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sundial & Earth's tilt questions
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sundial & Earth's tilt questions
"cgbusch" wrote in message om... Horizontal Dials The plane of the shadow-receiving surface is horizontal. Equatorial The plane of the shadow-receiving surface is parallel to the equator. Analemmatic Time is told by the sun's azimuth on a specific date. With horiz dials the face is a flat plane cut through a cylinder at the angle of the latitude. With an equatorial dial, the dial is at the angle of the latitude. My question is this, should the tilt of the Earth along its rotational axis (23.45°) be included? With an Equatorial dial, if you are at 45 deg lat, and it is winter, shouldn't the dail be set up varying from 68.45 deg in the winter to 21.55deg in the summer? Sundials are generally fixed permanently, you don't vary the orientation. You can make a sundial face for any angle you choose but the term "Equatorial dial" specifically refers to one that is parallel to the plane of the equator. George |
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sundial & Earth's tilt questions
"George Dishman" wrote in message ...
"Oriel36" wrote in message om... To prove that axial tilt does not have any effect on the Equation of Time involves a quite easy and inexpensive experiment involving only a sundial,a stopwatch, a clock and the Equation of Time correction tables which gives a value for each day of the year. The tables are produced using the tilt, you cannot calculate the correct values without it. Using only the factor due to the elliptical orbit you get a single peak: I had a look at the modern values against the values used by Roemer and they are different,the modern value gives a positive value for Oct 24th while it was a negative value in Roemer's calculations.I understand the value in context of the insight of Roemer and subsequently Newton's definition of the distinction between absolute time and relative time as the Equation of Time and as addition and subtraction of minutes are involved,it should be taken as a given that the Equation of Time parameter should be made distinct from the sidereal parameter. http://dibinst.mit.edu/BURNDY/OnlinePubs/Roemer/chapter3(part2).html http://www.jgiesen.de/SunView/ http://www.analemma.com/Pages/Ellipt...OrbitMath.html The full equation has two peaks: http://www.analemma.com/Graphics/sum...inedCharts.GIF The analemma is generated by putting clocks in the driver seat off civil time but the original use of the Equation of Time and the correction from natural noon to clock time involves the appropriate addition and subtraction of minutes as a planetary meridian aligns with the Sun depending on where the Earth is in its annual orbit,again AM and PM reflect the original determination of 24 hours off the inequality of natural noon to natural noon,there is nothing more basic and it has nothing to do with axial tilt.All that matters was the alignment regardless of latitude and it is good from pole to pole. George p.s. have you found out how to use Kepler's Second Law yet? George,I looked at your last posting in a different thread and you do something I would never do.I have kept this at a level of the relationship with the planet wrt the Sun and the difference between axial rotation and the difference in the distance the Earth covers in its annual orbit as the axial alignment to the Sun repeats itself (noon) and how this reflects the Equation of Time and ultimately the relationship between clocks,geometry and astronomy.Anyone who comes to know the intricate relationship will well acknowledge what Newton was saying in terms of the difference between absolute and relative time as the astronomical correction known as the Equation of Time,even a hasty glance at Roemer's work will show the principle in action.You think you are doing everyone a favor by bringing the stars and the sidereal parameter into it but if it comes down to that perhaps the discipline of astronomy is truly destroyed for against insincerity there is no amswer. "Absolute time, in astronomy, is distinguished from relative, by the equation or correlation of the vulgar time. For the natural days are truly unequal, though they are commonly considered as equal and used for a measure of time; astronomers correct this inequality for their more accurate deducing of the celestial motions." Principia By right any astronomer would recognise the definition/distinction for what it is but without the Equation figures from Newton's era your concept, that destroys the distinction, survives for another day. |
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sundial & Earth's tilt questions
There seems to be some debate here as for the influence the elliptical
