RE: Oblate Spheroid correction for computing distances?
Jim, For a simple mental arithmetic answer, I always understood that the English nautical mile (6080 feet when I was at school, about right for the English Channel - but 6076 or so for an International Nautical Mile) was by design very close to 1 minute of latitude, or longitude at the Equator. So 60 n.m. of 6080 feet = 69.09 English statute miles (of 5280 feet) = 1 degree. For metric users, the original definition (or rather the second, after they'd tried the length of a 1-second pendulum at Paris) of the metre was as 1/1000th of the quadrant of longitude through Paris. So taking 90 degrees = 10 million metres gives 1 degree = 111.111 km = 69.04 miles. Thus figures of 69 miles and 111 km are quite close enough for my everyday purposes. Multiply by cos(latitude) to get the length for a degree of longitude at any latitude. So here at 51 N, a degree of longitude is about 43.5 miles. The question of what do you mean by latitude has a bearing on the length of the degree of latitude. It is complicated by both the flattening of the Earth and the effect of the Earth's rotation on the apparent direction of gravity. The apparent direction of gravity affects what one practically measures as horizontal and vertical with level and plumb-line, as opposed to an imaginary vertical passing through the centre of the Earth - if you can decide where you think that is! At this point I'll retire and leave others who are better qualified to explain that and the resulting change in the length of a degree of latitude! Regards Andrew James -Original Message- From: J.Tallman [mailto:[EMAIL PROTECTED] Sent: 03 February 2004 15:58 To: sundial@rrz.uni-koeln.de Subject: Re: Oblate Spheroid correction for computing distances? Hello All, As previously mentioned, the earth is not a perfect sphere, and is distorted by the effects of gravity. So, is it flattened at the poles, or is it elongated at the equator? Is it a combination of both effects? I can envision a stretching effect at the poles, and a bulging effect at the equator, both of which I would think would affect the linear distances between theoretical degrees of latitude. If that is the case then I would think that the only true distances would be found in the mid-latitudes. I would really like to know how to calculate distances using the coordinates, as well. For example, the linear distance of a degree of longitude at the equator is greater than the linear distance that I would find here at 39 N. Every once in a while a sundial customer asks me how far away he can move before his sundial becomes inaccurate. I have always figured about 2 degrees of longitude is an acceptable range, but have no idea how to convert that to linear distance at a given latitude, other than manipulating the mapping sites that can handle coordinates. Best, Jim Tallman Sr. Designer FX Studios 513.829.1888 This message has been scanned for viruses by MailControl, a service from BlackSpider Technologies. This correspondence is confidential and is solely for the intended recipient(s). If you are not the intended recipient, you must not use, disclose, copy, distribute or retain this message or any part of it. If you are not the intended recipient please delete this correspondence from your system and notify the sender immediately. This message has been scanned for viruses by MailControl - www.mailcontrol.com -
Re: Was I half asleep?
I'll take a stab at this. I have attached a 7KB .gif, which I hope the list allows. 20 degrees of latitude of the spheroid near the poles is a larger ANGULAR distance, as measured by the celestial sphere, than at the spheroid's equator. I am guessing that they meant angular distance as measured against the celestial sphere. I am assuming that lines of latitude on the spheroid are defined by equal lengths, not angles, as measured on the surface of the spheroid. Any other takers? Bill Gottesman In a message dated 2/3/2004 9:15:50 AM Eastern Standard Time, [EMAIL PROTECTED] writes: Subj: Was I half asleep? Date:2/3/2004 9:15:50 AM Eastern Standard Time From:[EMAIL PROTECTED] (tony moss) Sender: [EMAIL PROTECTED] Reply-to:A HREF=mailto:sundial@rrz.uni-koeln.de; sundial@rrz.uni-koeln.de/A To: sundial@rrz.uni-koeln.de (Sundial Mail List) Fellow Shadow Watchers, There was a programme on UK Discovery yesterday - 2nd Feb - with some excellent material covering a thousand years of history. I must admit that I wan't paying 100% attention but one sequence caught my immediate attention. This described a French?? expedition to northern latitudes to determine the true shape of the earth which, as we now know, is an 'oblate spheroid' which is flattened near the poles. The whole thing was expensively restaged in costume with elegantly attired gentlemen trudging through deep snow on a frozen lake laying wooden poles end to end to measure surface distances. By comparing accurate astronomical positioning with linear measurements made on the surface they proved - accoding to the programme - that the distance between lines of latitude is GREATER at the poles. This 'concept' was supported by using a graphical representation of the earth with a superimposed protractor BOTH of which stretched as the earth was distorted. As the protractor stretched or rather distorted, with the earth image this point *appeared* to be true. Have I got it wrong? Surely the linear distance between lines of latitude will be decreased by flattening a sphere at its poles? Or had I missed something important by simultaneously watching TV and designing a heliochronometer base casting on my computer? Back on topic - ish. Tony Moss Attachment converted: Macintosh HD:OBLATE SPHERE LATITUDE.gif (GIFf/JVWR) (000B629D)
Be an optimist: Re: Was I half asleep?
