NavList:

Bill, you wrote:

"That caused me to wonder if at some time in the past there was
a conscious effort to link the equation of time to some celestial event."

 

er... how could there be? Its numerical value follows directly from its definition. The values on specific dates do change over the centuries and millennia. Is that what you were asking about?

 

And also:

"Looking at it from a purely (modern) calendar event, the central zero point
occurs close to the midpoint of a calendar year in June, but is past that
calendar midpoint."

 

Well, you could re-define the calendar in such a way that the midpoint falls on a specific date, but that has never been done. And there wouldn't be any reason to do so. In fact, two of the zeroes in the equation time presently fall on December 25 --Christmas in Western Christianity-- and April 15 --Fed Tax day in the US. That's how I remember the zero points when I'm trying to estimate the approximate time of apparent noon during the year, but there's no real "physical" significance to those dates, unless the IRS knows something that we don't!

 

You asked:
"When was the equation of time first understood and mapped?"

 

Thousands of years ago. Ptolemy knew about it and wrote a chapter on it in the Almagest. But for astronomers back then, it was merely a curiosity. It was the difference between time, as everyone understood it, and sidereal time, which was known and significant only to astronomers.

 

And:

"At that point, was there an attempt to link it to a celestial event that may
now be lost in change?"

 

As best as I can understand what you're asking, no, there couldn't be. There's no additional "freedom" in the definition of the equation of time that would allow that sort of linkage to a celestial event.

And:
"On a related issue: If I understand it the pole star will--within a
generation or two--come as close to earth's rotational axis as it will come
for 26,000 years. All things being equal, will the winter solstice occur
during June in approx. 13,000 years?
If yes to the above, will the northern hemisphere (like Australia now) pick
up a bit more heat by virtue of proximity in the summer, and a bit less in
the winter?"

 

Basically, yes. All other things being equal, that would be the case. In fact, there is a rather involved dance involving the precession of the equinoxes, the oscillating tilt of the Earth's axis, and the oscillating variation of the Earth's orbital eccentricity. These three cycles combined determine the net "insolation", the solar energy received by each patch of the Earth's surface, over thousands of years (under the assumption that the Sun's luminosity is relatively constant on that time scale). Almost a century ago, Serbian geophysicist Milutin Milankovitch proposed that these cycles of insolation are responsible for the cycles of the ice ages. There is very good, but not conclusive evidence that the long-term climate is controlled by these cycles in the Earth's precession, tilt, and eccentricity just as Milankovitch suggested. The problem is not simple because large ice sheets make the climate non-linear. Once a great sheet of ice forms, it tends to remain in place because the high albedo of the ice reflects sunlight and keeps the climate cold. Best guess right now is that the Milankovitch cycles control the ice ages, but strong non-linear dynamics are almost as important.