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Memorandum N 4
26.06.997
Precession and nutation according the classical procedure using ecliptics (the IAU 1980 theory)

Precession quantitieszA, qA, zA, eA(Lieske et al. (1977)) 1). The numerical expressions
zA=2306.2181"t+0.30188"t2+0.017998"t3,
qA=2004.3109"t–0.42665"t2–0.041833"t3,
zA=2306.2181"t+1.09468"t2+0.018203"t3,
eA=84381.448"–46.8150"t–0.00059"t2+0.001813"t3.
Nutation quantitiesDy and De to be used are the nutation angles in longitude and obliquity.
Dy=S(Ai+A'it)sin(ARGUMENT)
De=S(Bi+B'it)sin(ARGUMENT)
Arrangment on the ARGUMENT is the same, as in the memorandum N 3, but the table of multipliers and amplitudes is different.

To totalize the folowing table from the end!!!

Period LONGITUDE(0.0001") OBLIQUITY(0.0001")

l l' F D W Ai A'i Bi B'i

0 0 0 0 1 -6798.4 -171996 -174.2 92025 8.9

0 0 2 -2 2 182.6 -13187 -1.6 5736 -3.1

0 0 2 0 2 13.7 -2274 -0.2 977 -0.5

0 0 0 0 2 -3399.2 2062 0.2 -895 0.5

0 -1 0 0 0 -365.3 -1426 3.4 54 -0.1

1 0 0 0 0 27.6 712 0.1 -7 0.0

0 1 2 -2 2 121.7 -517 1.2 224 -0.6

0 0 2 0 1 13.6 -386 -0.4 200 0.0

1 0 2 0 2 9.1 -301 0.0 129 -0.1

0 -1 2 -2 2 365.2 217 -0.5 -95 0.3

-1 0 0 2 0 31.8 158 0.0 -1 0.0

0 0 2 -2 1 177.8 129 0.1 -70 0.0

-1 0 2 0 2 27.1 123 0.0 -53 0.0

1 0 0 0 1 27.7 63 0.1 -33 0.0

0 0 0 2 0 14.8 63 0.0 -2 0.0

-1 0 2 2 2 9.6 -59 0.0 26 0.0

-1 0 0 0 1 -27.4 -58 -0.1 32 0.0

1 0 2 0 1 9.1 -51 0.0 27 0.0

-2 0 0 2 0 -205.9 -48 0.0 1 0.0

-2 0 2 0 1 1305.5 46 0.0 -24 0.0

0 0 2 2 2 7.1 -38 0.0 16 0.0

2 0 2 0 2 6.9 -31 0.0 13 0.0

2 0 0 0 0 13.8 29 0.0 -1 0.0

1 0 2 -2 2 23.9 29 0.0 -12 0.0

0 0 2 0 0 13.6 26 0.0 -1 0.0

0 0 2 -2 0 173.3 -22 0.0 0 0.0

-1 0 2 0 1 27.0 21 0.0 -10 0.0

0 2 0 0 0 182.6 17 -0.1 0 0.0

0 2 2 -2 2 91.3 -16 0.1 7 0.0

-1 0 0 2 1 32.0 16 0.0 -8 0.0

0 1 0 0 1 386.0 -15 0.0 9 0.0

1 0 0 -2 1 -31.7 -13 0.0 7 0.0

0 -1 0 0 1 -346.6 -12 0.0 6 0.0

2 0 -2 0 0 -1095.2 11 0.0 0 0.0

-1 0 2 2 1 9.5 -10 0.0 5 0.0

1 0 2 2 2 5.6 -8 0.0 3 0.0

0 -1 2 0 2 14.2 -7 0.0 3 0.0

0 0 2 2 1 7.1 -7 0.0 3 0.0

1 1 0 -2 0 -34.8 -7 0.0 0 0.0

0 1 2 0 2 13.2 7 0.0 -3 0.0

-2 0 0 2 1 -199.8 -6 0.0 3 0.0

0 0 0 2 1 14.8 -6 0.0 3 0.0

2 0 2 -2 2 12.8 6 0.0 -3 0.0

1 0 0 2 0 9.6 6 0.0 0 0.0

1 0 2 -2 1 23.9 6 0.0 -3 0.0

0 0 0 -2 1 -14.7 -5 0.0 3 0.0

0 -1 2 -2 1 346.6 -5 0.0 3 0.0

2 0 2 0 1 6.9 -5 0.0 3 0.0

1 -1 0 0 0 29.8 5 0.0 0 0.0

1 0 0 -1 0 411.8 -4 0.0 0 0.0

0 0 0 1 0 29.5 -4 0.0 0 0.0

0 1 0 -2 0 -15.4 -4 0.0 0 0.0

1 0 -2 0 0 -26.9 4 0.0 0 0.0

2 0 0 -2 1 212.3 4 0.0 -2 0.0

0 1 2 -2 1 119.6 4 0.0 -2 0.0

1 1 0 0 0 25.6 -3 0.0 0 0.0

1 -1 0 -1 0 -3232.9 -3 0.0 0 0.0

-1 -1 2 2 2 9.8 -3 0.0 1 0.0

0 -1 2 2 2 7.2 -3 0.0 1 0.0

1 -1 2 0 2 9.4 -3 0.0 1 0.0

3 0 2 0 2 5.5 -3 0.0 1 0.0

-2 0 2 0 2 1615.7 -3 0.0 1 0.0

1 0 2 0 0 9.1 3 0.0 0 0.0

-1 0 2 4 2 5.8 -2 0.0 1 0.0

1 0 0 0 2 27.8 -2 0.0 1 0.0

-1 0 2 -2 1 -32.6 -2 0.0 1 0.0

0 -2 2 -2 1 6786.3 -2 0.0 1 0.0

