RAW DATA FOR THE IAU NUTATION SERIES 2000B (77 TERMS)
WITH FORMULAS FOR APPLICATION
In the nutation data table below, each data line represents one term in the
respective summation series.
******************************************************************************
NUTATIONS DATA TABLE FOR IAU NUTATION SERIES 2000B
The i column is NOT part of the actual data. It is the reference index number
of the nutation series terms to which the subsequent 11 data elements apply.
ARGUMENT MULTIPLIERS LONGITUDE COMPONENTS OBLIQUITY COMPONENTS
L Lp F D Om ARC SEC * 10000000 ARC SEC * 10000000
i m1 m2 m3 m4 m5 AA BB CC DD EE FF
1 0 0 0 0 1 -172064161 -174666 33386 92052331 9086 15377
2 0 0 2 -2 2 -13170906 -1675 13696 5730336 -3015 -4587
3 0 0 2 0 2 -2276413 -234 2796 978459 -485 1374
4 0 0 0 0 2 2074554 207 -698 -897492 470 -291
5 0 1 0 0 0 1475877 -3633 11817 73871 -184 -1924
6 0 1 2 -2 2 -516821 1226 -524 224386 -677 -174
7 1 0 0 0 0 711159 73 -872 -6750 0 358
8 0 0 2 0 1 -387298 -367 380 200728 18 318
9 1 0 2 0 2 -301461 -36 816 129025 -63 367
10 0 -1 2 -2 2 215829 -494 111 -95929 299 132
11 0 0 2 -2 1 128227 137 181 -68982 -9 39
12 -1 0 2 0 2 123457 11 19 -53311 32 -4
13 -1 0 0 2 0 156994 10 -168 -1235 0 82
14 1 0 0 0 1 63110 63 27 -33228 0 -9
15 -1 0 0 0 1 -57976 -63 -189 31429 0 -75
16 -1 0 2 2 2 -59641 -11 149 25543 -11 66
17 1 0 2 0 1 -51613 -42 129 26366 0 78
18 -2 0 2 0 1 45893 50 31 -24236 -10 20
19 0 0 0 2 0 63384 11 -150 -1220 0 29
20 0 0 2 2 2 -38571 -1 158 16452 -11 68
21 0 -2 2 -2 2 32481 0 0 -13870 0 0
22 -2 0 0 2 0 -47722 0 -18 477 0 -25
23 2 0 2 0 2 -31046 -1 131 13238 -11 59
24 1 0 2 -2 2 28593 0 -1 -12338 10 -3
25 -1 0 2 0 1 20441 21 10 -10758 0 -3
26 2 0 0 0 0 29243 0 -74 -609 0 13
27 0 0 2 0 0 25887 0 -66 -550 0 11
28 0 1 0 0 1 -14053 -25 79 8551 -2 -45
29 -1 0 0 2 1 15164 10 11 -8001 0 -1
30 0 2 2 -2 2 -15794 72 -16 6850 -42 -5
31 0 0 -2 2 0 21783 0 13 -167 0 13
32 1 0 0 -2 1 -12873 -10 -37 6953 0 -14
33 0 -1 0 0 1 -12654 11 63 6415 0 26
34 -1 0 2 2 1 -10204 0 25 5222 0 15
35 0 2 0 0 0 16707 -85 -10 168 -1 10
36 1 0 2 2 2 -7691 0 44 3268 0 19
37 -2 0 2 0 0 -11024 0 -14 104 0 2
38 0 1 2 0 2 7566 -21 -11 -3250 0 -5
39 0 0 2 2 1 -6637 -11 25 3353 0 14
40 0 -1 2 0 2 -7141 21 8 3070 0 4
41 0 0 0 2 1 -6302 -11 2 3272 0 4
42 1 0 2 -2 1 5800 10 2 -3045 0 -1
43 2 0 2 -2 2 6443 0 -7 -2768 0 -4
44 -2 0 0 2 1 -5774 -11 -15 3041 0 -5
45 2 0 2 0 1 -5350 0 21 2695 0 12
46 0 -1 2 -2 1 -4752 -11 -3 2719 0 -3
47 0 0 0 -2 1 -4940 -11 -21 2720 0 -9
48 -1 -1 0 2 0 7350 0 -8 -51 0 4
49 2 0 0 -2 1 4065 0 6 -2206 0 1
50 1 0 0 2 0 6579 0 -24 -199 0 2
51 0 1 2 -2 1 3579 0 5 -1900 0 1
52 1 -1 0 0 0 4725 0 -6 -41 0 3
53 -2 0 2 0 2 -3075 0 -2 1313 0 -1
54 3 0 2 0 2 -2904 0 15 1233 0 7
55 0 -1 0 2 0 4348 0 -10 -81 0 2
56 1 -1 2 0 2 -2878 0 8 1232 0 4
57 0 0 0 1 0 -4230 0 5 -20 0 -2
58 -1 -1 2 2 2 -2819 0 7 1207 0 3
59 -1 0 2 0 0 -4056 0 5 40 0 -2
60 0 -1 2 2 2 -2647 0 11 1129 0 5
61 -2 0 0 0 1 -2294 0 -10 1266 0 -4
62 1 1 2 0 2 2481 0 -7 -1062 0 -3
63 2 0 0 0 1 2179 0 -2 -1129 0 -2
64 -1 1 0 1 0 3276 0 1 -9 0 0
65 1 1 0 0 0 -3389 0 5 35 0 -2
66 1 0 2 0 0 3339 0 -13 -107 0 1
67 -1 0 2 -2 1 -1987 0 -6 1073 0 -2
68 1 0 0 0 2 -1981 0 0 854 0 0
