Space Forum / Astronomy / January 2006

Can you define your terms more precisely?  What exactly
do you mean by the degree and minute of your birth?
The position of the Sun (presumably in equatorial
coordinates) at that time?

The sidereal year is 365.256363 days in length.
The Julian year is 365.25 days.

After four years the difference in the two amounts
to 4*(0.006363day) = 36.6 minutes.  Perhaps this is
what is turning up in your calculations.

The effect you're seeing has very little to do with precession, but
is mostly due to the mismatch between the 365-day calendar year and
the 365.2422-day tropical year--most of which gets corrected for each
leap-year. Specifically, any four calendar years (that don't include
a century-year indivisible by 400) contain a total of 1461 days,
while there are about 1460.97 days in four tropical years: the
discrepancy is therefore about three-quarters of an hour every four
years. (Most of this error is corrected for by omitting a leap-year
in three of every four centuries, which was introduced with the
Gregorian reform to the Julian calendar.)

Over the short term, however, in three of every four years the time
the Sun reaches a given longitude advances by about 6 hours, falling
back by about 18 hours in those yearly intervals that contain a
February 29th. Note that the same is true of e.g. the vernal equinox,
which by definition is unaffected by precession. (That is, while of
course its position moves WRT the stars, its ecliptic longitude is
fixed at 0°, when the Sun appears to reach the point where the
ecliptic crosses the equator from south to north.)