Tony, it impugns your image to think of you as half asleep. For the record, I prefer to think that you were half awake. -Bill In a message dated 2/3/2004 9:15:50 AM Eastern Standard Time, [EMAIL PROTECTED] writes: Subj: Was I half asleep? Date:2/3/2004 9:15:50 AM Eastern Standard Time From:[EMAIL PROTECTED] (tony moss) Sender: [EMAIL PROTECTED] Reply-to:A HREF=mailto:sundial@rrz.uni-koeln.de; sundial@rrz.uni-koeln.de/A To: sundial@rrz.uni-koeln.de (Sundial Mail List) Fellow Shadow Watchers, There was a programme on UK Discovery yesterday - 2nd Feb - with some excellent material covering a thousand years of history. I must admit that I wan't paying 100% attention but one sequence caught my immediate attention. This described a French?? expedition to northern latitudes to determine the true shape of the earth which, as we now know, is an 'oblate spheroid' which is flattened near the poles. The whole thing was expensively restaged in costume with elegantly attired gentlemen trudging through deep snow on a frozen lake laying wooden poles end to end to measure surface distances. By comparing accurate astronomical positioning with linear measurements made on the surface they proved - accoding to the programme - that the distance between lines of latitude is GREATER at the poles. This 'concept' was supported by using a graphical representation of the earth with a superimposed protractor BOTH of which stretched as the earth was distorted. As the protractor stretched or rather distorted, with the earth image this point *appeared* to be true. Have I got it wrong? Surely the linear distance between lines of latitude will be decreased by flattening a sphere at its poles? Or had I missed something important by simultaneously watching TV and designing a heliochronometer base casting on my computer? Back on topic - ish. Tony Moss -
Re: Was I half asleep?
In regards to the magnificent old Chinese astronomical instruments, I picked up a book in Hong Kong called Heavenly Creations, Gems of Ancient Chinese Invention, produced by the Hong Kong Museum of History, 1998. This book has photographs and descriptions of some of the instruments that may have been featured on the History Channel program. This abreviated list of the instruments from the book may help you research for pictures or visits. 1. Stone Sundial, Han dynasty (206 B.C.-A.D 220, Excavated at Tuoketuo, Inner Mongolia in 1897, National Museum of Chinese History. 2. Armillary Sphere (reconstruction) Northern Song (960-1127). This is one of the brass, dragon supported instruments that may have been featured. It is a reconstruction of one part of a three story water clock which used a povotal cogwheel and an escape wheel. 3. Celestial globe (reconstruction) Northern Song (960-1127). This is a second component of the water clock and had a brass sphere of the heavens in which an observer could sit and rotate a sphere showing the night sky above him. 4. Equatorial torquetum (model) Ming dynasty, built 1437-1442. This model may have been featured on the program because the picture shows a beautiful brass, dragon supported instrument. The description from the book: This is a model of the simplified instrument (jian yi) sometimes translated as abridged armilla, which was made for the observatory in Beijing. It was moved to the Zijinshan Observatory in Nanjing in 1935. The Ming instrument was based on that designed by the Yuan astronomer Guo Shoujing, who built a total of 13 instruments around the year 1276. In the abridged armilla Guo made a breaktgrough by separating the three rings of the armillary sphere and mounting them separately, and in this way they became far easier to install and more useful. At the time it ranked as the most advanced astronomical instrument in the world. 5. The Old Beijing Observatory, Ming dynasty, consruction began in 1442. (the photograph shows several large brass instruments in close proximity in an outdoor setting with platforms for viewers to walk around the instruments). The description: Originally erected at hte southeastern corner of the Beijing city wall, this was the national astronomical observatroy in the Ming and Qing dynasties. The Ming astronomical instruments were either destroyed or, like the abridged armilla and the armillary sphere, were moved elsewhere. All of the instruments now preserved in the observatory-the equatorial armillary sphere, the celestial globe, the quadrant, the ecliptic armillary sphere, the horizon circle, the quadrant