zodiac lengths
Hi, a lot of sundials show the tweleve zodiac signs. Eg Gemini (♊) and Cancer (♋) do share the same region on the sundial. My question is: do they share *exactly* the same region or not? Is the starting date May 20 of one in line with the end-date July 22 of the other or not? The angles of the ecliptic longitude for the zodiacs are equally distributed (each 30°), but what about the angles in the earth's orbit around the sun (ellipse)? And what about the dates? The lengths (in terms of time) of the zodiacs are not equal, but are they constant each year? Can anybody give me a better reference than http://en.wikipedia.org/wiki/Zodiac#Table_of_dates or even improve this table? Thanks a lot, thomas --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: zodiac lengths
Dear Thomas, You ask interesting questions and the answers depend slightly on just how precisely you want the model the way the sun goes round the ecliptic. QUESTION 1 ... do [Gemini and Cancer] share *exactly* the same region [on a sundial] or not? I think it is reasonable to DEFINE the 12 regions of the Zodiac as being bounded at 30-degree intervals of solar *longitude*. So Aries extends from 0 to 30 and so on. On the ecliptic, these 12 regions are distinct and there is no sharing. When you look at the corresponding intervals of solar *declination* you do, as you say, get sharing. In your example: Sign Longitude Declination range range Gemini60 to 90 20.15 to 23.44 Cancer90 to 12023.44 to 20.15 As you see, Gemini and Cancer share the same range of declinations but for Gemini the declination is increasing and for Cancer is decreasing. The answer to your question is YES. So far, this theory has nothing to do with the *shape* of the Earth's orbit but it does assume that the orbit is a plane which is isn't exactly. [Solar latitude hovers around zero but it isn't exactly zero. A REALLY pedantic discussion about whether Gemini and Cancer exactly overlap would take a book!] You then ask about dates. That makes the story very much more complicated but it doesn't stop Gemini and Cancer sharing the same region on a sundial. QUESTION 2 Is the starting date May 20 of one in line with the end-date July 22 of the other or not? You go too fast. Who says the starting date is May 20? It sometimes is and it sometimes isn't. You have to worry about the leap-year cycle and Pope Gregory XIII and his friends. At the moment we are living close to the middle of an almost 200-year run of pure Julian calendar. There are no omitted leap-years between 1904 and 2096 inclusive. This means there is a steady drift in all the dates you are interested in. The starting *declination* of one IS in line with the ending *declination* of the other but when you worry about dates everything becomes harder. The only sensible answer to this second question is NO. It is no because the dates change from year to year. See the answer to Question 4, but first... QUESTION 3 The angles of the ecliptic longitude for the zodiacs are equally distributed (each 30°), [YES that's right] but what about the angles in the earth's orbit around the sun (ellipse)? I don't quite understand this. The ecliptic longitude is the same as the angle of the Earth's orbit round the sun (though you might want to change the sign or add 180 degrees). The answer is THEY ARE THE SAME. QUESTION 4 And what about the dates? They are horrible! I have already said there is a steady drift in the dates but it is worse than that because of the precession of the equinoxes. The answer is THE DATES ARE A MESS and... QUESTION 5 The lengths (in terms of time) of the zodiacs are not equal, but are they constant each year? The answer is UNFORTUNATELY NO. It is easy to see that they are not constant by thinking about this time of year. We have just entered the sign of Capricorn and at this time of year the Earth is closest to the sun. That's good news because it gets winter over quicker. Capricorn doesn't last long! Also, this explains why the lengths are not constant. Unfortunately, there will come a time when we are furthest from the sun in winter. Capricorn will take longer and we could find the northern hemisphere covered in ice. [ There will then be conferences about trying to raise the levels of carbon dioxide :-) ] QUESTION 6 Can anybody give me a better reference than Wikipedia... The best thing you can do is to ask your girlfriend to buy you a copy of Astronomical Algorithms by Jean Meeus as a Christmas present. You can then write a proper program to model the Earth-Sun system. It took me about 2000 lines of code before I was happy with it but it is a very good way of answering your questions! Best wishes Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: zodiac lengths
