[dpsi, deps] = ERFA.nut00a(date1, date2)Nutation, IAU 2000A model (MHB2000 luni-solar and planetary nutation with free core nutation omitted).
date1,date2 double TT as a 2-part Julian Date (Note 1)
dpsi,deps double nutation, luni-solar + planetary (Note 2)
- The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.
-
The nutation components in longitude and obliquity are in radians and with respect to the equinox and ecliptic of date. The obliquity at J2000.0 is assumed to be the Lieske et al. (1977) value of 84381.448 arcsec.
Both the luni-solar and planetary nutations are included. The latter are due to direct planetary nutations and the perturbations of the lunar and terrestrial orbits.
-
The function computes the MHB2000 nutation series with the associated corrections for planetary nutations. It is an implementation of the nutation part of the IAU 2000A precession- nutation model, formally adopted by the IAU General Assembly in 2000, namely MHB2000 (Mathews et al. 2002), but with the free core nutation (FCN - see Note 4) omitted.
-
The full MHB2000 model also contains contributions to the nutations in longitude and obliquity due to the free-excitation of the free-core-nutation during the period 1979-2000. These FCN terms, which are time-dependent and unpredictable, are NOT included in the present function and, if required, must be independently computed. With the FCN corrections included, the present function delivers a pole which is at current epochs accurate to a few hundred microarcseconds. The omission of FCN introduces further errors of about that size.
-
The present function provides classical nutation. The MHB2000 algorithm, from which it is adapted, deals also with (i) the offsets between the GCRS and mean poles and (ii) the adjustments in longitude and obliquity due to the changed precession rates. These additional functions, namely frame bias and precession adjustments, are supported by the ERFA functions eraBi00 and eraPr00.
-
The MHB2000 algorithm also provides "total" nutations, comprising the arithmetic sum of the frame bias, precession adjustments, luni-solar nutation and planetary nutation. These total nutations can be used in combination with an existing IAU 1976 precession implementation, such as eraPmat76, to deliver GCRS- to-true predictions of sub-mas accuracy at current dates. However, there are three shortcomings in the MHB2000 model that must be taken into account if more accurate or definitive results are required (see Wallace 2002):
(i) The MHB2000 total nutations are simply arithmetic sums,
yet in reality the various components are successive Euler
rotations. This slight lack of rigor leads to cross terms
that exceed 1 mas after a century. The rigorous procedure
is to form the GCRS-to-true rotation matrix by applying the
bias, precession and nutation in that order.
(ii) Although the precession adjustments are stated to be with
respect to Lieske et al. (1977), the MHB2000 model does
not specify which set of Euler angles are to be used and
how the adjustments are to be applied. The most literal
and straightforward procedure is to adopt the 4-rotation
epsilon_0, psi_A, omega_A, xi_A option, and to add DPSIPR
to psi_A and DEPSPR to both omega_A and eps_A.
(iii) The MHB2000 model predates the determination by Chapront et al. (2002) of a 14.6 mas displacement between the J2000.0 mean equinox and the origin of the ICRS frame. It should, however, be noted that neglecting this displacement when calculating star coordinates does not lead to a 14.6 mas change in right ascension, only a small second- order distortion in the pattern of the precession-nutation effect.
For these reasons, the ERFA functions do not generate the "total nutations" directly, though they can of course easily be generated by calling eraBi00, eraPr00 and the present function and adding the results.
- The MHB2000 model contains 41 instances where the same frequency appears multiple times, of which 38 are duplicates and three are triplicates. To keep the present code close to the original MHB algorithm, this small inefficiency has not been corrected.
eraFal03 mean anomaly of the Moon
eraFaf03 mean argument of the latitude of the Moon
eraFaom03 mean longitude of the Moon's ascending node
eraFame03 mean longitude of Mercury
eraFave03 mean longitude of Venus
eraFae03 mean longitude of Earth
eraFama03 mean longitude of Mars
eraFaju03 mean longitude of Jupiter
eraFasa03 mean longitude of Saturn
eraFaur03 mean longitude of Uranus
eraFapa03 general accumulated precession in longitude
Chapront, J., Chapront-Touze, M. & Francou, G. 2002, Astron.Astrophys. 387, 700
Lieske, J.H., Lederle, T., Fricke, W. & Morando, B. 1977, Astron.Astrophys. 58, 1-16
Mathews, P.M., Herring, T.A., Buffet, B.A. 2002, J.Geophys.Res. 107, B4. The MHB_2000 code itself was obtained on 9th September 2002 from ftp//maia.usno.navy.mil/conv2000/chapter5/IAU2000A.
Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, Astron.Astrophys.Supp.Ser. 135, 111
Wallace, P.T., "Software for Implementing the IAU 2000 Resolutions", in IERS Workshop 5.1 (2002)
This revision: 2021 May 11
Copyright (C) 2013-2021, NumFOCUS Foundation. Derived, with permission, from the SOFA library.