Several notes n the table of differences of the nutation tables
MHB2000 and IAU1980 (CPO_MHB). (Cyril Ron, October 2001, Paris)
- The task has been initiated by the Christian's need of Christian to have
the table of the CPO_MHB ( term by term ) for direct computation of
the differences in the program for interpolation in the EOPC04 combinations.
- The original tables and subroutines are available at Tom Herring's web site:
http://bowie.mit.edu/~tah/mhb200 in two versions:
- the pure MHB_2000 series
- the fine tuned series MHB with fitted amplitudes of the 5 long-period
terms from the observations of VLBI referred to as
MHB_2000ft.series and MHB_2000ft.f.
for more details, see the Tom Herring's web site.
The unix script is prepared that compiles the table from the original Tom
Herring's data sets. It can be used in compilation any more recent versions of
the series.
- The table MHB_2000.series doesn't contain the planetary terms which
are included in the MHB_2000.f. The planetary terms were taken into
the differences CPO_MHB without any change from MHB_2000.f. On the other
hand the file MHB_2000.series contains several secular rates of the
out-of-phase terms that are not included in the tables in the subroutine
MHB_2000.f due to their small values (3mus/cy) (see the e-mail of Tom Herring).
. >Date: Thu, 25 Oct 2001 10:16:49 -0400 (EDT)
. >From: Tom Herring
. >To: Cyril RON
. >Subject: Re: mhb_2000.f ?
.
. Hello Cyril:
.
. The secular rates on the out-of-phase terms are derived from the secular
. rates for the rigid nutation series propagated through the complex
. transferr function. These are in the table for completenss but since the
. largest rate is 3 micro-asec/century we did not add them the computation
. of the series. MHB2000 was meant to be used over intervals of 20-30 yrs
. (around J2000) in which case these terms will not exceed 1 micro-arc-sec.
. For the long period variations we think the accuracy of MHB2000 is in the
. 10's of uas range. They do not appear in the internal tables used by
. MBH2000 but rather are only output in the table form.
.
. Regards Tom Herring.
.
. ---------------------------------------------------------------------------
. Thomas A Herring Scientific Director UNAVCO
. Room 54-618, MIT 3340 Mitchell Lane
. 77 Massachusetts Avenue, Boulder, CO 80301
. Cambridge, MA 02139 http://www.unavco.ucar.edu
. Phone (617) 253-5941; Fax (617) 253-1699
. web: http://www-gpsg.mit.edu/~tah
- The FCN terms are not included in the table. To imply them, see MHB_2000.f.
- The different values of fundamental arguments used in the MHB_2000 and
IAU1980, respectively, evoke the out-of-term that reach the value
0.0175mas in case of the semiannual term in dpsi. dpsi_MHB and deps_MHB are
the amplitudes in MHB2000, dpsi_IAU80 and deps_IAU80 are the
amplitudes in IAU1980. The fundamental arguments of MHB2000 are referred as to
a+bt. da and db are the differencesof the constant and secular terms of
the fundamental arguments used in MHB2000 and IAU1980.
dpsi_MHB * sin(a+bt) - dpsi_IAU80 * sin[(a+bt)+(da+dbt)] =>
in-phase term: (dpsi_MHB-dpsi_IAU80) * sin(a+bt)
ot-of-phase : - dpsi_IAU80*da * cos(a+bt) -
- dpsi_IAU80*db*t * cos(a+bt)
and for deps similarly
deps_MHB * cos(a+bt) - deps_IAU80 * cos[(a+bt)+(da+dbt)] =>
in-phase term: (deps_MHB-deps_IAU980) * cos(a+bt)
out-of-phase : + deps_IAU80*da * sin(a+bt) +
+ deps_IAU80*db*t * sin(a+bt)
Table of the out of phase terms evoked by the differences in the
fundamental arguments [in .1 mus]
dpsi*cos deps*sin
l l' F D Om B d/dt B d/dt
0 0 0 0 1 -98 32 -53 4
0 0 0 0 2 2 0 1 0
-2 0 2 0 1 0 0 0 0
0 0 2 -2 2 -175 34 -76 7
0 1 0 0 0 34 -16 -1 5
0 1 2 -2 2 -19 3 -8 1
0 -1 2 -2 2 -2 0 -1 -1
0 0 2 -2 1 2 0 1 0
2 0 0 -2 0 1 0 0 0
0 2 0 0 0 1 0 0 0
0 2 2 -2 2 -1 0 0 0
0 0 2 0 2 -17 8 -7 2
1 0 0 0 0 5 2 0 0
0 0 2 0 1 -3 2 -1 1
1 0 2 0 2 -4 0 -2 0
1 0 0 -2 0 -2 -1 0 0
-1 0 2 0 2 0 -1 0 0
1 0 0 0 1 0 0 0 0
-1 0 2 2 2 0 0 0 0
1 0 2 0 1 -1 0 0 0
1 0 2 -2 2 1 0 0 0
2 0 2 0 2 -1 0 0 0
--------------------------------------------------------------
- The fundamental arguments follow:
**** DATA statements for the fundamental arguments.
**** (extracted from the MHB2000.f)
* Simon et al. (1994) values (t in centuries since 2000.0)
for lunisolar nutation ["]
*t**4 *t**3 *t**2 *t *1
l = -2.4470d-4 + 5.1635d-2 + 31.8792d0 + 1717915923.2178d0 + 485868.249036d0
l'= -0.1149d-4 + 0.0136d-2 - 0.5532d0 + 129596581.0481d0 + 1287104.79305d0
F = 0.0417d-4 - 0.1037d-2 - 12.7512d0 + 1739527262.8478d0 + 335779.526232d0
D = -0.3169d-4 + 0.6593d-2 - 6.3706d0 + 1602961601.2090d0 + 1072260.70369d0
Om= -0.5939d-4 + 0.7702d-2 + 7.4722d0 - 6962890.5431d0 + 450160.398036d0
for planetary nutation [rad]
*1 *t
l = 2.355 555 98 d0 +8328.6914 269 554d0
l' = 6.240 060 13 d0 + 628.3019 55 d0
F = 1.627 905 234d0 +8433.4661 581 31 d0
D = 5.198 466 741d0 +7771.3771 468 121d0
Om = 2.182 439 20 d0 - 33.7570 45 d0
lMe = 4.402 608 842d0 + 2608.7903 141 574d0
lVe = 3.176 146 697d0 + 1021.3285 546 211d0
lEa = 1.753 470 314d0 + 628.3075 849 991d0
lMa = 6.203 480 913d0 + 334.0612 426 700d0
lJu = 0.599 546 497d0 + 52.9690 962 641d0
lSa = 0.874 016 757d0 + 21.3299 104 960d0
lUr = 5.481 293 871d0 + 7.4781 598 567d0
lNe = 5.321 159 000d0 + 3.8127 774 000d0
pa = 0.2438175d-1*t + 0.0005 386 91d-2*t
----------------------------------------------------------------------------
- The terms with the same arguments were compacted into one term only.
- The biases and linear rates of change of nutation should be added
to get the values of CPO 'observed'
- The linear rate of change of nutation used in MHB_2000.f are
in longitude Dpsi= -.29965"/cent and
in obliquity Deps = -.02524"/cent
- The biases (from the procedure IAU200A.f that is presented at the web site of the
IERS Conventions 2000).
Dpsi = -41.775 mas
Deps = -6.8192 mas