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This article has an erratum: [https://doi.org/10.1051/0004-6361/201834344e]

Table F.1

Quasi-periodic representation of the orbital dynamics of Mercury.

z ζ
Ej × 108 Sj × 108
5.59644 18337396 110.35 −5.61755 3995819 348.70
5.47449 6902428 275.01 −7.07963 3015900 273.77
5.71670 5240271 120.52 −7.19493 1505361 105.16
4.24882 3635276 30.67 −6.96094 1429554 97.95
5.35823 2815900 94.89 −5.50098 1424811 342.89
7.45592 2786428 20.24 0.00000 1372386 107.59
4.36906 1312738 220.84 −6.84091 1183049 107.89
5.99227 1035633 113.56 −7.33264 872607 196.75
5.65485 998897 39.22 −5.85017 481844 165.47
6.93423 934569 166.16 −5.21610 360659 18.91
5.23841 829067 272.97 −5.37178 358805 35.48
7.05595 634974 357.62 −5.10025 351141 195.38
7.34103 235292 27.85 −6.73842 285961 44.50
17.91550 165568 335.25 −7.40536 264351 233.35
7.57299 164186 191.47 −7.48780 245583 47.95
17.36469 157893 303.95 −6.56016 230801 303.47
6.82468 77097 14.53 −5.96899 205822 350.64
16.81285 70120 91.98 −8.42342 192248 211.21
3.08952 60554 121.36 −3.00557 159813 140.33
18.46794 48514 9.97 −18.85115 156874 240.43
7.20563 48115 323.91 −6.15490 149031 89.77
17.08266 43934 359.38 −17.74818 119892 303.28
17.63081 39761 202.03 −0.69189 70222 23.96
7.71663 29983 273.52 18.14984 53922 111.19
28.22069 21356 307.83 −18.30007 47541 269.86
17.81084 15980 58.56 −19.40256 33322 29.01
19.01870 15738 39.75 −19.13075 14506 125.90
17.15752 15119 145.02 −26.33023 13964 127.29
18.18553 14604 57.28 −18.01114 9092 62.09
17.72293 12073 48.46 −17.66094 8620 318.93
18.01611 10275 44.83 −17.83857 7011 109.13
16.52731 9115 311.91 −17.54636 6248 66.71
17.47683 7950 80.26 −18.97001 6027 253.36
16.26122 7118 58.89 −2.35835 4687 44.73
17.55234 6398 17.65 −17.94404 4398 32.26
5.40817 6086 120.60 −18.59563 4035 278.11
18.08627 5933 356.17 −1.84625 3435 41.72
52.19257 3589 225.59 −4.16482 3303 51.62
−19.72306 2363 113.24 −18.69743 3167 41.70
4.89647 922 292.23 −18.77933 3104 42.83
0.66708 717 73.98 −18.22681 3100 226.30
1.93168 618 39.55 −19.06544 2777 230.21
3.60029 447 121.40 −17.19656 1298 127.26
−56.90922 400 44.11 −3.11725 1067 326.97
53.35188 285 134.98 −0.58033 683 17.33
29.37998 169 37.61 −1.19906 372 133.87
2.97706 158 306.81 11.50319 341 281.02
−20.88236 75 203.93 −26.97744 244 44.61
28.86795 70 212.64 −50.30212 202 29.83
27.57346 62 223.74 0.46547 196 286.88
1.82121 50 146.09 10.34389 179 191.52
27.06140 45 38.56 20.96631 132 57.78
76.16447 16 323.03 0.57829 68 103.72
0.77840 12 65.10 82.77163 61 128.95
51.03334 9 136.30 9.18847 39 1.15
−0.49216 4 164.74 58.80017 36 212.90
34.82788 28 294.12
−27.48935 18 218.53
−25.17116 17 215.94
−28.13656 11 314.08
7.45592 2085594 200.24 0.00000 1377170 107.59
4.24882 1963621 30.67 −18.85115 953835 60.43
17.91550 1346128 335.25 −5.61755 671575 348.70
17.36469 1164633 123.95 −17.74818 575205 123.28
5.59644 659312 110.35 −7.07963 404368 93.77
17.08266 324058 179.38 −18.30007 298364 89.80
5.47449 248173 275.01 −5.50098 239467 342.89
16.81285 239435 274.43 −6.84091 208804 286.39
6.93423 216696 169.77 −7.19493 201837 285.16
17.63081 191660 193.67 −6.96094 191673 277.95
5.71670 188411 120.52 −19.40256 188959 209.10
7.05595 178786 358.98 −7.33264 116984 16.75
7.34103 176112 207.85 −3.00557 99208 140.33
17.81084 129713 58.56 −19.13075 88217 305.90
7.57299 122891 11.47 −5.85017 80983 165.47
18.18553 118540 57.28 −0.69189 65885 23.96
