be impossible. Simple experiments with the Foucault Pendulum continue to give perplexing results. When a Nobel Laureate observed the period changing rapidly during a solar eclipse, there was something funny going on. When this ""Allais Effect" was replicated by multiple independent observers, NASA got interested. The problem has not been resolved. The same goes for the Coriolis Effect. Did you ever actually try the sink drain / rotation experiment? The challenge remains. Can we prove the earth moves with a sundial and similar naked eye observations? If you want a naked eye result, then you need a phenomenon that occurs on the same time scale as the rotation. If you go to enough trouble you can keep a pendulum swinging for several hours, so that works. It is also direct enough that I'm willing to call it a proof of the Earth's rotation, convincing enough even for honest sceptics. The sink drain doesn't work because it takes only a few minutes to drain. Even tornados get whipped up so quickly that they can turn either way. Hurricanes brew over weeks, so they have plenty of time to be decisively influenced by the Earth's rotation. By the same token, a proof of the Earth's revolution about the sun would require a phenomenon on the time scale of a year, which we just don't have on Earth, other than the seasons themselves and maybe some ocean currents or glaciers. And if you had a slow scale phenomenon sensitive to rotation, you would always be swamped by the daily rotation. In other words, I concede defeat when it comes to finding a naked eye proof of the Revolution about the sun. But back to the daily rotation, are you saying you don't think a Foucault pendulum is convincing, naked eye proof of the Earth's rotation? Can you give any more details on these "unresolved problems"? OK. Google has thousands of references, once I realized that "Allais" was not a misprint of "Alias". I haven't looked at much of it yet, but I'm willing to bet the farm that it's Schmarn. Either way, I don't think it significantly weakens the status of the Foucault pendulum. It is admittedly a bit more difficult, but don't you think hurricane directions, given sufficiently many reliable naked eye observations, is a convincing proof? If you are looking for a purely kinematic proof, like sundials and records of planetary motion, then it is a mathematical triviality that the motion of everything can be described in the frame of reference of the Earth. Cheers, Art
Re: Birthday Challenge
W, the Foucalt Pendulum would prove that the Earth rotates, but I don't think it gives any evidence that it revolves about the Sun. What could we do to take it a step further? It does in principle, but it would be hard to get the accuracy. Other things, like parallax and astronomical aberration, are also impossible to measure with 15th-17th century technology. But I'm sure once you convinced people with a Foucault pendulum that the Earth moved *at all*, it would be only a small step from accepting rotation to accepting revolution. Art Carlson P.S. I can't leave that loaded pun lying around where children might play with it: The revolution was the rotation. Once that was accepted, the revolution (of the Earth around the sun) was no longer a revolution (in world view).
Re: Birthday Challenge
Thinking again about Foucalt's pendulum, I realize you're right: It makes a full turn (if situated at one of the poles) in a sidereal day, doesn't it? That would put it "off" a full day each (solar) year. What does happen at the equator, say? Simple geocentric mechanics would have the pendulum swing in an ideal straight line, if I recall. Does the annual motion introduce a small diurnal rotation, further reduced by the sine of the Earth's axial tilt? Accuracy in the mechanics of the pendulum would be overwhelming, but this *is* a thought experiment... I was thinking about the extra turn every year. With 20th century technology it would be no problem. I remember a talk around 1980 from a physicist who was thinking about setting up a Foucault pendulum at the South pole with sufficient accuracy to measure relativistic frame dragging. That's something absurdly small like an arc second per year, but that would be on the order of the accuracy he calculated. Actually he begged somebody to point out some effect that would make the measurement impossible so he could stop thinking about it and do something useful instead. Now satellites are doing the job, which is probably a better idea since they are cleaner in terms of systematic errors. The idea of putting the pendulum at the equator is interesting. The rotation of the Earth would not affect it, as can be shown already by symmetry, but the tilt of the Earth could result in a residual effect from the revolution around the sun. I'm not sure it really does, because the twist during the night should be in the opposite direction from that during the day. There are lots of proofs of the Earth's motion around the sun with 20th century technology, but I can't think of any that would work, even in afterthought, with renaissance, i.e., naked eye technology. In other words, from the perspective of a modern physicist, I can't think of any advice I could give Copernicus or Galileo to make their case other than a Foucault pendulum. Even then, they would face some major difficulties reliably eliminating systematic errors and explaining why the rotation of the plane of the pendulum takes a day and a half. One more thought: You could try putting together on argument based on the direction of rotation of hurricanes in the Northern and Southern hemispheres. Did early mariners like Magellan and Columbus realize that tropical storms have a certain sense of rotatation depending on the hemisphere? And when did artillary experts start to notice that projectiles curve over long distances? --Art Carlson