-2 0 0 0 1 -13.7 -2 0.0 1 0.0

2 0 0 0 1 13.8 2 0.0 -1 0.0

3 0 0 0 0 9.2 2 0.0 0 0.0

1 1 2 0 2 8.9 2 0.0 -1 0.0

0 0 2 1 2 9.3 2 0.0 -1 0.0

1 0 0 2 1 9.6 -1 0.0 0 0.0

1 0 2 2 1 5.6 -1 0.0 1 0.0

1 1 0 -2 1 -34.7 -1 0.0 0 0.0

0 1 0 2 0 14.2 -1 0.0 0 0.0

0 1 2 -2 0 117.5 -1 0.0 0 0.0

0 1 -2 2 0 -329.8 -1 0.0 0 0.0

1 0 -2 2 0 23.8 -1 0.0 0 0.0

1 0 -2 -2 0 -9.5 -1 0.0 0 0.0

1 0 2 -2 0 32.8 -1 0.0 0 0.0

1 0 0 -4 0 -10.1 -1 0.0 0 0.0

2 0 0 -4 0 -15.9 -1 0.0 0 0.0

0 0 2 4 2 4.8 -1 0.0 0 0.0

0 0 2 -1 2 25.4 -1 0.0 0 0.0

-2 0 2 4 2 7.3 -1 0.0 1 0.0

2 0 2 2 2 4.7 -1 0.0 0 0.0

0 -1 2 0 1 14.2 -1 0.0 0 0.0

0 0 -2 0 1 -13.6 -1 0.0 0 0.0

0 0 4 -2 2 12.7 1 0.0 0 0.0

0 1 0 0 2 409.2 1 0.0 0 0.0

1 1 2 -2 2 22.5 1 0.0 -1 0.0

3 0 2 -2 2 8.7 1 0.0 0 0.0

-2 0 2 2 2 14.6 1 0.0 -1 0.0

-1 0 0 0 2 -27.3 1 0.0 -1 0.0

0 0 -2 2 1 -169.0 1 0.0 0 0.0

0 1 2 0 1 13.1 1 0.0 0 0.0

-1 0 4 0 2 9.1 1 0.0 0 0.0

2 1 0 -2 0 131.7 1 0.0 0 0.0

2 0 0 2 0 7.1 1 0.0 0 0.0

2 0 2 -2 1 12.8 1 0.0 -1 0.0

2 0 -2 0 1 -943.2 1 0.0 0 0.0

1 -1 0 -2 0 -29.3 1 0.0 0 0.0

-1 0 0 1 1 -388.3 1 0.0 0 0.0

-1 -1 0 2 1 35.0 1 0.0 0 0.0

0 1 0 1 0 27.3 1 0.0 0 0.0

Temporal argument. Generally adopted definition 2):
t=(TT–2000 January 1d 12h TT) in days/36525.
According to the notation accepted here our formula has the form:
t=(TT–0.5)/36525.

Passage from CRS to TRS. Transformation is given according the formula:
[1:2:3]TRS=
R2(–xp)R1(–yp)R3(GST)R1(–eADe)R3(Dy)R1(eA)R3(–zA)R2(qA)R3(–zA)[1:2:3]CRS
Here the s' is absent, which accounting correctly assigns a position of the instantaneous Greenwich (Prime) meridian. The concealment of this point is a manifestation of the mathematical incorrectness of the classical procedure, and expresses the absence of the strict determination of such notion as "Prime Meridian". 'Celestial pole offsets' are simply added to the corresponding values.

Geodesic nutation. It is an "ether drag" (of inertial reference system) by the rotating Earth. Described by the correction:
Dyg=–0.000153"sinl'–0.000002"sin2l', where l' is the mean anomaly of the Sun (see Memorandum N 3). The correction would be added to the uncorrected determination of y.

The construction of the IERS 1996 Theory of Precession/Nutation algorithm we propose to postpone, though is necessary notice that we have got the debugged in IERS algorithm of its calculation — Ceppred.f, including the planetary nutation Ksv_1996.f. I suppose however that they are coordinate, rather then vector.


1. Lieske, J. H., Lederle, T., Fricke, W., and Morando, B., 1977, "Expression for the Precession Quantities Based upon the IAU (1976) System of Astronomical Constants", Astron. Astrophys., 58, pp. 1--16.

2. This definition is consistent with Resolution C7 passed at the 1994 Hague General Assembly of the IAU which recommends that J2000.0 be defined at the geocenter and at the date 2000.0 January 1.5 TT = Julian Date 2451545.0 TT.