USNO Circular 179 - U.S. Naval Observatory

PRECESSION & NUTATION 39
Table 5.1 Precession-Nutation: Old & New
Values in arcseconds at J2000.0
Quantity Old value New value New–Old
General precession in longitude (/cen) 5029.0966 5028.796195 −0.3004
Mean obliquity 84381.448 84381.406 −0.042
Mean obliquity rate (/cen) −46.8150 −46.836769 −0.0218
In-phase nutation amplitudes:
18.6-year longitude −17.1966 −17.2064161 −0.0098
18.6-year obliquity 9.2025 9.2052331 0.0027
9.3-year longitude 0.2062 0.2074554 0.0013
9.3-year obliquity −0.0895 −0.0897492 −0.0002
annual longitude 0.1426 0.1475877 0.0050
annual obliquity 0.0054 0.0073871 0.0020
semiannual longitude −1.3187 −1.3170906 0.0016
semiannual obliquity 0.5736 0.5730336 −0.0006
122-day longitude −0.0517 −0.0516821 0.0000
122-day obliquity 0.0224 0.0224386 0.0000
monthly longitude 0.0712 0.0711159 −0.0001
monthly obliquity −0.0007 −0.0006750 0.0000
semimonthly longitude −0.2274 −0.2276413 −0.0002
semimonthly obliquity 0.0977 0.0978459 0.0001
equator, as appropriate for most observations, but generally use a moving ecliptic as a reference
plane for at least some of the angles involved (there are different formulations of precession using
different angle sets). This allows the precession and nutation transformations to properly account
for the motion of the equinox as well as that of the equator. The precession of the ecliptic is
obtained from theory (although indirectly tied to observations through the JPL DE405 ephemeris),
as are the high-order (unobserved) components of the precession of the equator. However, because
of the mix of theory and observation that is involved in the final expressions, raw corrections to
rates of precession from VLBI observations will not in general propagate exactly to the familiar
precession quantities.
The changes in the amplitudes of the nutation components are also not directly taken from
these observations; instead, a new nutation theory is developed and fit to observations by allowing
a small number of geophysical constants to be free parameters. These parameters are constants
in a “transfer function” that modifies the amplitudes of the terms from a rigid-Earth nutation
development. Since there are fewer solved-for geophysical constants than the number of terms with
observed amplitudes, the fit cannot be perfect. For the IAU 2000A model, 7 geophysical parameters
were determined based on the observed amplitudes of 21 nutation terms (prograde and retrograde
amplitudes for each) together with the apparent change in the rate of precession in longitude. Note
that the number of observational constraints and the number of free parameters in the model are
both quite small compared to the 1365 terms in the new, full nutation series.
Table 5.1 compares the old and new values, at epoch J2000.0, of some of the primary quantities
involved in the precession and nutation algorithms. In the table, all quantities are in arcseconds,
and the rates (marked /cen) are per Julian century of TDB (or TT). The longitude components
should be multiplied by the sine of the obliquity (≈0.3978) to obtain the corresponding motion of