Analemma
Daniel Lee Wenger [EMAIL PROTECTED] writes: On my globe the significance of the analemma is apparent. Each analemma represents the geographical position of the sun at mean time 6, 7, 8, 9, etc. for each day of the year. In fact the geographical postions of the sun at those mean time hours would be a collection of 365 dots but the analemma is interpolated to generate a semi continuous curve. Since the set of dots that would be generated during the following year would be slightly different the curve used represents some sort of average of the dots over a four year period. The set of dots that would be generated during the following year would lie on the same curve. The reason the dots are not in the same places is that the year is not a whole number of days long. The curve is not an average over a four year period. If you were to draw four years' curves separately, you would see that the curves are identical, but the points used to plot them are not. The curves are the graph of Equation of Time against declination, both of which are functions of the solar longitude. The particular values of solar longitude at, say, noon every day in 1999 are different from those in 2000, but the analemma points lie on exactly the same curve (ignoring only very long-term drift). To use straight lines as an illustration, the points (1,100) and (6,105) lie on the same line as the points (2,101) and (7,106) or the points (3,102) and (8,107) or the points (4,103) and (9,108). Chris Lusby Taylor Email: [EMAIL PROTECTED] (Formerly [EMAIL PROTECTED])
New Pictures of Wenger Sundial
Dear Fellow Dialists I promised photos of my newest sundial and they are now on my web site. A set of pictures is at http://www.wengersundial.com/dialPicture.html The photo at http://www.wengersundial.com/dial1.html shows the detail of the analemma and the scribed features of the dial. This photo is relavent to the recent discussions of analemmas and their placement on sundials. On my globe the significance of the analemma is apparent. Each analemma represents the geographical position of the sun at mean time 6, 7, 8, 9, etc. for each day of the year. In fact the geographical postions of the sun at those mean time hours would be a collection of 365 dots but the analemma is interpolated to generate a semi continuous curve. Since the set of dots that would be generated during the following year would be slightly different the curve used represents some sort of average of the dots over a four year period. The generation of an analemma on another type of sundial involves a projection of these geographical positions through the origin of the globe onto some surface, usually a horizonal or vertical plane. The photos are detailed and my take some time to download. Hope you enjoy them. Dan Wenger
Re: Calendar Reform
Since one major insurmountable objection to the Achelis-type World Calendar, especially to Jews and other religious groups to whom the preservation of the 7-day week is important, has anyone considered a calendar of 364 days, divided just as in the World Calendar, but instead of a Leap Day and a World Day, letting the error accumulate to a total of 7 days and then adding a Leap Week? There is no major problem in having the equinox off by 2 or 3 days in any year, except to astronomical types, who now have the advantage of high-speed computers, and the Leap Week could be used as an international holiday of good will, and yet not interfere with religious observations of any type. The calculation of Easter, Orthodox and Coptic Pascha, and Passover and other religious moveabledates might be a bit hairy, but still Incidentally, for those born during those additional days, the rule could be that they would celebrate their birthday in non-leap-week years on the day after which said week would begin. This is similar to the rule, adopted by the British Parliament that observances of events occurring on Feb. 29th be celebrated on the 28th in ordinary years. Does anyone want to discuss this further?? Good wishes, John
Re: Analemma
Hello, It is true that the Analemma is a graph of the EoT vs. Dec but I would recommend that EoT values that are the computed points of an Analemma be based on a four year average if one is, as I am guessing, correlating the imaged solar position along the Analemma to an exact date. One should also consider computing the four year average of declination too. The change in the shape of the Analemma i.e., the secular change of the EoT, is as you say, on a rather slow time scale but don't sell it short, the Vernal Equinox is shifting clockwise at 50 arc-secs/year and Perihelion is shifting counter-clockwise approx. 12 arc-secs/year and it is the phase relation between the two events (i.e., the maximum of eccentricity at Perihelion and the min(s) of obliquity at the Equinoxes) that drive the shape of the Analemma. Best Regards, Luke Coletti Chris Lusby wrote: Daniel Lee Wenger [EMAIL PROTECTED] writes: On my globe the significance of the analemma is apparent. Each analemma represents the geographical position of the sun at mean time 6, 7, 8, 9, etc. for each day of the year. In fact the geographical postions of the sun at those mean time hours would be a collection of 365 dots but the analemma is interpolated to generate a semi continuous curve. Since the set of dots that would be generated during the following year would be slightly different the curve used represents some sort of average of the dots over a four year period. The set of dots that would be generated during the following year would lie on the same curve. The reason the dots are not in the same places is that the year is not a whole number of days long. The curve is not an average over a four year period. If you were to draw four years' curves separately, you would see that the curves are identical, but the points used to plot them are not. The curves are the graph of Equation of Time against declination, both of which are functions of the solar longitude. The particular values of solar longitude at, say, noon every day in 1999 are different from those in 2000, but the analemma points lie on exactly the same curve (ignoring only very long-term drift). To use straight lines as an illustration, the points (1,100) and (6,105) lie on the same line as the points (2,101) and (7,106) or the points (3,102) and (8,107) or the points (4,103) and (9,108). Chris Lusby Taylor Email: [EMAIL PROTECTED] (Formerly [EMAIL PROTECTED])
Re: Analemma
Hello Again, My mistake below: I should have said the zero(s) of obliquity at the Equinoxes... Luke Luke Coletti wrote: it is the phase relation between the two events (i.e., the maximum of eccentricity at Perihelion and the min(s) of obliquity at the Equinoxes) that drive the shape of the Analemma.
