I want to see what the stars looked like up to 15,000 years into the past and future.

I've chosen 15,000 years in order to see a full precession cycle. To make things easier, I would be satisfied with a relatively low precision of 60 arcseconds. I want to calculate the equatorial positions of bright stars, and show the path of the ecliptic. (I have no need to calculate the positions of the Sun or planets.)

My source data is the *Yale Bright Star Catalog, revision 5*, for J2000,
which includes proper motion data. My core reference is *Astronomical Algorithms* by Jean Meeus (1991).

**Precession.** Is the algorithm in Meeus (equations 20.3 on page 126) suitable for
+/- 15,000 years? The non-linear terms get up to about 20 degrees. Is that a problem?

Would it be reasonable to update Meeus with this paper from Capitaine et al 2003
(page 572, equations 21)? It has a remark on accuracy:
"The following series with a 0.1 µas level of precision matches the canonical 4-rotation
series to sub-microarcsecond accuracy over 4 centuries." Those equations (21) are for accumulated amounts (subscript *A* for *accumulated*).
Is it OK to simply drop the constant terms in these expressions?
Meeus has no constant terms in his algorithm.

**Proper motion.** The YBS catalog has proper motion in declination and right ascension.
At what point would a simple linear treatment of proper motion start to be of dubious quality,
given that I can tolerate a full 60 arcseconds of error? (I mean by this using the simple 2D proper motion across the sky, with no 3D velocity vector.)

*Example*: for the year -3200, the max proper motion for all of the stars in the YBS, between J2000 and that date, is +10°12' (using YBS data).

**The ecliptic.** I would be satisfied with simply seeing the path of the ecliptic, without trying
to calculate the Sun's actual position. I'm assuming that all I really need is the value for the obliquity of the ecliptic. Meeus (page 135, equation 21.3) has an expression
for the obliquity of the ecliptic, but he says that it shouldn't be used outside of 10,000 years from J2000. Does anyone know of a replacement for this expression, which is valid for a longer period?