Re: Birthday Challenge
There is no proof that can be observed with the naked eye that the earth is not the center of the universe. The motions of the sun moon and planets, including the equation of time, tides, eclipses etc., are all adequately described by the geocentric model. We do not need to accept the revolutionary ideal of Copernicus. The heliocentric theory of Copernicus and Kepler cannot be demonstrated without resorting to magnifying instruments. Is anyone willing to take on this ancient challenge? The tides, especially the tidal bulge opposite the sun/moon, would do, but their description required a couple centuries and some of the greatest minds of science. My favorite would be a Foucault pendulum. It takes some care, but it's basically middle age technology. The quantitative explanation is tricky, but I think it makes it pretty clear that the Earth is spinning. Apparently there were contemporaries of Galileo who built such things but never understood their significance. --Art Carlson
Re: Reverse Engineering
I used Photoshop's image distortion, skew and perspective features extensively to "fix" many of the photos on the site so that it looks like the camera was centered in front of the center of the dial faces. Keep in mind that the gnomon in the processed picture will be "funny". If you only use the hour lines to calculate the latitude you will be OK. I think it should also be possible to determine the latitude from the gnomon without reference to the hour lines. You will still need to use clues about the vertical and horizontal, and you will need both the free edge of the gnomon and the line where it intersects the plate, plus the assumption that it is perpendicular to the plate. --Art Carlson
Re: Sundial inside a room, but room is inside a canyon!
This led me to consider an offshoot of the skylight concept. Some of my neighbors have installed a "solar tube" which provides a skylight effect in a remote room by reflecting the sunlight down the shiny inner wall of a tube roughly one foot in diameter. The light emerges at the lower end of the tube. It emerges quite brightly, I might add. I originally hoped I could install such a tube, mount a sundial beneath the lower end and watch the time go by from the comfort of my family room. I don't think it's that simple, though. If the sun's instant by instant azimuth and elevation in the sky is "information," then that information must get completely garbled up and lost as the rays bounce their way down the pipe. You don't want a tube, but a box. If you set up a rectangular prism so that sunlight can get in the top and out the bottom in your living room, then the rays will exit at the same angle they entered. (The prism need not be vertical.) Well, actually only those rays that make an even number of reflections from each pair of parallel faces will emerge in the same direction they entered. If you want to eliminate the rays emerging in the three wrong directions, you will have to get clever. The other solution is to use imaging optics. Put a small mirror near the "canyon rim" and another in your living room or just outside the window. Focus the image of the first mirror onto the second one with a lens or concave mirror. The first problem is that the f-number of the mirror must be small to catch the sun over most the day, so it will have to be very close to the first mirror. The angular deviations of the rays at the second mirror will then be very small, but you can either design the readout appropriately or re-expand them with another lens or spherical mirror. You must also be careful to keep the small mirrors near the axis of the focussing element to avoid distortion. Fiber optics is certainly a way of preserving and transmitting the information for use at a remote location. But is there another way? Could the incoming light be polarized -- maybe in four sectors for N, E, W, S information -- to preserve the azimuth and elevation in its travels down the tube? Could some esoteric principles of radar be invoked to usefully tap into the information at various points along the tube, or at the end? (All I know about radar is that the microwave energy bounces around in hollow waveguides and the practitioners of the black art are able to somehow work magic with it.) Fiber optics are the equivalent of radar waveguides for light. Both are usually, though not necessarily, operated in single-mode, in which case, as you say, the information they are capable of transmitting is limited. My first suggestion of a reflecting box can be considered a multi-mode waveguide that is capable of preserving some angular information. Have fun, Art Carlson
Re: Dial design