Well done, Frank! -Bill Gottesman Frank King wrote: Dear Thomas, You ask interesting questions and the answers depend slightly on just how precisely you want the model the way the sun goes round the ecliptic. QUESTION 1 ... do [Gemini and Cancer] share *exactly* the same region [on a sundial] or not? I think it is reasonable to DEFINE the 12 regions of the Zodiac as being bounded at 30-degree intervals of solar *longitude*. So Aries extends from 0 to 30 and so on. On the ecliptic, these 12 regions are distinct and there is no sharing. When you look at the corresponding intervals of solar *declination* you do, as you say, get sharing. In your example: Sign Longitude Declination range range Gemini60 to 90 20.15 to 23.44 Cancer90 to 12023.44 to 20.15 As you see, Gemini and Cancer share the same range of declinations but for Gemini the declination is increasing and for Cancer is decreasing. The answer to your question is YES. So far, this theory has nothing to do with the *shape* of the Earth's orbit but it does assume that the orbit is a plane which is isn't exactly. [Solar latitude hovers around zero but it isn't exactly zero. A REALLY pedantic discussion about whether Gemini and Cancer exactly overlap would take a book!] You then ask about dates. That makes the story very much more complicated but it doesn't stop Gemini and Cancer sharing the same region on a sundial. QUESTION 2 Is the starting date May 20 of one in line with the end-date July 22 of the other or not? You go too fast. Who says the starting date is May 20? It sometimes is and it sometimes isn't. You have to worry about the leap-year cycle and Pope Gregory XIII and his friends. At the moment we are living close to the middle of an almost 200-year run of pure Julian calendar. There are no omitted leap-years between 1904 and 2096 inclusive. This means there is a steady drift in all the dates you are interested in. The starting *declination* of one IS in line with the ending *declination* of the other but when you worry about dates everything becomes harder. The only sensible answer to this second question is NO. It is no because the dates change from year to year. See the answer to Question 4, but first... QUESTION 3 The angles of the ecliptic longitude for the zodiacs are equally distributed (each 30°), [YES that's right] but what about the angles in the earth's orbit around the sun (ellipse)? I don't quite understand this. The ecliptic longitude is the same as the angle of the Earth's orbit round the sun (though you might want to change the sign or add 180 degrees). The answer is THEY ARE THE SAME. QUESTION 4 And what about the dates? They are horrible! I have already said there is a steady drift in the dates but it is worse than that because of the precession of the equinoxes. The answer is THE DATES ARE A MESS and... QUESTION 5 The lengths (in terms of time) of the zodiacs are not equal, but are they constant each year? The answer is UNFORTUNATELY NO. It is easy to see that they are not constant by thinking about this time of year. We have just entered the sign of Capricorn and at this time of year the Earth is closest to the sun. That's good news because it gets winter over quicker. Capricorn doesn't last long! Also, this explains why the lengths are not constant. Unfortunately, there will come a time when we are furthest from the sun in winter. Capricorn will take longer and we could find the northern hemisphere covered in ice. [ There will then be conferences about trying to raise the levels of carbon dioxide :-) ] QUESTION 6 Can anybody give me a better reference than Wikipedia... The best thing you can do is to ask your girlfriend to buy you a copy of Astronomical Algorithms by Jean Meeus as a Christmas present. You can then write a proper program to model the Earth-Sun system. It took me about 2000 lines of code before I was happy with it but it is a very good way of answering your questions! Best wishes Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Nasa website
Brad, No, Meeus's Elements of Solar Eclipses book does not tell how to calculate the Besselian elements. Rather, it LISTS these elements for all solar eclipses from 1951-2200. Its real strength is that it provides detailed numerical examples of how to USE these elements to calculate the path of totality (northern and southern edge), as well as the appearance, magnitude, contact times, and limit curves of the partial phases. It also explains how to determine the circumstances of the eclipse at any specific latitude and longitude. To calculate the Besselian elements themselves, if you want to, first you need a source of highly accurate ephemerides for the Sun and Moon (such as from the Astronomical Almanac, NASA's Horizons, or Aldo Vatagliano's Solex shareware program). Then you need the algorithms for deriving the elements. These are given is such places as the Explanatory Supplement to the Astronomical Almanac (either the 1992 or 1961 edition), or William Chauvenet's Manual of Spherical Astronomy (various editions, 1863 to 1891; also reprinted by Dover in 1960). Calculating the elements is actually more straightforward than using them to get accurate local preditions and curves for an eclipse. -- Roger - Original Message - From: Brad Lufkin bradley.luf...@gmail.com To: Sundial Mailing List sundial@uni-koeln.de Sent: Tuesday, December 22, 2009 3:07 PM Subject: Re: Nasa website Speaking of Meeus, does anyone know if his Elements of Solar Eclipses includes algorithms for calculating the Besselian elements of eclipses or just presents tables of results? Also, does the book present algorithms for calculating the paths of eclipses? It's not clear from the description on the bookseller's website. Regards, Brad --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Nasa website