Re: Viscosity, GMT and UT1
Hi David, Richard et. al. None of us is picky, we are discussing things. 1. David, you wrote Flight would work quite well without viscosity. The lift generated by aircraft wings is due to a pressure difference above and below the wing, and this is created by the shape of the wing. Whilst viscosity is a consideration in the real world, lift effects can certainly be modelled in a non-viscous fluid. (I did a course in Fluid Dynamics with the Open University a couple of years ago.) A more interesting version occurs when a rotating cylinder is placed perpendicularly in a fluid flow. This generates lift too, at right angles to the direction of flow and the axis of the cylinder. This theory was used some time ago on German rotor ships, and I suspect is also the theory behind a new aeroplane shown on Tomorrow's World last week. The pressure difference is al right but how could you apply it to the wing if everything smoothly slides? It is even easier to explain with the rotating cylinder. If there is no viscosity it does not matter whether the cylinder rotates or not. It is not able to accelerate air particles on one side and deccelrate on the other because it is not able to catch them. The flow remains ideally symmetric so the lift force cannot appear. So no viscosity, no lift. BTW, flow around rotating cylinder may be transformed mathematically to flow around any other shape. 2. It is hard to say what is going to happen to GMT. Certainly international community is no longer using even the name. I do, because I am a bit traditionalist, like I think most of the list members. 3. Richard you mentioned that UT1 does not take into account polar movements, This is the citation from your paper on http://www.rnw.nl/realradio/information/html/universaltime.html There are actually a couple of variants of UT. UT as determined by actual astronomical observations at a particular observatory is known as UT0 (UT-zero). It is affected by the motion of the earth's rotation pole with respect to the crust of the earth. If UT0 is corrected for this effect, we get UT1 which is a measure of the true angular orientation of the earth in space. Whatever the interpretation (my secondary language is C++, not English) the paper is very good and you deserve any kind of malt you like (for now be happy with virtual one). Slawek At 07:37 AM 3/1/99 -0500, David Higgon wrote: Slawomir and all, I don't want to be too picky, but since you are interested in side threads... Flight would work quite well without viscosity. The lift generated by aircraft wings is due to a pressure difference above and below the wing, and this is created by the shape of the wing. Whilst viscosity is a consideration in the real world, lift effects can certainly be modelled in a non-viscous fluid. (I did a course in Fluid Dynamics with the Open University a couple of years ago.) A more interesting version occurs when a rotating cylinder is placed perpendicularly in a fluid flow. This generates lift too, at right angles to the direction of flow and the axis of the cylinder. This theory was used some time ago on German rotor ships, and I suspect is also the theory behind a new aeroplane shown on Tomorrow's World last week. Going back to GMT, UTC and Internet Time, maybe the latter will come into use, albeit in the far future... If the Earth is slowing in its rotation, there will come a time when a day last 25 of our present hours. GMT (I think, in its old sense) would still divide the day into 24 hours, and this is obviously well past the point where the introduction of some leap seconds is going to bring UTC back in line with GMT! People would be unwilling to use UTC as this would mean breakfast would be an hour later each day, and scheduling appointments in the future would require a knowledge of the date to determine where the time was. Similarly the scientific community could not use GMT as its seconds would be 4% too long. The solution would seem to be UTC for the scientists who need to measure seconds, and some sort of civil time for general use. To avoid confusion, the name seconds should probably not be used - why not beats - and while we're at it, why not embrace decimalisation and have ... Internet Time! I for one won't be touching Internet Time with a barge pole, and thankfully I'll be long gone before there's enough of a difference between GMT and UTC to warrant its introduction ;-) David Higgon Young stick in the mud! Slawek Grzechnik 32 57.4'N 117 08.8'W http://home.san.rr.com/slawek
