Bob Many thanks
The amazement produced by the method I used was the accuracy obtained by JUST SIX parameters. That came from an old-fashioned single body Keplerian approach that just requires the longitude at perihelion + eccentricity to get the Sun’s longitude. Add to that the obliquity to to give RA & Declination. Add to that RA at Epoch + length of tropical year + one precessional constant to find the connection between UT and GMST. In truth, if you look at the code in detail - you will see that I had to incorporate three simple linear expressions to account for the time variation of obliquity, eccentricity and perihelion to get my target accuracy over a 50 year period (the limit imposed by my use of MICA as ‘accuracy referee’). So sensu stricto, you are probably right that I have used more parameters. Best wishes Kevin On 24 Feb 2014, at 02:03, Robert Kellogg <rkell...@comcast.net> wrote: > Kevin, > > Welcome the the wonderful world of celestial mechanics ... you need to have > only six orbital parameters plus time epoch plus earth inclination and > sidereal spin, so total of 8 parameters are required .... > > Bob > > On 2/23/2014 6:49 PM, sundial-requ...@uni-koeln.de wrote: >> Send sundial mailing list submissions to >> sundial@uni-koeln.de >> >> To subscribe or unsubscribe via the World Wide Web, visit >> https://lists.uni-koeln.de/mailman/listinfo/sundial >> or, via email, send a message with subject or body 'help' to >> sundial-requ...@uni-koeln.de >> >> You can reach the person managing the list at >> sundial-ow...@uni-koeln.de >> >> When replying, please edit your Subject line so it is more specific >> than "Re: Contents of sundial digest..." >> >> >> Today's Topics: >> >> 1. Calculating the Equation of Time and other Solar Parameters >> (Kevin Karney) >> 2. CORRECTION Calculating the Equation of Time and other Solar >> Parameters (Kevin Karney) >> 3. Re: Calculating the Equation of Time and other Solar >> Parameters (Bill Gottesman) >> 4. online manuscript by Mayall and Mayall (Schechner, Sara) >> 5. Re: Calculating the Equation of Time and other Solar >> Parameters (Roger Bailey) >> >> >> ---------------------------------------------------------------------- >> >> Message: 1 >> Date: Sun, 23 Feb 2014 19:32:37 +0000 >> From: Kevin Karney <kar...@me.com> >> To: "sundial@uni-koeln.de List" <sundial@uni-koeln.de> >> Subject: Calculating the Equation of Time and other Solar Parameters >> Message-ID: <d9c80f35-d4a1-4414-bac3-d1074c51c...@me.com> >> Content-Type: text/plain; charset="windows-1252" >> >> Dear Friends >> >> I have spend many happy hours during this wet, wet winter investigating and >> learning how to calculate all the solar parameters that a gnomonist might >> possibly need - Equation of Time, Declination, RA, Altitude, Azimuth, Time >> of Sunset/Rise, etc, etc. >> >> I have been surprised to find that - with traditional calculation methods >> and an absolute minimum of astronomical information - it is possible to >> calculate everything from first principles to a surprising degree of >> accuracy. >> >> Other than location and local time, only six pieces of astronomical >> information are required - obliquity, eccentricity, Sun?s GHA at 1/1/2000, >> longitude of perihelion, a single precessional constant and the length of >> the tropical year. Accuracies for the EOT are +/- 2 seconds of time For >> altitudes/azimuths, less than 1 minute of arc - much better than needed by >> most gnomonic problems. >> >> If any of you are interested in such calculations, I have loaded a document >> with all the astronomical theory and background plus the code onto my website >> www.precisedirections.co.uk/sundials >> The code is written in Python, a language available on every type of >> computer, which is very easily understood, quite easily learnt and very >> easily translated into any other coding language you might like. >> >> If you own an iPad or iPhone, and are prepared to buy a cheap little app >> called Pythonista, the code will extract locational & time information from >> your phone - so you do not even have to input this to get your calculations >> done >> >> You might also like to see a graphic of a civil mean time horizontal dial, >> which I think is called a hectomoros dial, that is destined for my garden. >> This is also on the website. >> >> Enjoy >> Kevin >> -------------- next part -------------- >> An HTML attachment was scrubbed... >> URL: >> <https://lists.uni-koeln.de/mailman/private/sundial/attachments/20140223/b50a01bb/attachment-0001.html> >> >> ------------------------------ >> >> Message: 2 >> Date: Sun, 23 Feb 2014 20:06:51 +0000 >> From: Kevin Karney <kar...@me.com> >> To: "sundial@uni-koeln.de List" <sundial@uni-koeln.de> >> Subject: CORRECTION Calculating the Equation of Time and other Solar >> Parameters >> Message-ID: <dc4a7b4d-7d8f-4a83-97b9-c2ed7732c...