Roger: that's what I was afraid of. And that's why I held of buying the book until I was sure, though supporting Mr Meeus in his retirement(?) with meager book royalties is something I'm not loath to do--his Astronomical Algorithms is a masterpiece. The more I use it, the more I realize how well it's organized and how well the material is presented in each chapter. (BTW, thanks to you for your contribution to the solution of Kepler's equation; yours is the implementation I've used.) As to data sources, I'm using Meeus's abbreviated version of VSOP as well as his lunar model. With those, I can reproduce the images of eclipses on the NASA website for a given date/time/position. The next step seems to be to reproduce the maps as well, hence my interest in the Besselian elements and so on. Many thanks for the references. Best regards, Brad On Tue, Dec 22, 2009 at 6:00 PM, Roger W. Sinnott rsinn...@post.harvard.edu wrote: Brad, No, Meeus's Elements of Solar Eclipses book does not tell how to calculate the Besselian elements. Rather, it LISTS these elements for all solar eclipses from 1951-2200. Its real strength is that it provides detailed numerical examples of how to USE these elements to calculate the path of totality (northern and southern edge), as well as the appearance, magnitude, contact times, and limit curves of the partial phases. It also explains how to determine the circumstances of the eclipse at any specific latitude and longitude. To calculate the Besselian elements themselves, if you want to, first you need a source of highly accurate ephemerides for the Sun and Moon (such as from the Astronomical Almanac, NASA's Horizons, or Aldo Vatagliano's Solex shareware program). Then you need the algorithms for deriving the elements. These are given is such places as the Explanatory Supplement to the Astronomical Almanac (either the 1992 or 1961 edition), or William Chauvenet's Manual of Spherical Astronomy (various editions, 1863 to 1891; also reprinted by Dover in 1960). Calculating the elements is actually more straightforward than using them to get accurate local preditions and curves for an eclipse. -- Roger - Original Message - From: Brad Lufkin bradley.luf...@gmail.com To: Sundial Mailing List sundial@uni-koeln.de Sent: Tuesday, December 22, 2009 3:07 PM Subject: Re: Nasa website Speaking of Meeus, does anyone know if his Elements of Solar Eclipses includes algorithms for calculating the Besselian elements of eclipses or just presents tables of results? Also, does the book present algorithms for calculating the paths of eclipses? It's not clear from the description on the bookseller's website. Regards, Brad --- https://lists.uni-koeln.de/mailman/listinfo/sundial --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Nasa website
In the past couple of weeks I have seen several references to the JPL Horizons website for astronomical calculations. See http://ssd.jpl.nasa.gov/horizons.cgi . I used this site recently to generate a solar ephemeris for 300BC for a remote location in Peru. It took a while to learn how to choose among all the options available but in the end I found it easy to use. This web based program provided exactly what I wanted in a useful format to import into a spreadsheet. This is a powerful tool and I highly recommend it. The limited web version does provide the elements Brad wanted. Perhaps the full HORIZON system available by telnet does but I have not tested the advanced version. Celebrate the return of the sun. Regards, Roger Bailey -- From: Roger W. Sinnott rsinn...@post.harvard.edu Sent: Tuesday, December 22, 2009 3:00 PM To: Sundial Mailing List sundial@uni-koeln.de Subject: Re: Nasa website Brad, No, Meeus's Elements of Solar Eclipses book does not tell how to calculate the Besselian elements. Rather, it LISTS these elements for all solar eclipses from 1951-2200. Its real strength is that it provides detailed numerical examples of how to USE these elements to calculate the path of totality (northern and southern edge), as well as the appearance, magnitude, contact times, and limit curves of the partial phases. It also explains how to determine the circumstances of the eclipse at any specific latitude and longitude. To calculate the Besselian elements themselves, if you want to, first you need a source of highly accurate ephemerides for the Sun and Moon (such as from the Astronomical Almanac, NASA's Horizons, or Aldo Vatagliano's Solex shareware program). Then you need the algorithms for deriving the elements. These are given is such places as the Explanatory Supplement to the Astronomical Almanac (either the 1992 or 1961 edition), or William Chauvenet's Manual of Spherical Astronomy (various editions, 1863 to 1891; also reprinted by Dover in 1960). Calculating the elements is actually more straightforward than using them to get accurate local preditions and curves for an eclipse. -- Roger - Original Message - From: Brad Lufkin bradley.luf...@gmail.com To: Sundial Mailing List sundial@uni-koeln.de Sent: Tuesday, December 22, 2009 3:07 PM Subject: Re: Nasa website Speaking of Meeus, does anyone know if his Elements of Solar Eclipses includes algorithms for calculating the Besselian elements of eclipses or just presents tables of results? Also, does the book present algorithms for calculating the paths of eclipses? It's not clear from the description on the bookseller's website. Regards, Brad --- https://lists.uni-koeln.de/mailman/listinfo/sundial --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: zodiac lengths
