RE: Analemma intersection

[Roger W. Sinnott]

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 

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Re: Analemma intersection

[Roger Bailey]

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





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Analemma intersection

[Dan-George Uza]

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
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