orbit and axial tilt of the Earth has on a sundial. I don't believe the axial tilt will affect the noon time from day to day. From Kepler's 1st and 2nd laws, with Earth's orbit, the Sun is at one focal point. This varies the distance and speed at which the Earth orbits. Hence, the 2 unequal "peaks and valleys" in the Equation of Time. (http://www.school-for-champions.com/science/orbit.htm) Remember, a horizontal sundial has to be crafted specially for a latitude... Imagine a magical cylinder of cookie dough log straight from the Sun to the Earth. If you cut the log straight, you will notice 24 lines emanating from the center of the log at perfect 15 degree intervals (hour lines). If you cut the log at an angle, the lines would not be at 15 degree intervals to the diagonal plane. For this reason, the hour lines are not evenly marked on a horizontal sundial (except at the equator). The axial tilt can change the declination of the sun. This could change the accurate spacing of the hour lines. So axial tilt doesn't affect noon, but makes the other hours less accurate. I think that for a sundial to be most accurate, it needs to be set perpendicular to the orbital plane of the Earth (plane of the ecliptic). (http://www.wikipedia.org/wiki/Axial_tilt) One thing that I am also thinking about, is during the fall and spring (for example), the sun will not travel across the sky directly east and west but at an angle. I would presume on Equinox, an Equatorial dial set up exactly, would have one face lighted in the morning and the other in the afternoon. Comments? |
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sundial & Earth's tilt questions
In article ,
cgbusch wrote: There seems to be some debate here as for the influence the elliptical orbit and axial tilt of the Earth has on a sundial. I don't believe the axial tilt will affect the noon time from day to day. You believe wrong..... It often helps one to understand if one considers an extreme situation. So let's for a moment imagine that the Earth's axial tilt was exactly 90 degrees. What would happen in such a case? Let's follow the Sun from the Vernal Equinox (in the northern hemisphere), assuming the Earth's axial tilt is 90 degrees: at the Vernal Equinox the Sun is at 0h RA and 0d Decl. Then it moves straight northward, remaining at 0h RA. The sidereal day and the solar day will have the same length --- until the northern Summer Solstice, when the Sun will cross the North Celestial Pole. Then something dramatic will happen: the RA of the Sun will suddenly jump from 0h RA to 12h RA --- and the moment of true solar noon will likewise suddenly jump by 12 hours. For the next half year, the Sun will have RA = 12h as it travels southward, until the Winter Solstice, when the Sun will cross the South Celestial Pole and another sudden jump of 12h in both the Sun's RA and the noon time. Thus, at least for an axial tilt of 90 degrees the noon time will be affected by the tilt. And in fact, the noon time will be affected by any non-zero tilt, although the effect will be less dramatic for lower tilts. Therefore, for the Earth's actual 23.4 degree tilt there will be no dramatic sudden jumps in the noon time, but merely gradual changes. From Kepler's 1st and 2nd laws, with Earth's orbit, the Sun is at one focal point. This varies the distance and speed at which the Earth orbits. Hence, the 2 unequal "peaks and valleys" in the Equation of Time. ....and if the Earth's orbit had been circular, these two "peaks and valleys" would have been equal, and due to the tilt of the Earth's axis. And if the tilt of the Earth's axis was zero, there would only be the effect of the Earth's elliptical orbit, which would produce only one "peak and valley" per year. (http://www.school-for-champions.com/science/orbit.htm) Remember, a horizontal sundial has to be crafted specially for a latitude... Imagine a magical cylinder of cookie dough log straight from the Sun to the Earth. If you cut the log straight, you will notice 24 lines emanating from the center of the log at perfect 15 degree intervals (hour lines). If you cut the log at an angle, the lines would not be at 15 degree intervals to the diagonal plane. For this reason, the hour lines are not evenly marked on a horizontal sundial (except at the equator). The axial tilt can change the declination of the sun. This could change the accurate spacing of the hour lines. So axial tilt doesn't affect noon, but makes the other hours less accurate. The axial tilt does not affect the direction of noon of course (which always is precisely towards the South --- or towards the North if you're in the southern hemisphere. But it does affect the time of noon. I think that for a sundial to be most accurate, it needs to be set perpendicular to the orbital plane of the Earth (plane of the ecliptic). (http://www.wikipedia.org/wiki/Axial_tilt) ....and how would you keep it at that orientation? Remember that the sundial rests on an Earth which rotates along a tilted axis ---- you'd need some clock machinery to accomplish this. And if you'd go to all that trouble, you might as well make a mechanical clock instead. One thing that I am also thinking about, is during the fall and spring (for example), the sun will not travel across the sky directly east and west but at an angle. I would presume on Equinox, an Equatorial dial set up exactly, would have one face lighted in the morning and the other in the afternoon. Comments? You need to reconsider your erroneous idea that the Earth's axial tilt does not affect the noon time or the equation of time. -- ---------------------------------------------------------------- Paul Schlyter, Grev Turegatan 40, SE-114 38 Stockholm, SWEDEN e-mail: pausch at stockholm dot bostream dot se WWW: http://www.stjarnhimlen.se/ http://home.tiscali.se/pausch/ |
