re: Analemma intersection
Dan, Steve Regarding the exact time of intersection: It requires a rather interesting problem of simultaneously minimizing EOT and declination between spring and fall dates. Fortunately I have a spread sheet that implements the calculation of EOT to within a second or so and likewise precise declination. I set up the difference of EOT(spring) - EOT(fall) and DEC(spring)-DEC(fall) as a pair of 2D tables using date/time variables. To see small changes, I multiplied the DEC error in degrees by x100 and looked at EOT error in seconds. For this year, the result to the nearest hour is 11 April, 7:00 UTC and 28 Aug, 17:00 UTC corresponding to Julian Dates of 2458219.79167 and 2458359.20833. Regards, Bob --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Analemma intersection
Hello all, I subscribe to this Sundial List because I am working on an art project installation of a Sundial and a "Full Moondial" (however weird this sounds). I am an artist working on time, space and coincidences. I am writing you now because of this last question and answers entries. I find them inspiring and heartwarming. Usually, I know no answer to all entries, I just learn from you all. But today I can answer the question of Dan: *Does it have any special significance? * Yes, it does, since it arises the doubt of its significance. It definitely makes me start a new art project about it. Thank you Dan, and thank you all for this Sundial List. I will share with you my results. All the best and warm regards, Ale On Thu, Apr 12, 2018 at 6:55 PM, Roger W. Sinnott wrote: > Roger (and others), > > > > A slight correction concerning the motion of Earth's perihelion with > respect to the seasons. Owing to precession, the equinoxes and solstices > drift slowly westward along the ecliptic in a cycle of about 26,000 years. > But at the same time perturbations by the other planets cause the Earth's > perihelion point to drift slowly eastward along the ecliptic. The net > effect is that the perihelion migrates all the way around the ecliptic > (with respect to the seasons) in about 21,000 years. > > > > Bernard M. Oliver wrote a classic article about the changing shape of the > analemma for Sky & Telescope (July 1972, pages 20-22). He gave A.D. 1246 as > the year when perihelion and the winter solstice coincided. Among the > other effects he noted, in A.D. 6489 the two lobes of the analemma will be > essentially equal in size and perihelion will coincide with the vernal > equinox. > > > > (Full disclosure: I remember that article well, because one of its > diagrams was the very first one I prepared after joining the magazine > staff!) > > > > Roger S. > > > > > > *From:* sundial [mailto:sundial-boun...@uni-koeln.de] *On Behalf Of *Roger > Bailey > *Sent:* Thursday, April 12, 2018 6:13 PM > *To:* Dan-George Uza; Sundial List > *Subject:* Re: Analemma intersection > > > > Hi Dan, > > To me the value of the EQT at the intersection is an indication of the > asymmetry of the analemma caused by the difference between the solstice and > perihelion dates. The tilt of the earths axis is one parameter that defines > the analemma. This is shown at the extremes, the summer and winter > solstices. The eccentricity of the orbit is the other parameter that > defines the analemma. This is indicated by the perihelion. If the date of > the perihelion is the same as the solstice, I would expect the curve would > be symmetrical and the EQT at the intersection would be equal to zero. > Perihelion was 2 Jan 2018 and the winter solstice was 21 Dec 2018. This 12 > day difference defines the offset of the intersection of the analemma > loops. When was the perihelion on the winter solstice? The perihelion > changes in a cycle of 25,800 years. So 12 days gives 12/365.25x25,800 or > 878 years ago. In 1140 AD I would expect a symmetrical analemma. > > > > Of course there is more to this than this simple approximation of orbital > dynamics. What was the actual date when the perihelion and solstice were > the same? I offer this as quick answer to the question on the significance > of the analemma curve intersection. > > > > Regards, Roger Bailey > > Walking Shadow Designs > > > > *From:* Dan-George Uza > > *Sent:* Thursday, April 12, 2018 3:46 AM > > *To:* Sundial List > > *Subject:* Analemma intersection > > > > Hello, > > > > Tomorrow the Sun will have reached the point of intersection in the > analemma 8-curve. How do you compute the exact time of intersection (i.e. > when both the hour angle and the solar declination match for two days)? And > does it have any special significance? > > > > Dan > -- > > --- > https://lists.uni-koeln.de/mailman/listinfo/sundial > > > -- > > [image: Image removed by sender. Avast logo] > <https://www.avast.com/antivirus> > > This email has been checked for viruses by Avast antivirus software. > www.avast.com <https://www.avast.com/antivirus> > > > > > --- > https://lists.uni-koeln.de/mailman/listinfo/sundial > > > -- ... *Ale de la Puente* www.aledelapuente.org skype: aledelapuente T: + 52 55 55 54 0895 M: + 52 1 55 54 34 8548 Twitter: @aledelapuente instagram @aledelapuente --- https://lists.uni-koeln.de/mailman/listinfo/sundial