@me.com> >> Content-Type: text/plain; charset="windows-1252" >> >> My website is ? >> http://www.precisedirections.co.uk/Sundials >> with a capital S for Sundial >> >> Sorry >> K >> -------------- next part -------------- >> An HTML attachment was scrubbed... >> URL: >> <https://lists.uni-koeln.de/mailman/private/sundial/attachments/20140223/75ac7917/attachment-0001.html> >> >> ------------------------------ >> >> Message: 3 >> Date: Sun, 23 Feb 2014 15:52:57 -0500 >> From: Bill Gottesman <billgottes...@comcast.net> >> To: Kevin Karney <kar...@me.com> >> Cc: "sundial@uni-koeln.de List" <sundial@uni-koeln.de> >> Subject: Re: Calculating the Equation of Time and other Solar >> Parameters >> Message-ID: >> <CAMDsn==32iapzw47q7zo4-wwyxbcttzcjcjax+y8vvtv_fd...@mail.gmail.com> >> Content-Type: text/plain; charset="iso-8859-1" >> >> Kevin, >> >> I am excited about your article "Basic Astronomy for the Gnomonist." It >> will take some time to digest, but it seems to have a very nice graphic >> analysis for the many formulas and solar positioning we deal with. I >> appreciate you making this reference available. >> >> I think what you call a Hectoromos dial is what I have heard described as a >> Singleton dial. Here is a link to a similar (vertical) dial at the >> University of Vermont. Fred Sawyer wrote about the Hectoromos dial in an >> early NASS compendium. I think Plato might have had something to do with >> it. >> >> -Bill >> >> >> On Sun, Feb 23, 2014 at 2:32 PM, Kevin Karney <kar...@me.com> wrote: >> >>> Dear Friends >>> >>> I have spend many happy hours during this wet, wet winter investigating >>> and learning how to calculate all the solar parameters that a >>> gnomonist might possibly need - Equation of Time, Declination, RA, >>> Altitude, Azimuth, Time of Sunset/Rise, etc, etc. >>> >>> I have been surprised to find that - with traditional calculation methods >>> and an absolute minimum of astronomical information - it is possible to >>> calculate everything from first principles to a surprising degree of >>> accuracy. >>> >>> Other than location and local time, only six pieces of astronomical >>> information are required - obliquity, eccentricity, Sun's GHA at 1/1/2000, >>> longitude of perihelion, a single precessional constant and the length of >>> the tropical year. Accuracies for the EOT are +/- 2 seconds of time For >>> altitudes/azimuths, less than 1 minute of arc - much better than needed by >>> most gnomonic problems. >>> >>> If any of you are interested in such calculations, I have loaded a >>> document with all the astronomical theory and background plus the code onto >>> my website >>> *www.precisedirections.co.uk/sundials >>> <http://www.precisedirections.co.uk/sundials>* >>> The code is written in Python, a language available on every type of >>> computer, which is very easily understood, quite easily learnt and very >>> easily translated into any other coding language you might like. >>> >>> If you own an iPad or iPhone, and are prepared to buy a cheap little app >>> called Pythonista, the code will extract locational & time information from >>> your phone - so you do not even have to input this to get your calculations >>> done >>> >>> You might also like to see a graphic of a civil mean time horizontal dial, >>> which *I think* is called a hectomoros dial, that is destined for my >>> garden. This is also on the website. >>> >>> Enjoy >>> Kevin >>> >>> --------------------------------------------------- >>> https://lists.uni-koeln.de/mailman/listinfo/sundial >>> >>> >>> >> -------------- next part -------------- >> An HTML attachment was scrubbed... >> URL: >> <https://lists.uni-koeln.de/mailman/private/sundial/attachments/20140223/ecf6e400/attachment-0001.html> >> >> ------------------------------ >> >> Message: 4 >> Date: Sun, 23 Feb 2014 21:29:20 +0000 >> From: "Schechner, Sara" <sche...@fas.harvard.edu> >> To: "Sundial List (sundial@uni-koeln.de)" <sundial@uni-koeln.de> >> Subject: online manuscript by Mayall and Mayall >> Message-ID: >> <5739be999e14ea4c97335684ddae402d0d1d8...@harvandmbx04.fasmail.priv> >> Content-Type: text/plain; charset="us-ascii" >> >> Dear All, >> >> As those who attended last summer's meeting of the North American Sundial >> Society know, I have done some research on the Margaret Mayall and R. Newton >> Mayall, authors of the well-known, Sundials: How To Know, Use, and Make >> Them, and their connections to sundials presently in Harvard's Collection of >> Historical Scientific Instruments. My research paper has not yet been >> published. >> >> One of the manuscripts I have used was a typescript catalog of the Ernst >> Collection by the Mr. and Mrs. Mayall. The document is held at the Harvard >> College Observatory. It was recently digitized and is now available online. >> You can find it here: >> >> The Harold C. Ernst Collection of Portable Sundials >> Mayall, R. Newton >> Mayall, Margaret W. >> http://zenodo.org/record/8326 >> >> Best wishes, >> Sara >> >> Sara J. Schechner, Ph.D. >> David P. Wheatland Curator of the Collection of Historical Scientific >> Instruments >> Department of the History of Science, Harvard University >> Science Center 251c, 1 Oxford Street, Cambridge, MA 02138 >> Tel: 617-496-9542 | Fax: 617-496-5932 | >> sche...