altazimuth, the sextant, the elaborate qouatorial armillary sphere--were built in the early Qing period. I hope these descriptions help you find the pictures, documentation or item locations you are looking for. Original Message Follows From: tony moss [EMAIL PROTECTED] Mike at al, Can you recall the name of the programme? Unlikely, I know, in your semi-conscious state. Mmmmh! Discovery Channel often have repeats, we may have a chance to see it again. Mike Shaw Ooops! When I came to look it up in the TV mag' it was on the 'UK History Channel' (digital freeview). I *said* I wasn't paying full attention. It was called Millennium: A Thousand Years of History (Five editions in omnibus.) Another half-aware glimpse was of the astronomical contributions of the Jesuits in China and their BEAUTIFUL astronomical instruments made for them by Chinese craftsmen. Enormous bronze astronomical quadrants sprouting dragons etc. I *think* these were real and not electronic creations so I wonder if and where they still exist? Tony M. - _ Get reliable dial-up Internet access now with our limited-time introductory offer. http://join.msn.com/?page=dept/dialup -
Re: scratch dials
Hello all I'm collecting all sundials existing in my area, Touraine (centre of France) and I am very surprised by the large number of mass dial I have found. At this time, about 100 mass dials (sometime 7 or 8 on the same church) in a 100 km diameter area around Tours, and I'm sure to find much many more. There are about 350 churches in Touraine and I have check only 100, so still I have a big job !!! à bientôt François - Message d'origine - De : Th. Taudin-Chabot [EMAIL PROTECTED] À : sundial@rrz.uni-koeln.de Envoyé : mardi 3 février 2004 11:59 Objet : scratch dials I noticed that there are several scratch dials in the UK and Ireland, but there are hardly any on the continent. When I mentioned this to a historian he right away said: but there was never anyone of the Benedictine order in the UK or Ireland, so that sounds logic. Is there an explanation for this difference? Thibaud Chabot - Thibaud Taudin-Chabot 52°18'19.85 North 04°51'09.45 East home email: [EMAIL PROTECTED] - Thibaud Taudin-Chabot 52° 18' 19.85 North, 04° 51' 09.45 East, alt. -4.50 m home email: [EMAIL PROTECTED] - -
Re: Oblate Spheroid correction for computing distances?
Dear Thad As many of us know, we can geometrically compute the distance between two locations (lat, long) and (lat2, long2) assuming that the Earth is a perfect sphere (which of course it isn't). Has anyone seen a correction for this flattening at the poles, or bowing around the equator? As always, Meeus has the answer. The crucial difference is that between geographic latitude and geocentric latitude: The geographic latitude is the apparent altitude of the nearer celestial pole measured above the northern (or southern) horizon. Meeus calls this phi. The geocentric latitude is the angle that a radius from the centre of the Earth to the observer makes with the plane of the Equator. Meeus calls this phi'. The difference is given as: phi - phi' = 692.73 sin(2 phi) - 1.16 sin(4 phi) The constants are arc-seconds. The greatest difference is at a latitude of 45 degrees when the difference is about 11.5 arc-minutes. This translates into about 11.5 nautical miles. This is the about the error where you live! Geographic latitude is what is normally measured and used. This is what is marked on maps. There is an implicit assumption that the plane of the horizon is perpendicular to the local gravitational vector. This means you can use a normal sextant or other instrument that measures relative to the horizon or you can use an instrument that has some kind of spirit-level built in. Beware of massive mountains nearby! Frank King University of Cambridge England -
Re: Salvador Dal� and Sundials
Hi Richard all, There is a picture of a Dali dial (:-) in the site of Andreas Hänel from Osnabrück (in German): http://www.physik.uni-osnabrueck.de/~ahaenel/sonnuhr/ Scroll to Spanien/Katalonien - Cadaques. It is dated 1966. Judging from the hour line pattern, the dial is east-declining by 60° or so. The pole-style possibly suffered from some 'restoration'. The site does not give additional information. Note the disclaimer that some attributions may be incorrect. Cadaqués is a village on the east coast of Spain, close to the French border and close to Dali's native town Figueras. Regards, Frans Maes 53.1N 6.5E - Original Message - From: Richard Langley [EMAIL PROTECTED] To: