The past and future obliquity of Saturn as Titan migrates

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Table A.2

Quasi-periodic decomposition of Saturn’s inclination and longitude of ascending node (variable ζ).

k		S_k × 10⁸
1	0.00000	1 377 395	107.59
2	−26.33023	785 009	127.29
3	−0.69189	55 969	23.96
4	−3.00557	39 101	140.33
5	−26.97744	5889	43.05
6	82.77163	3417	128.95
7	58.80017	2003	212.90
8	34.82788	1583	294.12
9	−5.61755	1373	168.70
10	−17.74818	1269	123.28
11	−27.48935	1014	218.53
12	−25.17116	958	215.94
13	−50.30212	943	209.84
14	−1.84625	943	35.32
15	−2.35835	825	225.04
16	−4.16482	756	51.51
17	−7.07963	668	273.79
18	−28.13656	637	314.07
19	−0.58033	544	17.32
20	−5.50098	490	162.89
21	−6.84091	375	106.28
22	−7.19493	333	105.15
23	−6.96094	316	97.96
24	−3.11725	261	326.97
25	−7.33264	206	196.75
26	−18.85115	168	60.48
27	−5.85017	166	345.47
28	0.46547	157	286.88
29	−19.40256	141	208.18
30	−17.19656	135	333.96
31	−5.21610	124	198.91
32	−5.37178	123	215.48
33	−5.10025	121	15.38
34	−18.01114	96	242.09
35	−17.66094	91	138.93
36	11.50319	83	281.01
37	−17.83857	74	289.13
38	−5.96899	71	170.64
39	−6.73842	67	44.50
40	−17.54636	66	246.71
41	−7.40536	62	233.35
42	−7.48780	58	47.95
43	−6.56016	54	303.47
44	0.57829	54	103.72
45	−6.15490	51	269.77
46	−17.94404	47	212.26
47	−8.42342	45	211.21
48	−18.59563	43	98.11
49	20.96631	32	57.78
50	9.18847	31	1.15
51	−1.19906	30	132.74
52	10.34389	20	190.42
53	18.14984	19	291.19
54	−19.13075	18	305.90
55	−18.97001	8	73.36
56	−18.30007	7	250.45
57	−18.69743	4	221.70
58	−18.77933	4	222.83
59	−18.22681	4	46.30
60	−19.06544	4	50.21

Notes. This solution has been directly obtained from Laskar (1990) as explained in the text. The phases are given at time J2000.

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