Who, how, and where is the Winter Solstice determined to happen at exactly 12:11 Ct 12/21/13?

High precision statements of the time of the solstices is done from mathematical formulas for the movement of the Earth and Sun. The formulas are calibrated from telescope, radar, and space probe observations, with new data and new formula being figured every year or two. The formulas are accurate to a small fraction of a second and about 1 km in planet or sun positions, for a few years after they are published.

From the formula, the apparent right ascension of the sun is 18h 0m 0.00s, at 17:11:01.5 Zulu, or 12:11:01.5 CT.

P.S. The old definition, of the sun directly over the tropic of Capricorn, has not been used by astronomers for several centuries. That is, as you point out, difficult to measure. The sun is over latitude -23.57617 degrees (plus or minus 0.00001 degrees = 0.036" = 1.11 meters on the Earth's surface) from 16:09:46Z to 18:11:38Z; the mid-point of that time span is 17:10:42Z, about 19 or 20 seconds before the official solstice time. To actually measure this directly, would take a 3.8 meter solar telescope. Such a thing does not exist, although a 4-meter one is planned.

http://en.wikipedia.org/wiki/Advanced_Technology_S...

P.S. #2. A very good amateur telescope setup *might* be able to measure when the sun is at its southernmost point, to an accuracy of 20 minutes. I would have my doubts about that, however.

First, are you referring to the US Naval Observatory? Or something else? Because what you have there, seems to be a portmanteau of several actual organizations.

Secondly, what motion of the Sun are you referring to ('1/60 angular diameter per day')? It moves about [1º ≈ 2 of its diameters] per day, year-round, against the background stars. In its north-south motion, it is exactly stationary at both solstices.

It all boils down to celestial mechanics -- the application of Newton's Laws of Motion and Gravity to the motions of major bodies in the Solar System. And it isn't based on any single observation of anything, no matter how precise.

For this purpose, that's mainly just the Sun, Earth and Moon. When one of these is said to be in some precise location, it is the centroid of that object that is at that spot. Now the motions of all the major Solar System bodies have been tracked quite precisely for centuries, and especially so, since the era of spacecraft observations. Each orbit is an ellipse, to first approximation, and there are six orbital elements that describe the shape and position in space of that ellipse, and where the body lies along that track at any given moment. And in a two-body system, those 6 orbital elements would never change.

But there are several large bodies in the Solar System that interact with each other and with the Earth in ways that are quite significant over time. So these interactions need to be taken into account, by techniques broadly falling under the term, "perturbation theory." Doing this, leads to the second approximation, in which formulas are found to give the relatively slow changes in those orbital elements with time. This allows for very good predictions of positions ("ephemerides," pronounced, "eff-em-AIR-uh-deez") to be computed.

The Moon, however, presents some special problems, because, together with the Earth and Sun, it forms a pretty complex 3-body system. The same laws still apply, of course, it's just harder computationally to apply them well. Not to mention, that when it comes to motions of these 3 bodies, ocean tides on Earth start to play a role in the total energy and angular momentum of the system, and this has an effect on the Moon's orbit.

One of the best ways to sharpen the ephemerides of this system, is by careful observation of solar eclipses, and that trick has been used for centuries. Just as useful, and more numerous, are timings of occultations (covering up) of stars and planets by the Moon.

In determining the times of equinoxes and solstices, the Moon is important, in that its mutual orbit with the Earth, consists of both bodies orbiting a common center of mass (CM), which is about 3000 miles from Earth's center, or about 1000 miles below its surface. It is that CM that orbits the Sun in a steady motion, so that the Moon can effectively advance or delay the Earth in its path around the Sun, which can advance or delay any given equinox or solstice by several minutes.

Putting all this together allows calculation of an equinox or solstice accurate to the minute, if not better.

And OBTW, it was 11:11 CST = 12:11 CDT = 12:11 EST = 17:11 UT.

The "moment" of (boreal) winter solstice is the moment when the subsolar point on earth is as far south as it's going to get. Thus, the observing equipment is not very complicated at all. The predictions are based on years of observing, and of course take into account the leap years and other much smaller perturbations such as the precession of the perihelion.

I'd be surprised if the predictions are wrong by even a millisecond.

Simple historic observation and calculation.