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sundial & Earth's tilt questions
"cgbusch" wrote:
I don't believe the axial tilt will affect the noon time from day to day. From Kepler's 1st and 2nd laws, with Earth's orbit, the Sun is at one focal point. This varies the distance and speed at which the Earth orbits. Hence, the 2 unequal "peaks and valleys" in the Equation of Time. Can you explain that? In January, when Earth is at perihelion, closest to the Sun and moving fastest, noon should be at 12:00 on a standard meridian. The next day, noon should come a bit later, since the Earth has moved more than the average amount in that time. By April, the Earth has slowed to its average speed in orbit, and noon should be as late as it gets. The next day, noon should come a little bit sooner. Noon should come a little bit sooner each day for the next six months. By July, Earth is at perihelion, farthest from the Sun and moving slowest. Noon should again be at 12:00. By October, Earth is moving at its average speed again, and noon should be occurring at its earliest time. The next day, noon should come a little bit later. Noon should come a little bit later each day for the next six months. By January, Earth is closest to the Sun again, moving fastest. Noon should again be at 12:00. One minimum, when the Sun is as far behind the clock as it gets, creating a single valley in the graph, in April. One maximum, when the Sun is as far ahead of the clock as it gets, creating a single peak in the graph, in October. Two days during the year when noon is right at 12:00, in January and July. So why are there actually two unequal peaks and two unequal valleys in the graph of the equation of time? Why are there four days during the year when noon is at 12:00? Why are those four days in April, June, September, and December? -- Jeff, in Minneapolis .. |
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sundial & Earth's tilt questions
(Paul Schlyter) wrote in message ...
In article , cgbusch wrote: There seems to be some debate here as for the influence the elliptical orbit and axial tilt of the Earth has on a sundial. I don't believe the axial tilt will affect the noon time from day to day. You believe wrong..... He is correct,the tilt of the Earth may lenghten and shorten the shadow cast on a sundial but it does not affect the pace of the shadow across the sundial.Common sense should tell you that the axial alignment of a planetary longitude meridian at noon when the location faces the Sun directly and when it repeats it is the only factor that counts,tilt the Earth anyway you want,as long as axial rotation is constant it neither accelerates on retards the observed motion of the Sun this being basic mechanics never mind astronomy. It often helps one to understand if one considers an extreme situation. So let's for a moment imagine that the Earth's axial tilt was exactly 90 degrees. What would happen in such a case? This bluster often begs an explanation and diverts attension from the fact that the Equation of Time applies addition and subtraction of minutes and seconds when a longitude meridian faces the Sun directly,because of the natural variation from one alignment to another the addition and subtraction of minutes and seconds brings it in line with a 24 hour clock which is fixed to the longitude meridians. Let's follow the Sun from the Vernal Equinox (in the northern hemisphere), assuming the Earth's axial tilt is 90 degrees: at the Vernal Equinox the Sun is at 0h RA and 0d Decl. Then it moves straight northward, remaining at 0h RA. The sidereal day and the solar day will have the same length --- until the northern Summer Solstice, when the Sun will cross the North Celestial Pole. Why introduce the sidereal parameter when sundials refer only to the shadow cast by the Earth's rotation on its axis and its orbital rotation around the Sun and the question refers only to axial tilt in determination of the noon alignment.You are going to an awful lot of trouble to introduce imaginary tilts and references to the stars for an instrument that makes use of the Earth's rotations, the Sun and the Equation of Time correction which has been known for centuries. Then something dramatic will happen: the RA of the Sun will suddenly jump from 0h RA to 12h RA --- and the moment of true solar noon will likewise suddenly jump by 12 hours. For the next half year, the Sun will have RA = 12h as it travels southward, until the Winter Solstice, when the Sun will cross the South Celestial Pole and another sudden jump of 12h in both the Sun's RA and the noon time. Yeah,something dramatic happened alright,the guys in the early part of the 20th century misread Newton and his phrasing of the inequality of the natural days of longitudinal planetary alignment from one axial rotation to the next,forgot or did'nt know what the Equation of Time