I give an explanation of this ill-behavior in my website: www.fransmaes.nl/sundials, choose Index and goto Kvaerndrup. I think I have a quantitative handle on this now. So we don't have to worry about hyperbolic surfaces and such, let's simplify the twisted strip by removing everything except the edges. Now we have a double helix, and it is easy to see that this is still a proper sundial at the equinoxes. You just have to read the time from marks on one of the helices at the point where the shadow of the other helix crosses it. If the sun is at a declination d, then this shadow is moved parallel to the axis by a distance w*tan(d), where w is the width of the original strip. If this distance is not too far compared to the period of the twist, the point where the shadow crosses the other helix will move by half this distance. Since one full period L corresponds to 24 hours, we have a false reading by (24 hrs)*0.5*w*tan(d)/L. For d=23.5 degrees and w/L=1/8, this gives 39 minutes. The Moir model cited in the Web site above showed a maximum discrepancy of 25 minutes. OK, it's not exactly high precision agreement, but it's close enough for government work. I did some more algebra on the Sun Daggers, but got nothing essentially new except to verify that, if the slits are oriented so that a horizontal movement of the sun results in a pure vertical movement of the spot of light, there is indeed a term left over that shifts this path horizontally as a function of the declination. The spot will cross a horizontal line (or a spiral petroglyph) at a different time of day, though. As far as designing a new type of sundial, I have practically reduced the Sun Daggers to a bifilar dial. I have never understood how these work either, but at least I now know how to approach the problem. --Art Carlson
Re: Dial design
I did spend some time on the maths and, if you get it right, then each surface is actually required to bend in only one direction at any point so bending should work. Good point about lumps, bumps and other irregularities though. This isn't a problem with 60 thin hexagonal sheets, of course, but them you have to align each one correctly, 8 degrees with respect to the one below - not a trivial taks I think. I have my doubts. The edges of a spiral sheet are longer than the midline, so some streching, not just folding, will have to be done. I gave this question some more thought. What you probably proved is that there is a direction in which there is no bend, and then you assumed that meant all the bend is in the orthogonal direction. But a surface with negative curvature, like a saddle, actually has two line along which there is no curvature. For the surface z = xy, for example, these lines are the x- and y-axes. That the surface around the origin is nevertheless curved can be seen by examining the x = y and x = -y lines, which are curved convex upwards and convex downwards respectively. Around a point on the surface of a twisted band, there is no curvature in the radial direction and none in the circumferential direction. (By "circumferential" I mean the helical curve in the surface with a constant distance from the axis.) That the surface is nonetheless curved like a saddle can be seen by looking at the local tangent plane (the plane defined by the two lines without curvature). Since the circumferential spirals get steeper as you move toward the axis and flatter as you move out, the first and third quadrants will buckle one way and the second and fourth quandrants will buckle the other way. (Well, it's clear to me!) I'm still working on the implications for the sun daggers. Wish me a few insomiacal nights and I'll have it. --Art Carlson
Re: Dial design
Hi Richard, It seems you have reinvented Piet Hein's helical dial. See the home page of Egeskov Castle, http://www.egeskov.dk/english/sightseeing/index.htm and click nr. 25 on the map or in the list below it. John Moir showed already that the dial does not function well outside the equinoxes in BSS Bulletin 95.1. I give an explanation of this ill-behavior in my website: www.fransmaes.nl/sundials, choose Index and goto Kvaerndrup. Regards, Frans Maes 53.1N 6.5E Back to my latest hobby horse, do you see how your explanation applies to the Sun Daggers? Is a helical gap fundamentally different from a helical band? Is it possible to control this effect such that the spot of light has different horizontal positions depending on the declination? It's still a bit too complicated for my brain without making models or programming computers (but I afraid it's going to come to that). --Art Carlson
Re: Dial design
I've just realized, thinking about it again, that the simplest realization of a 'helical' dial is a single sheet of metal given a half-twist of 180 degrees. So long as the edges are straight and the twist is distributed uniformly then the desired "line o'light" effect will be achieved. And so we converge with the Sun Dagger thread. Like the rock slabs on Fajada Butte, your spiral converts a "horizontal" movement of the sun into a "vertical" movement of a shadow, a neat trick. What has me worried is the effect of a "vertical" movement of the sun, i.e., the seasonal change in declination. With a spiral having a finite period, won't the declination introduce an offset in the time? I did spend some time on the maths and, if you get it right, then each surface is actually required to bend in only one direction at any point so bending should work. Good point about lumps, bumps and other irregularities though. This isn't a problem with 60 thin hexagonal sheets, of course, but them you have to align each one correctly, 8 degrees with respect to the one below - not a trivial taks I think. I have my doubts. The edges of a spiral sheet are longer than the midline, so some streching, not just folding, will have to be done. --Art Carlson
Re: Two links to Sun Dagger of Chaco Canyon Re: Stab Dial