sundial@rrz.uni-koeln.de Sent: Monday, February 02, 2004 3:08 PM Subject: Salvador Dalí and Sundials While on a recent holiday in southern Florida, my wife and I visited the Salvador Dalí Museum in St. Petersburg http://www.salvadordalimuseum.org/. Currently running is the exhibition Dalí Centennial: An American Collection which celebrates the 100th anniversary of the birth of Dalí. One of the paintings on display is Noon (Barracks Port Lligat) which Dalí painted in 1954 http://dali.karelia.ru/html/works/1954_07.htm. The painting shows a vertical sundial on the wall of the barracks. Can any of our Spanish colleagues tell us if the building and the sundial still exist? Of course, Dalí was no stranger to sundials as witnessed by his famous sundial at 27, rue Saint-Jacques, Paris 5ème arrondissement http://www2.iap.fr/saf/csmp/arr5n/centrea51.html constructed in 1968. The image on the sundial bears a bit of a resemblance to his 1966 painting Self Portrait Sundial http://www.elainefineart.com/dali/self_portrait_sundial.htm Are there any other Dalí sundials -- real or painted? -- Richard Langley P.S. Fredericton is home to Dalí's huge Satiago El Grande. It is on permanent display in the city's Beaverbrook Art Gallery http://www.beaverbrookartgallery.org/, one of 4 Dalí paitings it owns. The gallery was a gift to New Brusnwick from its native son Lord Beaverbrook (Sir Max Aitken) who served in the wartime cabinet of Winston Churchill. Lord Beaverbrook was chancellor of my university from 1947 until his death in 1964. === Richard B. LangleyE-mail: [EMAIL PROTECTED] Geodetic Research Laboratory Web: http://www.unb.ca/GGE/ Dept. of Geodesy and Geomatics EngineeringPhone:+1 506 453-5142 University of New Brunswick Fax: +1 506 453-4943 Fredericton, N.B., Canada E3B 5A3 Fredericton? Where's that? See: http://www.city.fredericton.nb.ca/ === - -
RE: sundials in the Frankfurt region
Wolfgang R. Dick wrote: You should visit the Historisches Museum in Frankfurt, which have a good collection of sundials and other astronomical and scientific instruments. You may find the museum by searching the Internet with Google for Historisches Museum Frankfurt. There is also a catalog of their collection (which I do not have at hand, so that I cannot tell you now the exact title). However, it was made for a temporary exhibition, and only a smaller part of the items in the catalog are also in the permanent exhibition. The catalog is Reinhard Glasemann, _Erde, Sonne, Mond Sterne: Globen, Sonnenuhren und astronomische Instrumente im Historischen Museum Frankfurt am Main_ (Verlag Waldemar Kramer, Frankfurt am Main, 1999 [= _Schriften des Historischen Museums Frankfurt am Main_, nr. 20]), 166 pp, ISBN 3-7829-0504-0. About a year ago, the catalog was still available. === * Robert H. van Gent * * E-mail: [EMAIL PROTECTED] * * Homepage: http://www.phys.uu.nl/~vgent/homepage.htm * === -
Re: Oblate Spheroid correction for computing distances?
Hello All, As previously mentioned, the earth is not a perfect sphere, and is distorted by the effects of gravity. So, is it "flattened" at the poles, or is it "elongated" at the equator? Is it a combination of both effects? I can envision a stretching effect at the poles, and a bulging effect at the equator, both of which I would think would affect the linear distances between theoretical degrees of latitude. If that is the case then I would think that the only "true" distances would be found in the mid-latitudes. I would really like to know how to calculate distances using the coordinates, as well.For example, the linear distance of adegree of longitude at the equator is greater than the linear distance that I would find here at 39 N. Every once in a while a sundial customer asks me how far away he can move before his sundial becomes inaccurate. I have always figured about 2 degrees of longitude is an acceptable range, but have no idea how to convert that to linear distance at a given latitude, other than manipulating the mapping sites that can handle coordinates. Best, Jim Tallman Sr. Designer FX Studios 513.829.1888
Re: Size of degree of latitude
Perfect! Thank you Richard! Jim Tallman Sr. Designer FX Studios 513.829.1888 - Original Message - From: Richard Koolish [EMAIL PROTECTED] To: sundial@rrz.uni-koeln.de Sent: Tuesday, February 03, 2004 11:01 AM Subject: Size of degree of latitude http://pollux.nss.nima.mil/calc/degree.html this page will compute the size of a degree of latitude and longitude -
Re: Was I half asleep?
