### SLA_PREC

Precession Matrix (FK5)

ACTION:
Form the matrix of precession between two epochs (IAU 1976, FK5).
CALL:
CALL sla_PREC (EP0, EP1, RMATP)
##### GIVEN:
 EP0 D beginning epoch EP1 D ending epoch

##### RETURNED:
 RMATP D(3,3) precession matrix

NOTES:
(1)
The epochs are TDB Julian epochs.
(2)
The matrix is in the sense:

v${}_{1}$ = M$\cdot$v${}_{0}$

where v${}_{1}$ is the star vector relative to the mean equator and equinox of epoch EP1, M is the $3×3$ matrix RMATP and v${}_{0}$ is the star vector relative to the mean equator and equinox of epoch EP0.
(3)
Though the matrix method itself is rigorous, the precession angles are expressed through canonical polynomials which are valid only for a limited time span. There are also known errors in the IAU precession rate. The absolute accuracy of the present formulation is better than ′′01 from 1960 AD to 2040 AD, better than $1\phantom{\rule{-0.54753pt}{0ex}}$${}^{\prime }{\phantom{\rule{-1.09506pt}{0ex}}}^{\prime }$ from 1640 AD to 2360 AD, and remains below $3\phantom{\rule{-0.54753pt}{0ex}}$${}^{\prime }{\phantom{\rule{-1.09506pt}{0ex}}}^{\prime }$ for the whole of the period 500 BC to 3000 AD. The errors exceed $10\phantom{\rule{-0.54753pt}{0ex}}$${}^{\prime }{\phantom{\rule{-1.09506pt}{0ex}}}^{\prime }$ outside the range 1200 BC to 3900 AD, exceed $100\phantom{\rule{-0.54753pt}{0ex}}$${}^{\prime }{\phantom{\rule{-1.09506pt}{0ex}}}^{\prime }$ outside 4200 BC to 5600 AD and exceed $1000\phantom{\rule{-0.54753pt}{0ex}}$${}^{\prime }{\phantom{\rule{-1.09506pt}{0ex}}}^{\prime }$ outside 6800 BC to 8200 AD. The SLALIB routine sla_PRECL implements a more elaborate model which is suitable for problems spanning several thousand years.
REFERENCES:
(1)
Lieske, J.H., 1979. Astr.Astrophys. 73, 282; equations 6 & 7, p283.
(2)
Kaplan, G.H., 1981. USNO circular no. 163, pA2.