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.
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NUTATION DATA TABLE FOR IAU NUTATION SERIES 2000B
The i column is NOT part of the actual data. It is simply the reference index
number of the 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 (TDB) in question: --------------------------------------------------------------- Compute time in Julian centuries corresponding to the JD number and reckoned from J2000.0 (2000 Jan 01 at 12:00:00 TDB) 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. DegToRad = 3.141592653589793 / 180.0 ------------------------------------------- Compute 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) ------------------------------------------ Compute 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) ------------------------------------------------------------ Compute 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) ----------------------------------------------------------- Compute 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) ------------------------------------------------------------------- Compute 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 11 data elements of the 2000B series are: 5 fundamental 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) ------------------------------------------------- Compute the angular argument for the series term. Angles are assumed to be in radians. 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: DeltaPsiTerm = (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: DeltaEpsTerm = (DD + EE*T)*cos(arg) + FF*sin(arg) All terms in each respective series are summed and the result divided by 36000000000.0 to obtain the nutation expressed in decimal degrees. =========================================================================== THE FOLLOWING ARE FUNCTION ALGORITHMS IN PSEUDO-CODE FOR THE NUTATION IN ECLIPTICAL LONGITUDE AND IN OBLIQUITY OF THE ECLIPTIC FOR ANY GIVEN JD NUMBER ARGUMENT CORRESPONDING TO THE DATE AND TIME (TDB) IN QUESTION. -------------------------------------------------------------------- COMPUTE NUTATION IN LONGITUDE ACCORDING TO IAU 2000B NUTATION SERIES s = 0 s = s + (-172064161 - 174666*T)*sin(Om) + 33386*cos(Om) s = s + (-13170906 - 1675*T)*sin(2*(F - D + Om)) - 13696*cos(2*(F - D + Om)) s = s + (-2276413 - 234*T)*sin(2*(F + Om)) + 2796*cos(2*(F + Om)) s = s + (2074554 + 207*T)*sin(2*Om) - 698*cos(2*Om) s = s + (1475877 - 3633*T)*sin(Lp) + 11817*cos(Lp) s = s + (-516821 + 1226*T)*sin(Lp + 2*(F - D + Om)) - 524*cos(Lp + 2*(F - D + Om)) s = s + (711159 + 73*T)*sin(L) - 872*cos(L) s = s + (-387298 - 367*T)*sin(2*F + Om) + 380*cos(2*F + Om) s = s + (-301461 - 36*T)*sin(L + 2*(F + Om)) + 816*cos(L + 2*(F + Om)) s = s + (215829 - 494*T)*sin(2*(F - D + Om) - Lp) + 111*cos(2*(F - D + Om) - Lp) s = s + (128227 + 137*T)*sin(2*(F - D) + Om) + 181*cos(2*(F - D) + Om) s = s + (123457 + 11*T)*sin(2*(F + Om) - L) + 19*cos(2*(F + Om) - L) s = s + (156994 + 10*T)*sin(2*D - L) - 168*cos(2*D - L) s = s + (63110 + 63*T)*sin(L + Om) + 27*cos(L + Om) s = s + (-57976 - 63*T)*sin(Om - L) - 189*cos(Om - L) s = s + (-59641 - 11*T)*sin(2*(F + D + Om) - L) + 149*cos(2*(F + D + Om) - L) s = s + (-51613 - 42*T)*sin(L + 2*F + Om) + 129*cos(L + 2*F + Om) s = s + (45893 + 50*T)*sin(2*(F - L) + Om) + 31*cos(2*(F - L) + Om) s = s + (63384 + 11*T)*sin(2*D) - 150*cos(2*D) s = s + (-38571 - T)*sin(2*(F + D + Om)) + 158*cos(2*(F + D + Om)) s = s + 32481*sin(2*(F - Lp - D + Om)) s = s - 47722*sin(2*(D - L)) + 18*cos(2*(D - L)) s = s + (-31046 - T)*sin(2*(L + F + Om)) + 131*cos(2*(L + F + Om)) s = s + 28593*sin(L + 2*(F - D + Om)) - cos(L + 2*(F - D + Om)) s = s + (20441 + 21*T)*sin(2*F + Om - L) + 10*cos(2*F + Om - L) s = s + 29243*sin(2*L) - 74*cos(2*L) s = s + 25887*sin(2*F) - 66*cos(2*F) s = s + (-14053 - 25*T)*sin(Lp + Om) + 79*cos(Lp + Om) s = s + (15164 + 10*T)*sin(-L + 2*D + Om) + 11*cos(-L + 2*D + Om) s = s + (-15794 + 72*T)*sin(2*(Lp + F - D + Om)) - 16*cos(2*(Lp + F - D + Om)) s = s + 21783*sin(2*(D - F)) + 13*cos(2*(D - F)) s = s + (-12873 - 10*T)*sin(L - 2*D + Om) - 37*cos(L - 2*D + Om) s = s + (-12654 + 11*T)*sin(-Lp + Om) + 63*cos(-Lp + Om) s = s - 10204*sin(2*(F + D) + Om - L) - 25*cos(2*(F + D) + Om - L) s = s + (16707 - 85*T)*sin(2*Lp) - 10*cos(2*Lp) s = s - 7691*sin(L + 2*(F + D + Om)) - 44*cos(L + 2*(F + D + Om)) s = s - 11024*sin(2*(F - L)) + 14*cos(2*(F - L)) s = s + (7566 - 21*T)*sin(Lp + 2*(F + Om)) - 11*cos(Lp + 2*(F + Om)) s = s + (-6637 - 11*T)*sin(2*(F + D) + Om) + 25*cos(2*(F + D) + Om) s = s + (-7141 + 21*T)*sin(2*(F + Om) - Lp) + 8*cos(2*(F + Om) - Lp) s = s + (-6302 - 11*T)*sin(2*D + Om) + 2*cos(2*D + Om) s = s + (5800 + 10*T)*sin(L + 2*(F - D) + Om) + 2*cos(L + 2*(F - D) + Om) s = s + 6443*sin(2*(L + F - D + Om)) - 7*cos(2*(L + F - D + Om)) s = s + (-5774 - 11*T)*sin(2*(D - L) + Om) - 15*cos(2*(D - L) + Om) s = s - 5350*sin(2*(L + F) + Om) - 21*cos(2*(L + F) + Om) s = s + (-4752 - 11*T)*sin(2*(F - D) + Om - Lp) - 3*cos(2*(F - D) + Om - Lp) s = s + (-4940 - 11*T)*sin(Om - 2*D) - 21*cos(Om - 2*D) s = s + 7350*sin(2*D - L - Lp) - 8*cos(2*D - L - Lp) s = s + 4065*sin(2*(L - D) + Om) + 6*cos(2*(L - D) + Om) s = s + 6579*sin(L + 2*D) - 24*cos(L + 2*D) s = s + 3579*sin(Lp + 2*(F - D) + Om) + 5*cos(Lp + 2*(F - D) + Om) s = s + 4725*sin(L - Lp) - 6*cos(L - Lp) s = s - 3075*sin(2*(F + Om - L)) + 2*cos(2*(F + Om - L)) s = s - 2904*sin(3*L + 2*(F + Om)) - 15*cos(3*L + 2*(F + Om)) s = s + 4348*sin(2*D - Lp) - 10*cos(2*D - Lp) s = s - 2878*sin(L - Lp + 2*(F + Om)) - 8*cos(L - Lp + 2*(F + Om)) s = s - 