Hi Tony and all No you are not wrong. And happily for your heliochronometer you were not half asleep. There was indeed a french expedition in Lapland in 1736 sent by the then french king Louis XV and lead by P de Maupertuis. He found that the length of a degree of the meridian was longer in Lapland (66° latitude) than in France (46°). He found 57437 french toises in Lapland instead of 57030 found in France by Abbé Picard. For information 57030 toises are equal to 111,153 km; a toise is 1,95 m. At the same time another expedition was sent to Peru for the same job, lead by M. Bouguer. He found a length of 56750 toises for a degree at Equator. The result is not surprising. As Bill Gottesman recalls, an arc of one degree is defined by the distance of two points of a meridian such that the angle between vertical lines at these points is 1 degree. As the Earth globe is a ellipsoid flattened at the pole the vertical lines do not always intersect at the center. Near the pole they intersect beyond the center, (radius of curvature of earth surface is larger) ; at the equator they intersect between center and surface, (radius of curvature is smaller). Distance between intersection points and earth center is about 30 km in both cases. So the meridian arc between two points 1 degree apart is shorter at the equator than at the pole. Have a look for instance at J. Meus book Astronomical algorithms chapter 10 for more technical details. Or draw a very very flat ellipse to convince yourself. Regards Jean-Paul Cornec - Original Message - From: tony moss [EMAIL PROTECTED] To: Sundial Mail List sundial@rrz.uni-koeln.de Sent: Tuesday, February 03, 2004 1:32 PM Subject: Was I half asleep? Fellow Shadow Watchers, There was a programme on UK Discovery yesterday - 2nd Feb - with some excellent material covering a thousand years of history. I must admit that I wan't paying 100% attention but one sequence caught my immediate attention. This described a French?? expedition to northern latitudes to determine the true shape of the earth which, as we now know, is an 'oblate spheroid' which is flattened near the poles. The whole thing was expensively restaged in costume with elegantly attired gentlemen trudging through deep snow on a frozen lake laying wooden poles end to end to measure surface distances. By comparing accurate astronomical positioning with linear measurements made on the surface they proved - accoding to the programme - that the distance between lines of latitude is GREATER at the poles. This 'concept' was supported by using a graphical representation of the earth with a superimposed protractor BOTH of which stretched as the earth was distorted. As the protractor stretched or rather distorted, with the earth image this point *appeared* to be true. Have I got it wrong? Surely the linear distance between lines of latitude will be decreased by flattening a sphere at its poles? Or had I missed something important by simultaneously watching TV and designing a heliochronometer base casting on my computer? Back on topic - ish. Tony Moss - -
Anniversary-of-a-date dial
Message text written by INTERNET:sundial@rrz.uni-koeln.de This request is not limited to tubes. Any clever idea is welcome. How about the Liberation Monument WW2 Memorial, St Peter Port in Guernsey? That is calibrated so that on the anniversary of the Island's liberation (May 9th I think) the show of a column passes over the plaques each containing the name of one who died. Patrick -
scratch dials
Message text written by INTERNET:sundial@rrz.uni-koeln.de I noticed that there are several scratch dials in the UK and Ireland, but there are hardly any on the continent. When I mentioned this to a historian he right away said: but there was never anyone of the Benedictine order in the UK or Ireland, so that sounds logic.Is there an explanation for this different It's true that a lot of people think there are not many such dials on the continent. However when you start to keep records you find that there are actually quite a lot in France and even a few in the Channel Islands. Also their presence in Britain is very much restricted to the southern half of the country. Very few in Northern England and almost none in Scotland. I don't know about any Benedictine connexion - it might be worth following up. Dom Horne (in his book 1929) gave his view that the scratch dials in Britain and Ireland 'spread' there from Normandy. They certainly seem to be concentrated on Norman Churches here. Patrick -
Oblate Spheroid correction for computing distances?