@fas.harvard.edu<mailto:sche...@fas.harvard.edu> >> http://scholar.harvard.edu/saraschechner/ >> http://chsi.harvard.edu/ >> >> >> -------------- next part -------------- >> An HTML attachment was scrubbed... >> URL: >> <https://lists.uni-koeln.de/mailman/private/sundial/attachments/20140223/76f16be7/attachment-0001.html> >> >> ------------------------------ >> >> Message: 5 >> Date: Sun, 23 Feb 2014 15:48:53 -0800 >> From: "Roger Bailey" <rtbai...@telus.net> >> To: "Kevin Karney" <kar...@me.com>, <sundial@uni-koeln.de> >> Subject: Re: Calculating the Equation of Time and other Solar >> Parameters >> Message-ID: <F7EE14E0C34B4B4BB91DADFD6E444B9D@DellVista> >> Content-Type: text/plain; charset="windows-1252" >> >> Thanks Kevin, >> >> A quick review demonstrated how useful your work can be for folk like us. >> Here is a specific example. I have been working with solar and lunar >> ephemerides date from the JPL Horizons website. >> http://ssd.jpl.nasa.gov/horizons.cgi#top This site provides a wealth of data >> that the user can customize for their own purposes. The problem is the user >> does not know how the data was calculated nor how it is to be used The >> Explanatory Supplement helps but it is difficult to understand. One simple >> example is understanding a solar data compilation that provided among other >> things Right Ascension and Declination. But I really wanted the EQT. Your >> formula 9 in Part 1 gave me the simple relationship, obvious in hindsight >> that I was looking for, the conversion of RA to EQT. >> >> I look forward making good use of your work. Thank you for making it >> available. >> >> Thanks again, >> Roger Bailey >> Walking Shadow Designs >> >> >> >> >> From: Kevin Karney >> Sent: Sunday, February 23, 2014 11:32 AM >> To: sundial@uni-koeln.de List >> Subject: Calculating the Equation of Time and other Solar Parameters >> >> >> Dear Friends >> >> >> I have spend many happy hours during this wet, wet winter investigating and >> learning how to calculate all the solar parameters that a gnomonist might >> possibly need - Equation of Time, Declination, RA, Altitude, Azimuth, Time >> of Sunset/Rise, etc, etc. >> >> >> I have been surprised to find that - with traditional calculation methods >> and an absolute minimum of astronomical information - it is possible to >> calculate everything from first principles to a surprising degree of >> accuracy. >> >> >> Other than location and local time, only six pieces of astronomical >> information are required - obliquity, eccentricity, Sun?s GHA at 1/1/2000, >> longitude of perihelion, a single precessional constant and the length of >> the tropical year. Accuracies for the EOT are +/- 2 seconds of time For >> altitudes/azimuths, less than 1 minute of arc - much better than needed by >> most gnomonic problems. >> >> >> If any of you are interested in such calculations, I have loaded a document >> with all the astronomical theory and background plus the code onto my website >> www.precisedirections.co.uk/sundials >> The code is written in Python, a language available on every type of >> computer, which is very easily understood, quite easily learnt and very >> easily translated into any other coding language you might like. >> >> >> If you own an iPad or iPhone, and are prepared to buy a cheap little app >> called Pythonista, the code will extract locational & time information from >> your phone - so you do not even have to input this to get your calculations >> done >> >> >> You might also like to see a graphic of a civil mean time horizontal dial, >> which I think is called a hectomoros dial, that is destined for my garden. >> This is also on the website. >> >> >> Enjoy >> Kevin >> >> >> -------------------------------------------------------------------------------- >> >> >> --------------------------------------------------- >> https://lists.uni-koeln.de/mailman/listinfo/sundial >> >> >> >> >> -------------------------------------------------------------------------------- >> >> >> No virus found in this message. >> Checked by AVG - www.avg.com >> Version: 2014.0.4335 / Virus Database: 3705/7118 - Release Date: 02/23/14 >> >> >> >> ----- >> No virus found in this message. >> Checked by AVG - www.avg.com >> Version: 2014.0.4335 / Virus Database: 3705/7118 - Release Date: 02/23/14 >> -------------- next part -------------- >> An HTML attachment was scrubbed... >> URL: >> <https://lists.uni-koeln.de/mailman/private/sundial/attachments/20140223/822876d9/attachment.html> >> >> ------------------------------ >> >> Subject: Digest Footer >> >> _______________________________________________ >> sundial mailing list >> sundial@uni-koeln.de >> https://lists.uni-koeln.de/mailman/listinfo/sundial >> >> >> ------------------------------ >> >> End of sundial Digest, Vol 98, Issue 3 >> ************************************** >> >> > > --------------------------------------------------- > https://lists.uni-koeln.de/mailman/listinfo/sundial > --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
