Frankly, I think using a 6th order polynomial to approximate data with so much uncertainty is questionable. I would use linear, piece-wise interpolation on the tables and the trends outside the range of the tables (suitably adjusted to match the values at the beginning and end of the tables). Brad
On Thu, Mar 4, 2010 at 1:16 PM, [email protected] <[email protected]>wrote: > Jim, I agree with you about all but one detail : the current value of > DeltaT. > > The last measured values I know are the following ( > http://maia.usno.navy.mil/ser7/deltat.data) : > > ............................ > 2008 1 65.4574 > 2008 2 65.4868 > 2008 3 65.5152 > 2008 4 65.5450 > 2008 5 65.5781 > 2008 6 65.6127 > 2008 7 65.6288 > 2008 8 65.6370 > 2008 9 65.6493 > 2008 10 65.6760 > 2008 11 65.7097 > 2008 12 65.7461 > 2009 1 65.7768 > 2009 2 65.8025 > 2009 3 65.8237 > 2009 4 65.8595 > 2009 5 65.8973 > 2009 6 65.9323 > 2009 7 65.9509 > > Therefore 72 s looks too much to me. > > As the value of DeltaT cannot be known in advance but just assumed from > previous measurements, Orologi Solari uses the following polynomial > expansion as suggested by Espenak and Meeus ( > http://eclipse.gsfc.nasa.gov/SEhelp/deltatpoly2004.html) > > ΔT = 62.92 + 0.32217 * t + 0.005589 * t^2 > where: t = y - 2000 > > that gives 66.7 s for 2010. > > Regards. > > Gian > > ----Messaggio originale---- > Da: [email protected] > Data: 04/03/2010 3.48 > A: <[email protected]> > Ogg: Fwd: Re: Re: Solar position calculator > > > Dipping my oar in the water, Delta-T is absolutely required for accurate > calculations. Almost all of the published polynomials for calculating > orbital values are in the form of a polynomical based on the fraction of a > Julian century for the epoch. This variable, T, is calculated from the > Julian day number. The fraction of the Julian day number is the the > fraction of the day since noon in dynamical time (which is now called > Terrestrial Time, TT). To calculate values for a given UT, you have to > adjust Terrestrial (i.e. dynamical) time by the factor Delta-T = TT-UT. > > So, if you want to do a calculation at noon UT, it is not for Julian day > number xxx.5, but at xxx.5 - delta T (currently about 72 sec.). Clearly, > the adjustment is not a big deal for a contemporary sundial, but is very, > very important for reproductions or studies for times far in the past. Note > that almost all values in the Astronomical Almanac are for 12 hr TT. The > only subject that uses UT is eclipses (I think). > > I trust my program, "The Electric Astrolabe" which can be downloaded from > my web site. I trust it because of the hundreds of hours I have spent > confirming it gives good answers and I know how it works. It's hard to > trust any program that doesn't tell you how the answers are calculated. > > Best regards, > > Jim > > James E. Morrison > [email protected] > Astrolabe web site at http://astrolabes.org > > > ------------ Forwarded message ------------ > From: *Aimo Niemi* <[email protected]> > Date: Mar 3, 2010 > Subject: Re: Re: Solar position calculator > To: [email protected] <[email protected]> > > > Hi > > 2010/3/3 [email protected] <[email protected]> > > I think that no comparison can be made between different programs results > without knowing the value of DeltatT that has been used. > > I again think that DeltaT is not needed if we calculate apparent places and > use UT. > Most accurate link capable for that (what I know) is at > http://ssd.jpl.nasa.gov/horizons.cgi#results > If refraction is not calculated, the link gives > azimuth=200.7239 and altitude = 39.1824 (39.2031 if refraction is included) > Regards > Aimo > > Ephemeris tables usually declare the value of DeltaT that was used. > It is also worthy to note that for gnomonic applications all these results > are more than correct :-) > Regards. > Gian > > ----Messaggio originale---- > Da: [email protected] > Data: 03/03/2010 20.51 > A: "John Goodman"<[email protected]> > Cc: "Sundial List"<[email protected]> > Ogg: Re: Solar position calculator > > > Hi > I got following results from the link > http://www.roman-britain.org/astronomy/astro.htm# > which I believe is trustworthy > > azimuth=200.7233 (20.7233 if south is the zeropoint) > altitude= 39.1827 > I also tested the results with my own semi-accurate PcAllakka > with following results > azimuth=200.715 and altitude=39.188 > Anyone interested can load the program from > http://pc-calculator.110mb.com/allakka/ > or perhaps some of you is curious enough to visit my solar tracking sundial > pages at > http://pc-calculator.110mb.com/tracker/solartracker.html > Greetings > Aimo Niemi > > > 2010/3/3 John Goodman <[email protected]> > > If anyone needs to make precise solar position calculations, the following > software may be useful. There are a few caveats. The software is not a > stand-alone application, it's a software library. The software library needs > to be used from the command line and it runs using the Python programming > language. > > > I'm a Mac user and this is one of those rare occasions when an arcane set > of requirements actually favors the Mac. While Macintosh users tend to be > allergic to the command line, it has existed in the OS for the past 10 > years. Python is there too, lurking under the surface. > > I don't know enough about the PC, but clearly the command line is there and > Python is available too. ( http://www.python.org/download/windows/ ) > > With all that preface, here's what the code can do. Once the necessary > files are installed, you can type the following commands and see the > following results: > > >>> import datetime, solar > >>> d = datetime.datetime(2010, 3, 3, 18, 0, 0) > >>> lat = 42.0 > >>> long = -71 > >>> solar.GetAltitude(lat, long, d) > 39.203509044804704 > >>> solar.GetAzimuth(lat, long, d) > -20.717667802423591 > >>> > > Someone with an ephemeris can check these results. The format for datetime > is "yyyy, mm, dd, hh, mm, ss", optionally followed by a number of > microseconds. The time value entered is for UTC. > > There are other functions for calculations that I haven't explored. You can > read more about the software tools at http://pysolar.org/ Example uses > are shown at http://wiki.github.com/pingswept/pysolar/examples The > software itself is at http://github.com/pingswept/pysolar/downloads > > All of this software is the work of Brandon Stafford, who has generously > offered his code free of charge to anyone who may find it useful. I have > little experience with this software but, as much as I can, I'll be happy to > help anyone trying to use it. > > If there are any questions, I can pass them on to Brandon. I hope this is > helpful to some. > > --------------------------------------------------- > https://lists.uni-koeln.de/mailman/listinfo/sundial > > > > > > --------------------------------------------------- > https://lists.uni-koeln.de/mailman/listinfo/sundial > > > > > ------------------------------ > > --------------------------------------------------- > https://lists.uni-koeln.de/mailman/listinfo/sundial > > > > > --------------------------------------------------- > https://lists.uni-koeln.de/mailman/listinfo/sundial > > >
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