To be or not to LST, the question is how long is a year.

In class the other day, I got to talking with a few people about local apparent sidereal time (LST or LAST) and its relation to solar time.  Our discussion came to an interesting place when we started talking about a sidereal year compared to a solar year.  I seemed to be the one who was causing a discussion because I was interested in thinking about what time LST the new sidereal year would start at each year.  Would an LST clock be at 11:59 before turning to 12:00 the next year?  Having since looked up more about this, I should probably go back and talk about some definitions and such.

The way we had had LST defined for us was that the sidereal year started at noon on the vernal equinox and that noon LST would occur each day following when a star that was on the meridian (a great circle drawn imaginarily north to south passing through the zenith, which is a point in the sky directly above the observer) at noon the previous day again passed the observer's meridian.  As a solar day is defined so that at noon each day the sun should pass through the meridian, the same is true of a sidereal day except that the star is not the sun, but instead a more distance star that seems to not move relative to our motion in the solar system.  A solar day and a sidereal day are different because the earth moves in its yearly path around the sun which changes the background stars' position relative to the sun in our daily rotation.  That may sound complicated, but it really is not.  For a nice diagram, see this picture from wikipedia here.  As can be seen from the diagram, because the earth moves relative to the sun along its orbit each day, but the earth does not seem to move relative to distant stars, causing noon LST to occur earlier each day relative to noon solar time, about 4 minutes earlier each day.

So, on to my original question, what time does the new sidereal year start in LST?  Based on the definition above, an LST clock would not go smoothly across the change in year because the equinox moves relative to the background stars very slightly.  According to the wikipedia article, LST is really based on the local of the vernal equinox relative to the meridian and the background stars relative to the meridian.  While these are not very different, it does still make a difference how LST is defined.  Though, looking back to what I was thinking in class, I think I was wrong on the magnitude of the difference I was thinking of at the time.  I think my problem then was that I didn't think of the fact that in a sidereal year, there are approximately 366.24 sidereal days, one more day than a solar year because we orbit around the sun.

I think most interesting though was what I found when I was looking for more information on this.  As before, using wikipedia and just clicking random links that I wanted to know more about, I've found that (as really makes sense when you think about it) pretty much nothing about earth's motion is very nice.  We don't travel in a circle around the sun, it's more of an ellipse, but then that isn't even true.  Because the earth/moon orbit the sun together, that gives the earth an even more irregular motion.  Then of course the earth's axis of rotation is precessing, which is also affected by the sun and moon.  Then, lest we forget the other planets in the solar system, they also affect earth's orbit and its precession.

One last fact: the change in the precession of the earth is called nutation and seems to be mostly affected by the sun and the moon, but wikipedia also lists ocean currents, wind, and even the motions of the earth's molten core as affecting this motion.

I'm just glad that my watch fairly accurately tells me what time of the day it is despite all these perturbing factors.

For these thoughts, I'd like to acknowledge some helpful conversations with Prof. Johnson, Jackie, and whoever I was working with in class that day, I believe David, Dan, and Mee.