69 -1 0 0 1 0 4026 0 -353 -553 0 -139
70 0 0 2 1 2 1660 0 -5 -710 0 -2
71 -1 0 2 4 2 -1521 0 9 647 0 4
72 -1 1 0 1 1 1314 0 0 -700 0 0
73 0 -2 2 -2 1 -1283 0 0 672 0 0
74 1 0 2 2 1 -1331 0 8 663 0 4
75 -2 0 2 2 2 1383 0 -2 -594 0 -2
76 -1 0 0 0 2 1405 0 4 -610 0 2
77 1 1 2 -2 2 1290 0 0 -556 0 0
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===================================================================
Given the JD number corresponding to the date and time in question:
------------------------------------------------------
Compute time in Julian centuries reckoned from J2000.0
T = (JD - 2451545.0) / 36525.0
-------------------
Compute powers of T
T2 = T * T
T3 = T * T2
T4 = T * T3
-----------------------------------------------------------------
Define conversion factor to convert degrees to radians. Multiply
degrees by this factor to obtain the equivalent radians. In most
programming languages, trigonometric functions require arguments
to be expressed in radians rather than in degrees.
DegToRad = 3.141592653589793 / 180.0
-----------------------------------
Mean anomaly of the Moon in radians
L = DegToRad*((485868.249036 + 1717915923.2178*T + 31.8792*T2
+ 0.051635*T3 - 0.00024470*T4) / 3600.0)
----------------------------------
Mean anomaly of the Sun in radians
Lp = DegToRad*((1287104.79305 + 129596581.0481*T
- 0.5532*T2 + 0.000136*T3 - 0.00001149*T4) / 3600.0)
----------------------------------------------------
Mean argument of the latitude of the Moon in radians
F = DegToRad*((335779.526232 + 1739527262.8478*T
- 12.7512*T2 - 0.001037*T3 + 0.00000417*T4) / 3600.0)
---------------------------------------------------
Mean elongation of the Moon from the Sun in radians
D = DegToRad*((1072260.70369 + 1602961601.2090*T
- 6.3706*T2 + 0.006593*T3 - 0.00003169*T4) / 3600.0)
-----------------------------------------------------------
Mean longitude of the ascending node of the Moon in radians
Om = DegToRad*((450160.398036 - 6962890.5431*T
+ 7.4722*T2 + 0.007702*T3 - 0.00005939*T4) / 3600.0)
--------------
TERM FORMULAS:
Each data line contains the data for one term of
each nutation series. The i column is NOT part of
the data. It is the index of the series term.
There are 11 numerical data elements on each line.
They are:
5 Delaunay argument multipliers (m1, m2, m3, m4, m5)
3 coefficients for nutation in longitude (AA, BB, CC)
3 coefficients for nutation in obliquity (DD, EE, FF)
--------------------------------------------------
Construct the angular argument for the series term.
arg = (m1*L + m2*Lp + m3*F + m4*D + m5*Om)
--------------------------------------------------
Longitude terms use the AA,BB,CC coefficients from
the data table and take the general form:
dPsiTerm = (AA + BB*T)*sin(arg) + CC*cos(arg)
--------------------------------------------------
Obliquity terms use the DD,EE,FF coefficients from
the data table and take the general form:
dEpsTerm = (DD + EE*T)*cos(arg) + FF*sin(arg)
-------------------------------------------------------------
All terms in each respective series are summed and the result
is divided by 36000000000.0 to obtain the nutation expressed
in decimal degrees (dEpsDeg).