OK, this may take a while to explain. This passage in Bad Astronomy is on page 55:
The last two sentences are in error, the key phrase is "our current calendar".

The Earth actually takes slightly more than 365.25 days to go around the Sun. Early calendars accounted for the extra quarter day or so, but because of precession, the date of the vernal equinox gradually changed. The first day of Spring was off by more than ten days, after a few hundred years. That effect is what is described in the Bad Astronomy book.

However, Pope Gregory decreed that the vernal equinox was to always occur late in March, and so they skipped the extra days to bring it back into place, and defined the length of the year to just a little bit less than 365.25 days. That is called the tropical year (or the astronomical year), and it is what our current calendar (the Gregorian calendar) is based upon. It is the time from one vernal equinox to the next.

It is defined that way so that the vernal equinox (and therefore the summer solstice) will always occur at the same time of the year, and so the Earth's north pole will always tilt towards the Sun in June.

Digging a little deeper, I found this page by Michael Allison, who keeps time on Mars. He points out that the time between vernal equinoxes is not constant, because of the wobble of precession. But it would probably only make a day or two difference in 13000 years.

Allison is at the Goddard Institute for Space Studies in New York, the BA used to be at Goddard Space Flight Center.

PS: in the upper right, one image down from the corner

<a name="20020525.3:00"> page 20020525.3:00 aka Equal Not
On 2002-03-11 03:23, GrapesOfWrath wrote: To: H
Digging a little deeper, I found this page by Michael Allison, who keeps time on Mars. He points out that the time between vernal equinoxes is not constant, because of the wobble of precession. But it would probably only make a day or two difference in 13000 years.

Allison is at the Goddard Institute for Space Studies in New York, the BA used to be at Goddard Space Flight Center.
--------3:01 A.M. PST May 25, 2002
i've always suspected the word myself
and do not attemp to take sides on this issue
However I do want to Push this to the top of
page one at this time 3:03 A.M. Pacific Standard

From Quote in OP

The earth's axis points toward the celestial pole at all times.

It is inclined toward the sun in the summer .
It is inclined away from the sun in the winter .

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Do nothing simply when a way can be found to make it complex and worderful.

If you mean what I think you mean, remember that the celestial pole is that point (currently) near Polaris, where a line from the South Pole through the North Pole would point at (all this refers to only the north celestial pole, of course). It has nothing to do with where the Sun appears to be. The apparent inclination towards and away from the Sun is just because we happen to be on the other side of the Sun at those times.

And welcome to the board! Don't mind me, I'm always picking the nits around here.

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Actually, the problem wasn't the precession, but a calendar with a year of 365.25 days, so the calendar year was slipping compared to the solar year.

The result of the precession is that the position of the sun at the vernal equinox will move relative to the stars, so the stars we're used to having high above the horizon in the winter will be high in the summer instead.

Depends on how you look at it. The solar year is about 11 minutes less than 365.25 days, but without precession, it would be 9 minutes more than 365.25 days. So, they would have added days rather than removed them, had there been no precession. The amount of precession determines the direction of the drift.

Which brings up an interesting point--if precession were about half of what it is, we would not have had to go through that exercise.