4230*sin(D) - 5*cos(D) s = s - 2819*sin(2*(F + D + Om) - L - Lp) - 7*cos(2*(F + D + Om) - L - Lp) s = s - 4056*sin(2*F - L) - 5*cos(2*F - L) s = s - 2647*sin(2*(F + D + Om) - Lp) - 11*cos(2*(F + D + Om) - Lp) s = s - 2294*sin(Om - 2*L) + 10*cos(Om - 2*L) s = s + 2481*sin(L + Lp + 2*(F + Om)) - 7*cos(L + Lp + 2*(F + Om)) s = s + 2179*sin(2*L + Om) - 2*cos(2*L + Om) s = s + 3276*sin(Lp + D - L) + cos(Lp + D - L) s = s - 3389*sin(L + Lp) - 5*cos(L + Lp) s = s + 3339*sin(L + 2*F) - 13*cos(L + 2*F) s = s - 1987*sin(2*(F - D) + Om - L) + 6*cos(2*(F - D) + Om - L) s = s - 1981*sin(L + 2*Om) s = s + 4026*sin(D - L) - 353*cos(D - L) s = s + 1660*sin(2*F + D + 2*Om) - 5*cos(D + 2*(F + Om)) s = s - 1521*sin(2*(F + 2*D + Om) - L) - 9*cos(2*(F + 2*D + Om) - L) s = s + 1314*sin(Lp + D + Om - L) s = s - 1283*sin(2*(F - D - Lp) + Om) s = s - 1331*sin(L + 2*F + 2*D + Om) - 8*cos(L + 2*(F + D) + Om) s = s + 1383*sin(2*(F - L + D + Om)) - 2*cos(2*(F - L + D + Om)) s = s + 1405*sin(2*Om - L) + 4*cos(2*Om - L) s = s + 1290*sin(L + Lp + 2*(F - D + Om)) dPsiDeg = s / 36000000000.0 =========================================================================== COMPUTE NUTATION IN OBLIQUITY (dEps) ACCORDING TO IAU 2000B NUTATION SERIES s = 0 s = s + (92052331 + 9086*T)*cos(Om) + 15377*sin(Om) s = s + (5730336 - 3015*T)*cos(2*(F - D + Om)) - 4587*sin(2*(F - D + Om)) s = s + (978459 - 485*T)*cos(2*(F + Om)) + 1374*sin(2*(F + Om)) s = s + (-897492 + 470*T)*cos(2*Om) - 291*sin(2*Om) s = s + (73871 - 184*T)*cos(Lp) - 1924*sin(Lp) s = s + (224386 - 677*T)*cos(Lp + 2*(F - D + Om)) - 174*sin(Lp + 2*(F - D + Om)) s = s - 6750*cos(L) - 358*sin(L) s = s + (200728 + 18*T)*cos(2*F + Om) + 318*sin(2*F + Om) s = s + (129025 - 63*T)*cos(L + 2*(F + Om)) + 367*sin(L + 2*(F + Om)) s = s + (-95929 + 299*T)*cos(2*(F - D + Om) - Lp) + 132*sin(2*(F - D + Om) - Lp) s = s + (-68982 - 9*T)*cos(2*(F - D) + Om) + 39*sin(2*(F - D) + Om) s = s + (-53311 + 32*T)*cos(2*(F + Om) - L) - 4*sin(2*(F + Om) - L) s = s - 1235*cos(2*D - L) - 82*sin(2*D - L) s = s - 33228*cos(L + Om) + 9*sin(L + Om) s = s + 31429*cos(Om - L) - 75*sin(Om - L) s = s + (25543 - 11*T)*cos(2*(F + D + Om) - L) + 66*sin(2*(F + D + Om) - L) s = s + 26366*cos(L + 2*F + Om) + 78*sin(L + 2*F + Om) s = s + (-24236 - 10*T)*cos(2*(F - L) + Om) + 20*sin(2*(F - L) + Om) s = s - 1220*cos(2*D) - 29*sin(2*D) s = s + (16452 - 11*T)*cos(2*(F + D + Om)) + 68*sin(2*(F + D + Om)) s = s - 13870*cos(2*(F - Lp - D + Om)) s = s + 477*cos(2*(D - L)) - 25*sin(2*(D - L)) s = s + (13238 - 11*T)*cos(2*(L + F + Om)) + 59*sin(2*(L + F + Om)) s = s + (-12338 + 10*T)*cos(L + 2*(F - D + Om)) - 3*sin(L + 2*(F - D + Om)) s = s - 10758*cos(2*F + Om - L) + 3*sin(2*F + Om - L) s = s - 609*cos(2*L) - 13*sin(2*L) s = s - 550*cos(2*F) - 11*sin(2*F) s = s + (8551 - 