* For example, at summer solstice, during the 18 minutes when light shines through the right gap, the sun has moved 4.5º westward almost horizontally across the sky. We would at first glance expect the projected pattern of sunlight to move horizontally across the spiral, shifting to the right on the cliff face. The observed vertical motion is thus in itself surprising. A simple way to picture how this downward motion is effected is as follows: Imagine a long narrow cylinder so oriented that the sun as it moves across the sky can shine through it only briefly onto the cliff to form a spot of light. Immediately below, picture a second cylinder so aligned that sunlight passes through it just as it stops shining through the first one, and now casts a second spot of light immediately below the first. Then continue in a like manner with further cylinders. The result will be that a succession of spots will appear on the cliff, moving downward as the sun moves horizontally. If the cylinders are now joined to form a continuous curved slit, the spot of light on the cliff will move smoothly downward. More generally, a form of light, rather than simply a spot, can be made to move vertically in a similar manner. Close inspection of the slabs shows that the front left edge of slab one and the right rear edge of slab two form just such a curving slit. * I draw particular attention to the sentence, "The observed vertical motion is thus in itself surprising." My interest in this topic was not initially acheoastronomy but geometry: How can any combination of solid forms cast shadows in the way described? I explained my way of looking at it and why that wouldn't work and asked the group if I was missing some "higher order effect". I was, namely that described above. The only remaining question in this context is whether this effect can be, or perhaps already has been used to create a sundial. The issue of the accuracy of the "18.6 years" is also blunted by reference to the spiral as having "nine and a half turns", suggesting an accuracy of (9.5 +/- 0.25) X 2 = (19 +/- 0.5). This seems halfway reasonable both in terms of the difficulty of counting spirals pecked in stone and that of making astronomical observations. Not the most accurate but the most natural way to measure a cycle is to count the time from one maximum to the next. The maximum is, however, hard to determine exactly. Say that two cycles are reasonably easy to distinguish when they are out of phase by 1/8 of a period. With this criteria, we can distinguish between a 19 year cycle and an 18.5 year cycle after (1/8)*1/(1/18.5-1/19)=88 years. This is a good long time, but not out of the question for a civilization that lasted, what, 400 years? I am willing to believe that the Anasazi knew about the lunar cycle. I still insist they could scarcely have known its length to one decimal place of accuracy: "The creators of the Fajada lunar markings did not necessarily know the standstill cycle to any better accuracy than approximately a year." --Art Carlson P.S. I'm sorry if my insistence, or the mode of my insistence, on a detailed explanation ruffled any feathers.
Re: Two links to Sun Dagger of Chaco Canyon Re: Stab Dial
My interest is personal, not professional, so I can't answser most of your questions. My educated guesses are no better than your educated guesses. For the physical structure and possible history of the petroglyphs: http://www.angelfire.com/indie/anna_jones1/sundagger.html Good site, It answers my questions pretty well. (At least the first round.) 1) The openings are the spaces between slabs, with a width of about 10 cm and a depth of 70 to 100 cm. This implies that the sun could shine between them for about an hour a day, reasonably in line with (or, as we scientists like to say, "not necessarily inconsistent with") the figures of 25 minutes and 3 hours cited. 2) The site faces south and the sun and moon shine through the slits when they are high in the sky. With this geometry, how should the dagger/sopt-of-light/inverse-shadow behave? On any given day, the dagger will start as a thin line. During the next half hour (or so) it will get thicker and move perpendicular to its direction. During the half hour after that it will keep moving but wane back to a thin line. During the course of a year, the dagger will take a path higher or lower on the wall according to the geometry of stones that we don't know much about. My problem is that this description is not consistent with the statements associating the horizontal position of the dagger with various times of year. If there were a thin slit facing east or west, then I could understand the dagger at the moment of sunrise or sunset being farther left or right depending on the time of year, but with a thick slit facing south, the dagger should appear and disaapear every day at positions determined by the geometry of the slit, independent of the height of the sun. Is there a higher order effect I am neglecting? (An alternative is that the photographers are taking the pictures that look most like what they want to see.) My "educated guess" is that the Sun Dagger and "18.6" year spiral were not calculated. The "astronomers"--who probably also were religious leaders--of the time were probably recording their observations for future reference. ; The Sun Daggers seen shining on the rock wall at already important times of the year were used to create the petroglyph in this location. Not the other way around. This is consistent with the information that the slabs, however unusual, are a natural formation. My opinion is that many archeoastronomy sites were observational in origin. I still agree that this is a type of stab dial. As you have probably noticed, I have my doubts. Not that the Anastazi counldn't have had astronomical observatories. I would even say they must have. It would also surprise me if they didn't know anything about the 18,6 year lunar cycle. But I think there is reason to doubt that the Fajada Butte site is evidence for any of this. --Art Carlson