Message text written by INTERNET:sundial@rrz.uni-koeln.de Has anyone seen a correction for this flattening at the poles, or bowing around the equator? If so, please share. Jan Meeus (who else??!!) gives such an approximation in Astronomical Algirithms 2nd Ed. p85. He attributes the equation to H Andoyer: 'Annuaire du Bureau des Longitudes pour 1950 (Paris) page 145'. He then works an example involving the distance between Paris and Washington DC and quoting the possible error of about 50 metres. To put it into perspective the difference between the simple spherical assumption and this 'better' formula is about 15km. Patrick -
Size of degree of latitude
http://pollux.nss.nima.mil/calc/degree.html this page will compute the size of a degree of latitude and longitude -
Re: Salvador Dal� and Sundials
Thanks, Frans. It looks like Dalí's Paris dial was based on this one in Cadaqués, predating it by 2 years. I wonder if there are any other Dalí dials of the same style? And thanks for pointing out the Dalí anagram -- I had missed that. By the way, the small fishing village of Portlligat (the site of the Dalí paianting) is just next door to Cadaqués. -- Richard P.S. Sorry for the earlier typo on the Fredericton Dalí painting; of course it should have been Santiago El Grande. ^ On Tue, 3 Feb 2004, Frans W. Maes wrote: Hi Richard all, There is a picture of a Dali dial (:-) in the site of Andreas Hänel from Osnabrück (in German): http://www.physik.uni-osnabrueck.de/~ahaenel/sonnuhr/ Scroll to Spanien/Katalonien - Cadaques. It is dated 1966. Judging from the hour line pattern, the dial is east-declining by 60° or so. The pole-style possibly suffered from some 'restoration'. The site does not give additional information. Note the disclaimer that some attributions may be incorrect. Cadaqués is a village on the east coast of Spain, close to the French border and close to Dali's native town Figueras. Regards, Frans Maes 53.1N 6.5E - Original Message - From: Richard Langley [EMAIL PROTECTED] To: sundial@rrz.uni-koeln.de Sent: Monday, February 02, 2004 3:08 PM Subject: Salvador Dalí and Sundials While on a recent holiday in southern Florida, my wife and I visited the Salvador Dalí Museum in St. Petersburg http://www.salvadordalimuseum.org/. Currently running is the exhibition Dalí Centennial: An American Collection which celebrates the 100th anniversary of the birth of Dalí. One of the paintings on display is Noon (Barracks Port Lligat) which Dalí painted in 1954 http://dali.karelia.ru/html/works/1954_07.htm. The painting shows a vertical sundial on the wall of the barracks. Can any of our Spanish colleagues tell us if the building and the sundial still exist? Of course, Dalí was no stranger to sundials as witnessed by his famous sundial at 27, rue Saint-Jacques, Paris 5ème arrondissement http://www2.iap.fr/saf/csmp/arr5n/centrea51.html constructed in 1968. The image on the sundial bears a bit of a resemblance to his 1966 painting Self Portrait Sundial http://www.elainefineart.com/dali/self_portrait_sundial.htm Are there any other Dalí sundials -- real or painted? -- Richard Langley P.S. Fredericton is home to Dalí's huge Satiago El Grande. It is on permanent display in the city's Beaverbrook Art Gallery http://www.beaverbrookartgallery.org/, one of 4 Dalí paitings it owns. The gallery was a gift to New Brusnwick from its native son Lord Beaverbrook (Sir Max Aitken) who served in the wartime cabinet of Winston Churchill. Lord Beaverbrook was chancellor of my university from 1947 until his death in 1964. === Richard B. LangleyE-mail: [EMAIL PROTECTED] Geodetic Research Laboratory Web: http://www.unb.ca/GGE/ Dept. of Geodesy and Geomatics EngineeringPhone:+1 506 453-5142 University of New Brunswick Fax: +1 506 453-4943 Fredericton, N.B., Canada E3B 5A3 Fredericton? Where's that? See: http://www.city.fredericton.nb.ca/ === - - === Richard B. LangleyE-mail: [EMAIL PROTECTED] Geodetic Research Laboratory Web: http://www.unb.ca/GGE/ Dept. of Geodesy and Geomatics EngineeringPhone:+1 506 453-5142 University of New Brunswick Fax: +1 506 453-4943 Fredericton, N.B., Canada E3B 5A3 Fredericton? Where's that? See: http://www.city.fredericton.nb.ca/ === -
Re: Oblate Spheroid correction for computing distances?