2*T)*cos(Lp + Om) - 45*sin(Lp + Om) s = s - 8001*cos(2*D - L + Om) + sin(2*D - L + Om) s = s + (6850 - 42*T)*cos(2*(Lp + F - D + Om)) - 5*sin(2*(Lp + F - D + Om)) s = s - 167*cos(2*(D - F)) - 13*sin(2*(D - F)) s = s + 6953*cos(L - 2*D + Om) - 14*sin(L - 2*D + Om) s = s + 6415*cos(Om - Lp) + 26*sin(Om - Lp) s = s + 5222*cos(2*(F + D) + Om - L) + 15*sin(2*(F + D) + Om - L) s = s + (168 - T)*cos(2*Lp) + 10*sin(2*Lp) s = s + 3268*cos(L + 2*(F + D + Om)) + 19*sin(L + 2*(F + D + Om)) s = s + 104*cos(2*(F - L)) + 2*sin(2*(F - L)) s = s - 3250*cos(Lp + 2*(F + Om)) + 5*sin(Lp + 2*(F + Om)) s = s + 3353*cos(2*(F + D) + Om) + 14*sin(2*(F + D) + Om) s = s + 3070*cos(2*(F + Om) - Lp) + 4*sin(2*(F + Om) - Lp) s = s + 3272*cos(2*D + Om) + 4*sin(2*D + Om) s = s - 3045*cos(L + 2*(F - D) + Om) + sin(L + 2*(F - D) + Om) s = s - 2768*cos(2*(L + F - D + Om)) + 4*sin(2*(L + F - D + Om)) s = s + 3041*cos(2*(D - L) + Om) - 5*sin(2*(D - L) + Om) s = s + 2695*cos(2*(L + F) + Om) + 12*sin(2*(L + F) + Om) s = s + 2719*cos(2*(F - D) + Om - Lp) - 3*sin(2*(F - D) + Om - Lp) s = s + 2720*cos(Om - 2*D) - 9*sin(Om - 2*D) s = s - 51*cos(2*D - L - Lp) - 4*sin(2*D - L - Lp) s = s - 2206*cos(2*(L - D) + Om) - sin(2*(L - D) + Om) s = s - 199*cos(L + 2*D) - 2*sin(L + 2*D) s = s - 1900*cos(Lp + 2*(F - D) + Om) - sin(Lp + 2*(F - D) + Om) s = s - 41*cos(L - Lp) - 3*sin(L - Lp) s = s + 1313*cos(2*(F - L + Om)) - sin(2*(F - L + Om)) s = s + 1233*cos(3*L + 2*(F + Om)) + 7*sin(3*L + 2*(F + Om)) s = s - 81*cos(-Lp + 2*D) - 2*sin(-Lp + 2*D) s = s + 1232*cos(L - Lp + 2*(F + Om)) + 4*sin(L - Lp + 2*(F + Om)) s = s - 20*cos(D) + 2*sin(D) s = s + 1207*cos(2*(F + D + Om) - L - Lp) + 3*sin(2*(F + D + Om) - L - Lp) s = s + 40*cos(2*F - L) - 2*sin(2*F - L) s = s + 1129*cos(2*(F + D + Om) - Lp) + 5*sin(2*(F + D + Om) - Lp) s = s + 1266*cos(Om - 2*L) - 4*sin(Om - 2*L) s = s - 1062*cos(L + Lp + 2*(F + Om)) + 3*sin(L + Lp + 2*(F + Om)) s = s - 1129*cos(2*L + Om) + 2*sin(2*L + Om) s = s - 9*cos(Lp + D - L) s = s + 35*cos(L + Lp) - 2*sin(L + Lp) s = s - 107*cos(L + 2*F) - sin(L + 2*F) s = s + 1073*cos(2*(F - D) + Om - L) - 2*sin(2*(F - D) + Om - L) s = s + 854*cos(L + 2*Om) s = s - 553*cos(D - L) + 139*sin(D - L) s = s - 710*cos(2*(F + Om) + D) + 2*sin(2*(F + Om) + D) s = s + 647*cos(2*(F + 2*D + Om) - L) + 4*sin(2*(F + 2*D + Om) - L) s = s - 700*cos(Lp + D + Om - L) s = s + 672*cos(2*(F - Lp - D) + Om) s = s + 663*cos(L + 2*(F + D) + Om) + 4*sin(L + 2*(F + D) + Om) s = s - 594*cos(2*(F - L + D + Om)) + 2*sin(2*(F - L + D + Om)) s = s - 610*cos(2*Om - L) - 2*sin(2*Om - L) s = s - 556*cos(L + Lp + 2*(F - D + Om)) dEpsDeg = s / 36000000000.0 =========================================================================== © Jay Tanner - PHP Science Labs - 2024
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