RE: Analemma intersection
Roger (and others), A slight correction concerning the motion of Earth's perihelion with respect to the seasons. Owing to precession, the equinoxes and solstices drift slowly westward along the ecliptic in a cycle of about 26,000 years. But at the same time perturbations by the other planets cause the Earth's perihelion point to drift slowly eastward along the ecliptic. The net effect is that the perihelion migrates all the way around the ecliptic (with respect to the seasons) in about 21,000 years. Bernard M. Oliver wrote a classic article about the changing shape of the analemma for Sky & Telescope (July 1972, pages 20-22). He gave A.D. 1246 as the year when perihelion and the winter solstice coincided. Among the other effects he noted, in A.D. 6489 the two lobes of the analemma will be essentially equal in size and perihelion will coincide with the vernal equinox. (Full disclosure: I remember that article well, because one of its diagrams was the very first one I prepared after joining the magazine staff!) Roger S. From: sundial [mailto:sundial-boun...@uni-koeln.de] On Behalf Of Roger Bailey Sent: Thursday, April 12, 2018 6:13 PM To: Dan-George Uza; Sundial List Subject: Re: Analemma intersection Hi Dan, To me the value of the EQT at the intersection is an indication of the asymmetry of the analemma caused by the difference between the solstice and perihelion dates. The tilt of the earths axis is one parameter that defines the analemma. This is shown at the extremes, the summer and winter solstices. The eccentricity of the orbit is the other parameter that defines the analemma. This is indicated by the perihelion. If the date of the perihelion is the same as the solstice, I would expect the curve would be symmetrical and the EQT at the intersection would be equal to zero. Perihelion was 2 Jan 2018 and the winter solstice was 21 Dec 2018. This 12 day difference defines the offset of the intersection of the analemma loops. When was the perihelion on the winter solstice? The perihelion changes in a cycle of 25,800 years. So 12 days gives 12/365.25x25,800 or 878 years ago. In 1140 AD I would expect a symmetrical analemma. Of course there is more to this than this simple approximation of orbital dynamics. What was the actual date when the perihelion and solstice were the same? I offer this as quick answer to the question on the significance of the analemma curve intersection. Regards, Roger Bailey Walking Shadow Designs From: Dan-George Uza <mailto:cerculdest...@gmail.com> Sent: Thursday, April 12, 2018 3:46 AM To: Sundial List <mailto:sundial@uni-koeln.de> Subject: Analemma intersection Hello, Tomorrow the Sun will have reached the point of intersection in the analemma 8-curve. How do you compute the exact time of intersection (i.e. when both the hour angle and the solar declination match for two days)? And does it have any special significance? Dan _ --- https://lists.uni-koeln.de/mailman/listinfo/sundial _ <https://www.avast.com/antivirus> Image removed by sender. Avast logo This email has been checked for viruses by Avast antivirus software. www.avast.com <https://www.avast.com/antivirus> --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Analemma intersection
Hi Dan, To me the value of the EQT at the intersection is an indication of the asymmetry of the analemma caused by the difference between the solstice and perihelion dates. The tilt of the earths axis is one parameter that defines the analemma. This is shown at the extremes, the summer and winter solstices. The eccentricity of the orbit is the other parameter that defines the analemma. This is indicated by the perihelion. If the date of the perihelion is the same as the solstice, I would expect the curve would be symmetrical and the EQT at the intersection would be equal to zero. Perihelion was 2 Jan 2018 and the winter solstice was 21 Dec 2018. This 12 day difference defines the offset of the intersection of the analemma loops. When was the perihelion on the winter solstice? The perihelion changes in a cycle of 25,800 years. So 12 days gives 12/365.25x25,800 or 878 years ago. In 1140 AD I would expect a symmetrical analemma. Of course there is more to this than this simple approximation of orbital dynamics. What was the actual date when the perihelion and solstice were the same? I offer this as quick answer to the question on the significance of the analemma curve intersection. Regards, Roger Bailey Walking Shadow Designs From: Dan-George Uza Sent: Thursday, April 12, 2018 3:46 AM To: Sundial List Subject: Analemma intersection Hello, Tomorrow the Sun will have reached the point of intersection in the analemma 8-curve. How do you compute the exact time of intersection (i.e. when both the hour angle and the solar declination match for two days)? And does it have any special significance? Dan --- https://lists.uni-koeln.de/mailman/listinfo/sundial --- This email has been checked for viruses by Avast antivirus software. https://www.avast.com/antivirus --- https://lists.uni-koeln.de/mailman/listinfo/sundial