does both astronomically and for purposes of navigation and went along with Flamsteed's botch job which included an axial tilt component to justify the sidereal parameter. Were it any less important I would not repeat it for historically accurate clocks were developed as physical rulers of distance in tandem with the Equation and determination of noon.No axial tilt was involved,only the determination of the alignment of the longitudinal alignment with the Sun.It would not have been possible for astronomers to make sense of planetary motion for the purpose of heliocentric modelling without the astronomical correction which removed the natural variation of a day and it was so commonplace in Newton's era that he hardly would expect his readers to make a fuss as he outlines it in terms of absolute and relative time. "Absolute time, in astronomy, is distinguished from relative, by the equation or correlation of the vulgar time. For the natural days are truly unequal, though they are commonly considered as equal and used for a measure of time; astronomers correct this inequality for their more accurate deducing of the celestial motions." Principia As clocks are rulers of physical distance,spacetime freaks as yourself can't have your silly 4th dimension bottled up in a clock but it all hinges on how you interpret Newton and his phrasing of the Equation of Time. Thus, at least for an axial tilt of 90 degrees the noon time will be affected by the tilt. And in fact, the noon time will be affected by any non-zero tilt, although the effect will be less dramatic for lower tilts. Therefore, for the Earth's actual 23.4 degree tilt there will be no dramatic sudden jumps in the noon time, but merely gradual changes. From Kepler's 1st and 2nd laws, with Earth's orbit, the Sun is at one focal point. This varies the distance and speed at which the Earth orbits. Hence, the 2 unequal "peaks and valleys" in the Equation of Time. ...and if the Earth's orbit had been circular, these two "peaks and valleys" would have been equal, and due to the tilt of the Earth's axis. And if the tilt of the Earth's axis was zero, there would only be the effect of the Earth's elliptical orbit, which would produce only one "peak and valley" per year. (http://www.school-for-champions.com/science/orbit.htm) Remember, a horizontal sundial has to be crafted specially for a latitude... Imagine a magical cylinder of cookie dough log straight from the Sun to the Earth. If you cut the log straight, you will notice 24 lines emanating from the center of the log at perfect 15 degree intervals (hour lines). If you cut the log at an angle, the lines would not be at 15 degree intervals to the diagonal plane. For this reason, the hour lines are not evenly marked on a horizontal sundial (except at the equator). The axial tilt can change the declination of the sun. This could change the accurate spacing of the hour lines. So axial tilt doesn't affect noon, but makes the other hours less accurate. The axial tilt does not affect the direction of noon of course (which always is precisely towards the South --- or towards the North if you're in the southern hemisphere. But it does affect the time of noon. Noon is a geometric alignment generated by the rotation of the Earth,you and George always slip 'time' in as relativists are want to do but fundamentally tilt is a property of equatorial orientation and neither accelerates or retards the observed motion of the Sun or what amounts to the same thing the axial rotation of the Earth from one noon alignment to another. I think that for a sundial to be most accurate, it needs to be set perpendicular to the orbital plane of the Earth (plane of the ecliptic). (http://www.wikipedia.org/wiki/Axial_tilt) ...and how would you keep it at that orientation? Remember that the sundial rests on an Earth which rotates along a tilted axis Don't be silly,the sundial rotates with the Earth and tilt the Earth all you want it has no effect on the pace of the shadow across the dial. ---- you'd need some clock machinery to accomplish this. And if you'd go to all that trouble, you might as well make a mechanical clock instead. Clocks emerged from the equality introduced by the Equation of Time from the inequality of the natural day.I'm sure in the era of cheap watches it is easy to forget which came first but obviously you and your spoacetime colleagues forgot or did'nt know and spent a lifetime chasing rainbows,no wonder you defend the nonsense tooth and nail instead of dumping it wholesale. One thing that I am also thinking about, is during the fall and spring (for example), the sun will not travel across the sky directly east and west but at an angle. I would presume on Equinox, an Equatorial dial set up exactly, would have one face lighted in the morning and the other in the afternoon. Comments? You need to reconsider your erroneous idea that the Earth's axial tilt does not affect the noon time or the equation of time. He may also consider that he can expect nothing but grief if he does'nt go along with axial tilt and the Equation of Time for the domino effect it would have with a century old concept and people like you who are proponents of that cult. |
