[FRIAM] the Analemma

[Barry MacKichan]

If the earth did not rotate with respect to the stars, each day would be 
a year long. The rotation of the earth adds (or subtracts, I’m too 
lazy now to figure out which) lots more days. The siderial day (the time 
of one rotation wrt the stars) is a few minutes different from the solar 
day (the time of one rotation wrt to the sun).

The second point is that the speed of that year-long day varies over the 
year. The earth’s orbit is elliptical, so its distance to the sun 
varies which means its speed varies (Kepler’s law: the earth sweeps 
equal areas in equal times). The variance between the earth’s actual 
orbital angular velocity and its average orbital angular velocity 
accounts for the variations you cite.

These are not two standards of time measurement, but rather two 
different things you can measure with time. The time zones have nothing 
to do with it except to determine the 3 days the sun is at the zenith at 
noon. (and in fact, if you measure accurately, the probability that the 
sun will ever be at the zenith exactly at noon at any given spot on 
earth is zero; usually it will happen just before noon on one day and 
just after noon on the next, or vice-versa).

--Barry


On 9 Dec 2018, at 19:35, Russell Standish wrote:

> Being a late riser, and a darkness hater, I regard December 7 (the day 
> after
>> St. Nicholas’s Day, by the way) as the first sign of spring, 
>> because it is the
>> day that the afternoons start getting longer.  The shortest morning, 
>> by the
>> way, appears to occur on January 7, One of 3 days in the year when 
>> the sun is
>> at the Zenith at noon.  In other words, noon is moving away from 
>> sunset faster
>> that the setting sun is moving toward the horizon so the sun starts 
>> arriving
>> later on the clock.  Or something like that.  The way I put it 
>> implies two
>> standards of time measurement and I cannot think what the second one 
>> is.