19.01870 116085 219.75 −5.21610 60616 18.91
17.15752 111520 325.02 −5.37178 60304 35.48
18.46794 110955 6.95 −5.10025 59016 195.38
5.35823 101244 94.89 −18.01114 43620 242.09
17.72293 97999 48.46 −17.66094 41358 138.93
18.01611 83405 44.83 −6.73842 38337 224.50
16.52731 67232 131.91 −18.97001 36654 73.36
17.47683 58638 260.26 −7.40536 35440 53.35
16.26122 57777 58.89 −5.96899 34592 350.64
6.82468 57706 194.53 −17.83857 33636 289.13
3.08952 54138 121.36 −7.48780 32924 227.95
18.08627 48156 356.17 −6.56016 30942 123.47
17.55234 47190 197.65 −17.54636 29977 246.71
5.99227 37236 113.56 −8.42342 25773 31.21
7.20563 36013 143.91 −6.15490 25048 89.77
5.65485 35915 39.22 −17.94404 21099 212.26
5.23841 29809 272.97 −18.59563 19361 98.11
7.71663 22441 93.52 −18.69743 19259 221.70
4.36906 20218 220.79 −18.77933 18879 222.83
28.22069 16949 308.38 −18.22681 18853 46.30
5.40817 3036 120.48 −19.06544 16888 50.21
−19.72306 1161 113.24 −17.19656 11902 171.81
0.66708 1088 73.98 18.14984 9063 111.19
27.06140 536 218.72 −26.33023 5577 127.29
4.89647 470 291.97 −2.35835 2677 44.72
29.37998 416 217.51 −1.84625 2187 40.13
52.19257 339 225.73 −4.16482 2022 51.60
28.86795 277 32.64 −3.11725 663 326.97
27.57346 244 43.74 −0.58033 641 17.33
3.60029 242 121.40 −50.30212 215 29.83
−56.90922 216 44.11 11.50319 212 281.02
2.97706 141 306.81 −1.19906 194 133.77
1.93168 69 93.94 0.46547 184 286.88
−20.88236 67 203.93 −26.97744 128 44.89
76.16447 63 143.03 10.34389 98 191.39
1.82121 46 148.00 20.96631 82 57.78
51.03334 35 316.30 0.57829 64 103.72
0.77840 19 65.10 9.18847 36 1.15
53.35188 16 135.62 82.77163 24 128.95
−0.49216 5 164.74 58.80017 14 212.90
34.82788 11 294.12
−27.48935 7 218.53
−25.17116 7 215.94
−28.13656 5 314.08
4.24882 1891285 30.67 0.00000 1377263 107.59
7.45592 1614222 200.24 −18.85115 875509 240.43
17.91550 1315949 155.25 −5.61755 496020 348.70
17.36469 938579 303.95 −17.74818 401987 303.28
5.59644 420011 110.35 −7.07963 343071 93.77
17.08266 261159 359.38 −18.30007 281401 269.74
17.63081 197777 14.78 −5.50098 176869 342.89
28.22069 168931 128.09 −6.84091 174079 286.47
16.81285 168064 95.11 −7.19493 171242 285.16
6.93423 161978 169.87 −6.96094 162618 277.95
5.47449 158097 275.01 −19.40256 162229 29.19
7.34103 136309 207.85 −26.33023 133519 127.29
7.05595 134274 359.01 −7.33264 99249 16.75
18.46794 131495 187.69 −3.00557 89258 140.33
17.81084 126776 238.56 −19.13075 80968 125.90
5.71670 120026 120.52 −0.69189 64554 23.96
18.18553 115855 237.28 −5.85017 59814 165.47
17.72293 95780 228.46 −5.21610 44770 18.91
7.57299 95116 11.47 −5.37178 44540 35.48
19.01870 93553 39.75 −5.10025 43589 195.38
17.15752 89874 145.02 −18.97001 33642 253.36
18.01611 81516 224.83 −6.73842 32525 224.50
5.35823 64497 94.89 −18.01114 30484 62.09
3.08952 56656 121.36 −7.40536 30067 53.35
16.26122 56468 238.89 −17.66094 28903 318.93
16.52731 54183 311.91 −7.48780 27932 227.95
17.47683 47256 80.26 −6.56016 26251 123.47
18.08627 47065 176.17 −17.19656 25667 341.65
6.82468 44664 194.53 −5.96899 25550 350.64
17.55234 38030 17.65 −17.83857 23507 109.13
7.20563 27874 143.91 −8.42342 21866 31.21
5.99227 23721 113.56 −17.54636 20949 66.71
5.65485 22879 39.22 −6.15490 18500 89.77
5.23841 18989 272.97 −18.69743 17676 41.70
7.71663 17369 93.52 −18.77933 17327 42.83
4.36906 9354 220.76 −18.22681 17304 226.30
52.19257 7041 225.56 −19.06544 15500 230.21
5.40817 2871 120.45 −17.94404 14745 32.26