WGS 84 ellipsoid semi-major (equatorial) axis: 6 378 137.0 m semi-minor (polar) axis: 6 356 752.3142 m (biaxial ellipsoid or just ellipsoid is the preferred (at least in North America) term for spheroid) What kind of differences might you see when comparing great circle routes on an approximating sphere with geodesics on the ellipsoid? As an example, the distance between Washington and L.A. on the sphere is approximately 3711 km. On the ellipsoid, it is 3719 km. Here are the expressions for computing the distance in km for one degree of latitude or longitude on the WGS 84 ellipsoid as a function of latitude, phi: lat = 111.13295 - 0.55982Cos 2 phi + 0.00117Cos 4 phi long = 111.41288 Cos phi - 0.09350 Cos 3 phi + 0.00012 Cos 5 phi See Navigation 101: Basic Navigation with a GPS Receiver http://gauss.gge.unb.ca/papers.pdf/gpsworld.october00.pdf for further details. Navigate is a handy application for computing geodesics on various ellipsoids for PDAs using the Palm OS: http://fermi.jhuapl.edu/navigate/index.html -- Richard Langley Professor of Geodesy and Precision Navigation On Tue, 3 Feb 2004, Thaddeus Weakley wrote: Hello All - Tony's posting reminds me of a question that I have had for a long time. As many of us know, we call geometrically compute the distance between two locations (lat, long) and (lat2, long2) assuming that the Earth is a perfect sphere (which of course it isn't). Has anyone seen a correction for this flattening at the poles, or bowing around the equator? If so, please share. Thanks, Thad Weakley 42.2N, 83.8W - Do you Yahoo!? Yahoo! SiteBuilder - Free web site building tool. Try it! === Richard B. LangleyE-mail: [EMAIL PROTECTED] Geodetic Research Laboratory Web: http://www.unb.ca/GGE/ Dept. of Geodesy and Geomatics EngineeringPhone:+1 506 453-5142 University of New Brunswick Fax: +1 506 453-4943 Fredericton, N.B., Canada E3B 5A3 Fredericton? Where's that? See: http://www.city.fredericton.nb.ca/ === -
RE: Was I half asleep?
Hi Tony and all, There was an excellent article on Beijing Ancient Observatory in the Journal of the Royal Astronomical Society of Canada, 1994, Vol 88, pages 24 to 38. My original copy did not survive the trip to the coast but a pdf scan is available on Harvard/NASA ADS Abstract Service Try this link. http://adsbit.harvard.edu/cgi-bin/nph-iarticle_query?bibcode=1994JRASC..88.. .24C I would recommend an excellent book on the survey of the meridian to establish the meter, The Measure of All Things by Ken Alder ISBN 0-7432-1675-x. It covers the survey of the meridian in France during the revolutionary turmoil and Napoleonic wars. It will remind you of the discussion we had some years ago on this list on the difference between accuracy and precision. I am glad that when you are half asleep you catch more than most people wide awake! Cheers, Roger Bailey M 48.6 W 123.4 -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] Behalf Of tony moss Sent: February 3, 2004 12:07 PM To: Sundial Mail List Subject: Re: Was I half asleep? Hi Chuck, In regards to the magnificent old Chinese astronomical instruments, I picked up a book in Hong Kong called Heavenly Creations, Gems of Ancient Chinese Invention, produced by the Hong Kong Museum of History, 1998. This book has photographs and descriptions of some of the instruments that may have been featured on the History Channel program. From your descriptions I'd say these have a strong possibility of being the instruments featured although the Jesuits did get a mention. If there isn't a website showing these fine creations then there certainly should be. Tony M. - -
Re: scratch dials
I noticed that there are several scratch dials in the UK and Ireland, but there are hardly any on the continent. When I mentioned this to a historian he right away said: "but there was never anyone of the Benedictine order in the UK or Ireland, so that sounds logic". Is there an explanation for this difference? Thibaud Chabot What do you mean by a scratch dial? An ordinary sundial scratched into the stone? Believe me you may fiind such dials from Greece till Denmark, from Portugal till Poland, and I would say there are about 500 of them on the continent, the first made in Roman times the last in the 17th century. With kind regards Karlheinz Schaldach
Re: sundials in the Frankfurt region
Hi friends, I am going to Frankfurt, Germany on business in mid-February, and am wondering if there are good collections of sundials (portable or fixed) in that neighborhood that I might visit, and whom I should contact locally to gain access to museum collections. I am also interested in medieval and early renaissance mirrors, so if any of you know of collections of those too, please let me know! Best regards, Sara Dear Sara, there are sundial collections in Frankfurt and nearby in Darmstadt and Fulda which are worthwhile to visit. I should recommend: Historisches Museum Frankfurt (30 portable dial), Hessisches Landesmuseum Darmstadt (14 portable), Stadtmuseum Fulda (11 portable). Kind regards Karlheinz Schalddach
Re: Capturing web pages/sites
Thanks Giovanni for your advice and offer but I have now managed to download the program via the PC World link by another sundialler. Agin thanks for the offer it was very kind. Terry Quoting Giovanni Bellina [EMAIL PROTECTED]: [EMAIL PROTECTED] wrote: I tried to log on to the site quoted and get an error message. Does anyone know if there is a problem with it? Terry Try these Linkhttp://www.webattack.com/get/httrack.html if not work I can send the program via e-mail to you (3315KB). Have you a fast connection? Giovanni Bellina --- This mail sent through http://webmail.zoom.co.uk -
Oblate Spheroid correction for computing distances?
