The Sun does not return to the same position in the sky every 24 hours. At local noon, for example, the Sun will appear higher in the sky as we move from winter to summer solstice. In addition, and perhaps more surprisingly, solar days (the roughly 24 hours between subsequent local noons) vary in length, causing the Sun to be east or west of its location 24 hours prior. Over a year, this variation traces out a figure 8, known as an analemma, as shown in Fig.1. It can also be seen in the sundial in Fig. 2, where the gnomon incorporates the analemma to produce an accurate reading of local time.
References
1.
“Analemma A14 2016” by gjdonatiello is licensed under CC0 1.0.
2.
A.
Gangui
, C.
Lastra
, and F.
Karaseur
, “On times and shadows: The observational analemma
,” Phys. Teach.
56
, 367
(Sept.
2018
).3.
J. S.
Chalmers
, “Ground trajectories of geosychronous satellites and the analemma
,” Am. J. Phys.
55
, 548
(May
1987
).4.
M.
Reinsch
, “A formula for the number of days between the winter solstice and the latest sunrise
,” Am. J. Phys.
71
, 1242
(Dec.
2003
).5.
G.
Hoban
and W.
Nielsen
, “Creating a narrated stop-motion animation to explain science: The affordances of ‘slowmation’ for generating discussion
,” Teach. Teach. Educ.
42
, 68
(2014
).6.
The trace of a point above/below the tropics will appear circular; it is moving in a figure 8 relative to the longitude of local noon but this is less obvious visually.
7.
When considering only axial tilt, the longest solar day is only minimally longer than the average day (24 hr 20 s). However, the accumulation of these longer days causes local noon to occur 10 minutes later than would otherwise be anticipated. This is captured in the equation of time, which describes the discrepancy between mean time, in which noon occurs every 24 hours, and apparent solar time, in which noon occurs when the Sun is at its highest point that day. Further details may be seen at the Desmos link https://www.desmos.com/calculator/gd3y9fn9wg.
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