Re: Two links to Sun Dagger of Chaco Canyon Re: Stab Dial
In regards to the spiral representing 18.6 years (and not 18.5 or some other close number), I believe the answer is that the observations are directly tied to the 18.6 year cycle. So, if the observations were properly recorded, the spiral would indeed represent 18.6 years. Albert Franco Do you see why I'm uncomfortable with the reasoning here? Somebody finds a spiral and counts 18 or 19 rings and asks if that could mean something. Somebody else points out that it could be related to the 18.6 year lunar cycle. A third person hears there are 18.6 rings and thinks, that can't be a coincidence that there are *exactly* the same number of rings as in the lunar cycle. That *proves* that they knew about it and created this site to commemorate it. It gets even worse because to clearly differentiate between an 18.6 and and 18.7 year cycle would require thousands of years of observations, so suddenly we have a civilization on a par with the Egyptians, capable of passing on astronomical observations for a hundred generations. And all that based on a washed out spiral that might have 18 or maybe 19 or even 20 rings, depending of whether that depression is part of the petroglyph or just a rough place in the rock. --Art Carlson
Re: Two links to Sun Dagger of Chaco Canyon Re: Stab Dial
The photo at top of the linked page makes me feel certain that the petroglyph was intentionall drawn to represent the location of the Sun in the sky. Then the photo has fulfilled what I believe to be its purpose, namely to make you feel certain of that. If my arguments are correct, a very similar photo can be made over much of the year. These other photos are not published because they could make you certain that it is all a coincidence. They would not be considering the 18.6 year cycle as such. They would merely be observing where the moon was, and that its position was cyclic. ... It would only take one lifetime to make such observations. You could certainly observe in one lifetime that there was a cycle. To determine in a mere lifetime that the cycle was closer to 19 than to 20 years would require some very precise observations and sophisticated analysis. --Art Carlson
Re: Two links to Sun Dagger of Chaco Canyon Re: Stab Dial
Photos of the Sun Dagger at various times can be seen here: http://www.cpluhna.nau.edu/People/sw_archaeoastronomy.htm The following page gives a concise description of the Sun Dagger in relation to Sun and Moon. http://paganastronomy.net/nahist.htm At Chaco Canyon, we find the most famous sun clock known. Discovered in 1977, the site includes two petroglyph carvings of spirals. The larger spiral has 18.6 grooves, representing the 18.6 year lunar standstill. At the summer solstice, sunlight causes a shaft or "sun dagger" of light to fall onto the large petroglyph spiral on an inner rock wall. At the winter solstice, two daggers appear on the spiral [46]. Summer solstice: Single dagger appears through center of large spiral Winter solstice: Two daggers bracket the large spiral Equinoxes: Single dagger appears through center of small spiral Lunar northern extreme: Moonlight shadow falls on first groove on large spiral Lunar southern extreme: Moonlight shadow falls on center groove on large spiral I haven't understood this yet. Can somebody help me? 1) How deep are the openings through which the light shines? Are they more like a narrow window or more like a separation between two slabs? Does light pass through for just a few minutes a day or for many hours. 2) Are the observations reported made at sun/moon-rise or at "noon-day"? (http://www.colorado.edu/Conferences/chaco/tour/fajada.htm refers to "noonday", "midday", and "moonrise".) Does the light enter through the same slit for all the observations? These are my main questions. Depending on the answers, I have other questions about how this is supposed to work. In addition, I have a couple secondary questions: 3) What process caused a "settling" between 1977 and now that spoiled the alignment, but which was apparently not active the 7 centuries before that? 4) How can the endpoints (especially the inner endpoint) of a spiral in rough stone be determined to be 18.6 revolutions, as opposed to, say, "about 18 and a half"? Thanks, Art Carlson
Re: Plekhnatons (slightly off-topic)
Quoted from a Google search of the encyclopedia Wikipedia: Plekhnatons The ancient Greeks used a type of sundial called a plekhnaton. The gnomon was a rod or pole upright in a horizontal face or half-spherical face. The shadow of the tip of the rod sweeps out hyperbolic curves on a flat face, or great-circles on a spherical face. The advantage of a plekhnaton is that it can be marked to tell the exact time for all times of year. A fun version of the plekhnaton is to lay out the hour lines on concrete, and then let the user stand in a square marked with the month. The month squares are arranged to correct the sundial for the time of year. The user's head then forms the gnomon of the plekhnaton. If the sundial is molded into the concrete, it is almost perfectly immune to vandalism, as well as truly fun and reasonably accurate. Quite a few mistakes in there, now, aren't there? For starters, lines cast in concrete can only be exact, in the sense of accounting for the equation of time, for half the year. Second, there is confusion between using a nodus (a point shadow-caster) and using a vertical gnomon (a line shadow-caster). Only the latter can/needs to be corrected for the equation of time by moving the gnomon (analemmic dial). Finally, using someone's head as a nodus is a bad idea since we are all different heights. With an analemmic dial it doesn't matter because it's not the tip of the shadow but the direction of the shadow that matters. --Art Carlson