Hi All, This reminds me of a sundial, made by Landscape artist Paul de Kort in Zaanstad/The Netherlands. For dialing usually the zodiac-signs are defined as 30 degrees of the ecliptica. However, the true sun will pass the 12 constellations of the zodiac and also the constellation Ophiuchus (dutch: 'slangedrager'). Paul did make a sundial in which this 13th 'zodiac'-constellation is incorporated. Very nice. for more work of Paul see: www.pauldekort.nl for the sundial, see (page 6): http://www.pauldekort.nl/_backgrounds/getijdenpark%20BROCHURE%20lowres.pdf kind regards, Hendrik Hollander -- Analemma zonnewijzers Hendrik Hollander tel: 020 637 43 83 mob: 06 16 462 879 www.analemma.nl www.linkedin.com/in/hendrikhollander -- lees de disclaimer: www.analemma.nl/maildisclaimer.htm -- - Original Message - From: Bill Gottesman billgottes...@comcast.net To: sundial@uni-koeln.de Sent: Tuesday, December 22, 2009 4:51 PM Subject: Re: zodiac lengths Well done, Frank! -Bill Gottesman Frank King wrote: Dear Thomas, You ask interesting questions and the answers depend slightly on just how precisely you want the model the way the sun goes round the ecliptic. QUESTION 1 ... do [Gemini and Cancer] share *exactly* the same region [on a sundial] or not? I think it is reasonable to DEFINE the 12 regions of the Zodiac as being bounded at 30-degree intervals of solar *longitude*. So Aries extends from 0 to 30 and so on. On the ecliptic, these 12 regions are distinct and there is no sharing. When you look at the corresponding intervals of solar *declination* you do, as you say, get sharing. In your example: Sign Longitude Declination range range Gemini60 to 90 20.15 to 23.44 Cancer90 to 12023.44 to 20.15 As you see, Gemini and Cancer share the same range of declinations but for Gemini the declination is increasing and for Cancer is decreasing. The answer to your question is YES. So far, this theory has nothing to do with the *shape* of the Earth's orbit but it does assume that the orbit is a plane which is isn't exactly. [Solar latitude hovers around zero but it isn't exactly zero. A REALLY pedantic discussion about whether Gemini and Cancer exactly overlap would take a book!] You then ask about dates. That makes the story very much more complicated but it doesn't stop Gemini and Cancer sharing the same region on a sundial. QUESTION 2 Is the starting date May 20 of one in line with the end-date July 22 of the other or not? You go too fast. Who says the starting date is May 20? It sometimes is and it sometimes isn't. You have to worry about the leap-year cycle and Pope Gregory XIII and his friends. At the moment we are living close to the middle of an almost 200-year run of pure Julian calendar. There are no omitted leap-years between 1904 and 2096 inclusive. This means there is a steady drift in all the dates you are interested in. The starting *declination* of one IS in line with the ending *declination* of the other but when you worry about dates everything becomes harder. The only sensible answer to this second question is NO. It is no because the dates change from year to year. See the answer to Question 4, but first... QUESTION 3 The angles of the ecliptic longitude for the zodiacs are equally distributed (each 30°), [YES that's right] but what about the angles in the earth's orbit around the sun (ellipse)? I don't quite understand this. The ecliptic longitude is the same as the angle of the Earth's orbit round the sun (though you might want to change the sign or add 180 degrees). The answer is THEY ARE THE SAME. QUESTION 4 And what about the dates? They are horrible! I have already said there is a steady drift in the dates but it is worse than that because of the precession of the equinoxes. The answer is THE DATES ARE A MESS and... QUESTION 5 The lengths (in terms of time) of the zodiacs are not equal, but are they constant each year? The answer is UNFORTUNATELY NO. It is easy to see that they are not constant by thinking about this time of year. We have just entered the sign of Capricorn and at this time of year the Earth is closest to the sun. That's good news because it gets winter over quicker. Capricorn doesn't last long! Also, this explains why the lengths are not constant. Unfortunately, there will come a time when we are furthest from the sun in winter. Capricorn will take longer and we could find the northern hemisphere covered in ice. [ There will then be conferences about trying to raise the levels of carbon dioxide :-) ] QUESTION 6 Can anybody give me a better reference than Wikipedia... The best thing you can do is to ask your girlfriend to buy you a copy of Astronomical