29.37998 1761 37.54 −18.59563 13530 278.11
27.06140 1669 38.70 18.14984 6694 111.19
−19.72306 1591 113.24 −2.35835 2098 44.69
0.66708 1259 73.98 −1.84625 1981 39.73
28.86795 1027 212.64 −4.16482 1812 51.59
27.57346 902 223.74 −26.97744 1074 43.23
53.35188 584 134.92 −0.58033 628 17.33
4.89647 447 291.91 −3.11725 596 326.97
76.16447 233 323.03 82.77163 581 128.95
3.60029 233 121.40 58.80017 341 212.90
−56.90922 208 44.11 34.82788 269 294.12
2.97706 148 306.81 11.50319 191 281.02
51.03334 129 136.30 0.46547 181 286.88
1.93168 70 148.98 −27.48935 173 218.53
−20.88236 70 203.93 −1.19906 167 133.74
1.82121 49 148.46 −25.17116 163 215.94
0.77840 22 65.10 −28.13656 108 314.08
−0.49216 6 164.74 10.34389 85 191.35
20.96631 74 57.78
0.57829 62 103.72
9.18847 36 1.15
−50.30212 25 29.78
17.91550 4902750 335.25 −17.74818 3464962 303.28
17.36469 4004873 303.95 −18.85115 1541097 60.43
4.24882 2030021 30.67 0.00000 1375324 107.59
16.81285 1853846 91.90 −18.30007 745752 89.07
18.46794 1357476 9.91 −17.19656 543058 154.89
17.63081 1139332 201.65 −26.33023 457927 127.29
17.08266 1114353 359.38 −18.01114 262761 62.09
28.22069 706337 128.11 −17.66094 249135 318.93
17.81084 472390 58.56 −17.83857 202620 109.13
18.18553 431698 57.28 −17.54636 180575 66.71
19.01870 399188 39.75 −19.13075 142530 305.90
17.15752 383488 145.02 −17.94404 127098 32.26
17.72293 356895 48.46 −18.59563 116625 278.11
18.01611 303744 44.83 −5.61755 105161 348.70
7.45592 295700 200.24 −19.40256 85957 23.33
16.52731 231195 311.91 −7.07963 77142 93.77
16.26122 210411 58.89 −3.00557 63897 140.33
17.47683 201641 80.26 −0.69189 60870 23.96
18.08627 175373 356.17 −18.97001 59221 73.36
17.55234 162274 17.65 −6.84091 38863 286.50
3.08952 73627 121.36 −7.19493 38505 285.16
52.19257 26717 225.55 −5.50098 37498 342.89
6.93423 25209 170.37 −6.96094 36566 277.95
7.34103 24970 207.85 −18.69743 31116 221.70
7.05595 21406 359.16 −18.77933 30502 222.83
7.57299 17424 11.47 −18.22681 30460 46.30
6.82468 8182 194.53 −19.06544 27285 50.21
29.37998 8059 37.54 −7.33264 22307 16.75
27.06140 8027 38.70 −5.85017 12681 165.47
5.59644 6750 110.35 −5.21610 9492 18.91
7.20563 5106 143.91 −5.37178 9443 35.48
28.86795 4795 212.64 −5.10025 9241 195.38
27.57346 4212 223.74 −6.73842 7310 224.50
7.71663 3182 93.52 −7.40536 6758 53.35
4.36906 3180 40.88 −7.48780 6278 227.95
−19.72306 3055 113.24 −6.56016 5900 123.47
5.40817 2931 120.37 −5.96899 5417 350.64
5.47449 2541 275.01 −8.42342 4915 31.21
53.35188 2250 134.91 −6.15490 3922 89.77
0.66708 2008 73.98 −26.97744 3471 43.07
5.71670 1929 120.52 82.77163 1993 128.95
76.16447 1090 323.03 −1.84625 1457 38.22
5.35823 1037 94.89 18.14984 1419 111.19
51.03334 605 136.30 −4.16482 1278 51.57
4.89647 464 291.74 58.80017 1169 212.90
5.99227 381 113.56 34.82788 924 294.12
5.65485 368 39.22 −2.35835 628 44.46
5.23841 305 272.97 −0.58033 592 17.33
3.60029 250 121.40 −27.48935 592 218.53
1.93168 227 192.09 −25.17116 559 215.94
−56.90922 223 44.11 −50.30212 458 209.84
2.97706 192 306.81 −3.11725 427 326.97
−20.88236 91 203.93 −28.13656 371 314.08
1.82121 65 149.54 0.46547 170 286.88
0.77840 35 65.10 11.50319 136 281.02
−0.49216 10 164.74 −1.19906 96 133.57
0.57829 59 103.72
20.96631 53 57.78
10.34389 52 191.16
9.18847 33 1.15

Notes. This representation is used in Fig. 3. It has been directly obtained from Laskar (1990), see text.

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