Idiot Savants
There's a question I've been pondering for years now, maybe somebody can help me. You know that idiot savants are rare individuals with extraordinary ability in one narrow area, and often intellectually and emotionally deficient in all other areas. A common form of this phenomenon is the ability to do calendrical calculations, such as finding the day of the week of a given date or the date of Easter in a given year, for dates even thousands of years in the future or the past. This is certainly impressive, but as we on this list know, the question is ill-posed. Is that the Gregorian calender forever, or do they take the transition from the Julian calendar into account? This transition is different for different countries, and there have been numerous other changes in the (Western) calendar over the centuries, and often several calendars have been in use in a given area at the same time. Easter is even more difficult. Roman Catholic or Orthodox (Greek or Russian)? Even within one church, Easter has been celebrated every year, but the algorithm used to decide the date, whether mathematical, astronomical, or political, has often changed. Do calendar savants know (passively or actively) anything about all these issues, or do they simply apply the currently used algorithm blindly into the indefinite past and future, or perhaps even memorize the dates? Thanks for the peace of mind. Art Carlson P.S. I have a similar set of questions about savants with mathematical abilities, like recognizing prime numbers.
Re: How do we call the equinoxes?
BUT... is anything unbiased??? I think that the calendar months are season neutral? They don't seem to have the right ring though, in English anyway. Whatever you settle on, make it something I am able to remember, or figure out when I hear it. I am just able to remember that "vernal" has something to do with spring, so that must mean the equinox in March. (Actually, I know less than this, namely, that the other one is called "autumnal", which means fall, so this one must be spring.) To get around the chauvinism (All this standing on my head to understand our friends from down under confuses me, too.), why not short circuit my thought processes and call them the "March equinox" and the "September equinox" from the beginning. It's not as elitist as some Latin or Babylonian name, but, hey, I'm American! --Art Carlson
Re: Low moon
Here, in our planetarium, we often say that the Moon is running on the Sun's path, 6 months later. summer : Sun's high, Moon's down winter : Sun's down, Moon's high in the sky; It's an easy, but not too wrong tip for non-astronomical public. It may not be "too wrong", but it is wrong. I'm not talking about the few degrees tilt of the plane of the Moon's orbit. Even ignoring that, your statement is only true for the full moon. At new moon, for example, the Moon is running on the current path of the sun, not that delayed by six months. Psychologically, it makes some sense, since we care less about the moon when it is "small" and when it is being out-shined by the sun. And you certainly run a risk of losing your public if you try to explain too much. But my nit-picking mind would be more comfortable if you would at least change "Moon" to "full Moon" (the restriction to be immediately forgotten by 99.9% of the public). --Art Carlson
Re: Equatorial monument in Brazil
That's a horse of a different color. Then you have a geometrical image of the hole rather than a pinhole image of the sun. The lack of "perfection" remains, but is no longer so apparent. Now you might want to ask for how many days around the equinox the image stays "pretty much" on the line. The deviation will be largest near dawn and dusk. Let's use 7 AM and 5 PM as reference times and 65' as the height, so the horizontal projection distance is 65'/tan(15 deg) = 240'. An offset of a quarter diameter -- 2' -- should be quite noticeable. That corresponds to an angle of 2/240 = 8.3 mrad = 29 arc-min, nearly equal to the change of declination in one day. It is also nearly equal to the angular diameter of the sun, so the image will be rather washed out at that distance. All in all, you should be able to determine the exact day of the equinox. That's close enough to perfection to leave me impressed. I'd love to see it in action. --Art
Re: Equatorial monument in Brazil
Hold still, I think I see a nit! The rate of change of the declination at the equinoxes is 24 arc-minutes per day, approximately equal to the size of the image of the solar disk, so if the spot is perfectly centered on the line at dawn, by dusk it should be nearly off one side. Actually, this is cool, because it means with appropriate and painstaking observations you can determine the moment of the equinox to within a few hours. Art Carlson