Hello All - Tony's posting reminds me of a question that I have had for a long time. As many of us know, we call geometrically compute the distance between two locations (lat, long) and (lat2, long2) assuming that the Earth is a perfect sphere (which of course it isn't). Has anyone seen a correction for this flattening at the poles, or bowing around the equator? If so, please share. Thanks, Thad Weakley 42.2N, 83.8W Do you Yahoo!? Yahoo! SiteBuilder - Free web site building tool. Try it!
Re: Size of degree of latitude
Thad Richard Koolish [EMAIL PROTECTED] wrote: http://pollux.nss.nima.mil/calc/degree.htmlthis page will compute the size of a degree oflatitude and longitude- Do you Yahoo!? Yahoo! SiteBuilder - Free web site building tool. Try it!
Was I half asleep?
Fellow Shadow Watchers, There was a programme on UK Discovery yesterday - 2nd Feb - with some excellent material covering a thousand years of history. I must admit that I wan't paying 100% attention but one sequence caught my immediate attention. This described a French?? expedition to northern latitudes to determine the true shape of the earth which, as we now know, is an 'oblate spheroid' which is flattened near the poles. The whole thing was expensively restaged in costume with elegantly attired gentlemen trudging through deep snow on a frozen lake laying wooden poles end to end to measure surface distances. By comparing accurate astronomical positioning with linear measurements made on the surface they proved - accoding to the programme - that the distance between lines of latitude is GREATER at the poles. This 'concept' was supported by using a graphical representation of the earth with a superimposed protractor BOTH of which stretched as the earth was distorted. As the protractor stretched or rather distorted, with the earth image this point *appeared* to be true. Have I got it wrong? Surely the linear distance between lines of latitude will be decreased by flattening a sphere at its poles? Or had I missed something important by simultaneously watching TV and designing a heliochronometer base casting on my computer? Back on topic - ish. Tony Moss -
Re: Was I half asleep?
Mike at al, Can you recall the name of the programme? Unlikely, I know, in your semi-conscious state. Mmmmh! Discovery Channel often have repeats, we may have a chance to see it again. Mike Shaw Ooops! When I came to look it up in the TV mag' it was on the 'UK History Channel' (digital freeview). I *said* I wasn't paying full attention. It was called Millennium: A Thousand Years of History (Five editions in omnibus.) Another half-aware glimpse was of the astronomical contributions of the Jesuits in China and their BEAUTIFUL astronomical instruments made for them by Chinese craftsmen. Enormous bronze astronomical quadrants sprouting dragons etc. I *think* these were real and not electronic creations so I wonder if and where they still exist? Tony M. -
Re: Was I half asleep?
Hi Chuck, In regards to the magnificent old Chinese astronomical instruments, I picked up a book in Hong Kong called Heavenly Creations, Gems of Ancient Chinese Invention, produced by the Hong Kong Museum of History, 1998. This book has photographs and descriptions of some of the instruments that may have been featured on the History Channel program. From your descriptions I'd say these have a strong possibility of being the instruments featured although the Jesuits did get a mention. If there isn't a website showing these fine creations then there certainly should be. Tony M. -
Re: sundials in the Frankfurt region
Sarah, You should visit the Historisches Museum in Frankfurt, which have a good collection of sundials and other astronomical and scientific instruments. You may find the museum by searching the Internet with Google for Historisches Museum Frankfurt. There is also a catalog of their collection (which I do not have at hand, so that I cannot tell you now the exact title). However, it was made for a temporary exhibition, and only a smaller part of the items in the catalog are also in the permanent exhibition. In case that you are interested also in historic geodetic instruments, I may arrange a visit to my institution (Federal Agency for Mapping and Geodesy) in Frankfurt. Best regards, Wolfgang Dick (Potsdam/Frankfurt am Main) -
