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Chavez Sun Calendar

Chavez horizon calendar

The official website of the Chavez Solar Calendar is

The word "solstice" comes from the Latin words "sol" (sun) and "stit" (stationary). Sunset and sunrise horizon positions do not change much from day to day around the solstice times. Likewise the position of the Sun at solar noon in the sky does not change much day to day around solstice times.  By contrast, equinoxes are the times of maximum rate of change of sunset and sunrise horizon positions as well as positions of the Sun at solar noon and number of hours of daylight.

Winter solstice gathering materials

  • Celebrations from many cultures—winter solstice (text only). Google Slides version.
  • The latest sunrises and earliest sunsets of the year do not occur on the winter solstice. Example—winter of 2019:
    • Latest sunrise(s) (7:25am) occur Jan 3-8 (6 days)
    • Earliest sunset(s) (4:49pm) occur Dec 4-10 (7 days)
    • Sunset on Dec 21 is 4:53pm and is only the same on one adjacent day, Dec 20.
    • 9:32:21 hours of sunlight on winter solstice
    • WHY? There are two elements that contribute to unusual variations in timing of sunsets & sunrises:
      • tilt of Earth's axis (23.5°with respect to its orbit) and
      • eccentricity of Earth's orbit (deviates from a perfect circle by 3%)
      Deviations in timings of sunsets are similar to deviations of apparent solar noon (the moment when the Sun crosses the north-south meridian line in the sky) from the mean solar noon (averaged over the whole year, as displayed in sundials). Deviations are referred to as the equation of time. Graphs of the equation of time:
      2 components --|-- components added  
      [references: and]
  • Solar Motion Demonstrator1 page version --|-- 12 page version
  • Sunset positions throughout the year
The Reason for Seasons
Let's assume for the moment that: "seasons are caused by how close the Earth is to the Sun at different times of year." 
In the diagram below, notice that
  • for the northern hemisphere Earth is closest to the Sun near the time of the winter solstice (December). The actual time of the closest separation of Earth and Sun is about January 3 each year, an event called perihelion
  • but for the southern hemisphere Earth is closest to the Sun near the time of the summer solstice (that also occurs in December).
So for people in the southern hemisphere, changes in the Sun-Earth distance may be a logical explanation for why it's warmer in summer than in winter.  But the logic completely fails for those of us in the northern hemisphere.
What does that mean for our assumption that 
"seasons are caused by how close the Earth is to the Sun at different times of year"?
[That assumption must be flat wrong!]

Solstices and Equinoxes for Earth's Northern Hemisphere

Diagram of Earth's orbit, indicating seasons and distances
The real Sun is 109 times bigger than Earth in diameter.

So what are the real reasons for the seasons? 
It's the tilt of the Earth's axis with respect to its orbit, as shown in the diagram. 
Earth's axis is always pointing towards the North Star, at a 23.5° angle from vertical to the plane of Earth's orbit. 
In the northern hemisphere's winter, less of the northern hemisphere is illuminated by sunlight, causing
  • fewer hours of daylight, more hours of night and
  • less intense sunlight due to lower angle of the Sun's rays striking the ground.
Alan Gould,
Dec 21, 2019, 7:42 PM
Alan Gould,
Dec 21, 2019, 7:40 PM
Alan Gould,
Dec 22, 2019, 9:23 AM
Alan Gould,
Dec 21, 2019, 8:15 PM
Alan Gould,
Dec 21, 2019, 8:10 PM