The analemma generator
The Sun's declination against the equation of time over a year — its position in the sky at the same clock time each day. The figure-of-eight is not symmetric: the lower lobe is larger because the Earth is nearest the Sun in January, and the whole shape is the eccentricity and the tilt plotted against each other.
3 essays call
analemma. The drawing above is what it returns with no arguments at all; every
call below passes it something, because a placement that passes nothing draws whichever member
of the family the generator happens to default to rather than the one its essay argues about.
Where it is called
Every figure listed here is the same construction drawn at different numbers, so a correction to one is a correction to all of them.
The observed sky
The Sun is a bad clock, by up to sixteen minutes
Solar noon and twelve o'clock are not the same instant, and the discrepancy runs through a fixed annual cycle. It has two causes, one from the shape of the orbit and one from the tilt of the axis.
The observed sky
Two fictitious suns in sequence
The equation of time is usually described as one quantity with two causes. It is better read as two separate reductions, each with its own imaginary body — one that moves uniformly along the ecliptic and one that moves uniformly along the equator — and the second is not the first.
The observed sky
The earliest sunset is not the shortest day
A sunset time is solar noon plus half the day length, and the two have different stationary points. The day length stops shortening at the solstice; the equation of time does not stop moving, so the sum keeps falling — and the earliest sunset comes days before the shortest day.