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sundial & Earth's tilt questions
"Oriel36" wrote in message om... "George Dishman" wrote in message ... p.s. have you found out how to use Kepler's Second Law yet? George,I looked at your last posting in a different thread and you do something I would never do. It would help if you had said what that is! All I asked is whether you had applied Kepler's second law or not. My web page drawings assumed you had done this calculation and were familiar with the result. If you have not then it will appear as though I am just inventing the numbers so we should go over how I got them using Kepler's first and second laws. I just don't want to waste our time doing that if you have already done that calculation, but if you have I expect you to know the answers or be able to work them out. I have kept this at a level of the relationship with the planet wrt the Sun and the difference between axial rotation and the difference in the distance the Earth covers in its annual orbit as the axial alignment to the Sun repeats itself (noon) and how this reflects the Equation of Time and ultimately the relationship between clocks,geometry and astronomy. Same here, but I am taking it one step at a time. The first is to apply Kepler's Laws to the orbit of the Earth. If you haven't already done that, we should go through it. Your comments suggest you have not, is that correct? George |
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sundial & Earth's tilt questions
"Oriel36" wrote in message om... "George Dishman" wrote in message ... "Oriel36" wrote in message om... To prove that axial tilt does not have any effect on the Equation of Time involves a quite easy and inexpensive experiment involving only a sundial,a stopwatch, a clock and the Equation of Time correction tables which gives a value for each day of the year. The tables are produced using the tilt, you cannot calculate the correct values without it. Using only the factor due to the elliptical orbit you get a single peak: I had a look at the modern values against the values used by Roemer and they are different,the modern value gives a positive value for Oct 24th while it was a negative value in Roemer's calculations. If you look at the vertical scale on the Analemma site graph http://www.analemma.com/Graphics/sum...inedCharts.GIF you will see that the value for late october is nearly +16 minutes and the scale is marked "True sun ahead -" meaning that the natural noon is fifteen minutes ahead of noon based on mean time. Now look at the annotation on the right of Roemer's notes http://dibinst.mit.edu/BURNDY/OnlinePubs/Roemer/chapter3(part2).html He starts with 'Solar Time' which is ahead so he has to subtract the 15 minutes, 45 seconds to get back to mean time. The values are the same but one gives solar relative to mean while the other is finding mean from solar, hence the sign changes. Both tell you that natural or observed noon is ahead of noon, mean time in October. I understand the value in context of the insight of Roemer and subsequently Newton's definition of the distinction between absolute time and relative time as the Equation of Time and as addition and subtraction of minutes are involved,it should be taken as a given that the Equation of Time parameter should be made distinct from the sidereal parameter. Right, the Equation of Time is the difference between natural noon and mean noon and does not directly involve sidereal time. http://www.analemma.com/Pages/Ellipt...OrbitMath.html The full equation has two peaks: http://www.analemma.com/Graphics/sum...inedCharts.GIF The analemma is generated by putting clocks in the driver seat off civil time but the original use of the Equation of Time and the correction from natural noon to clock time involves the appropriate addition and subtraction of minutes as a planetary meridian aligns with the Sun depending on where the Earth is in its annual orbit,again AM and PM reflect the original determination of 24 hours off the inequality of natural noon to natural noon,there is nothing more basic and it has nothing to do with axial tilt.All that matters was the alignment regardless of latitude and it is good from pole to pole. This is Flamsteed's table: http://www.burnley.gov.uk/towneley/tryall/jftable.htm Look along the row just above the figures where he indicates A for Add or S for Subtract. It goes "A S S A A A S S S S A A" but again note this is to give you mean time from observation of natural time whereas the modern graph is the other way round so 'S' in Flamsteed's table corresponds to a positive value in the modern table. Notice that there are two periods in the year when you add and two when you subtract. Plot these values on a graph and you should get something very similar to the Analemma site graph. The elliptical motion of the Earth would only give one cycle such as "A A A A S S S S S S A A". The question you have to answer is why does Flamsteed's table say "S" for May and June when the effect of the elliptical motion should produce an "A"? George |
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