Monday, January 29, 2007

1st TABLE: 2 YEAR CYCLER at q=0.622 AU.


Perihelion (q) is an orbit's closest point to Sol, our sun.

Reference ray (ν=0°) usually extends from Sol to object's perihelion.

All other angles, ν (Greek "nu"), measure from this reference.

For the orbital period (P) to be 2 years, Kepler's 3rd Law requires semimajor axis (a) to be 1.58 AU.

Cycler orbit's semilatis rectum, C, is distance from focus (i.e. Sol) to cycler at ν = 90°.  
For following table, let be 1.0 AU.

Cycler
Angle
Radius Coordinates Incr. Dist Velocity Incr.
Time
Cumm.
Time
Earth
Angle
Coordinates Mars
Angle
Radius Coordinates
νC RC X C YC ΔdC V ΔtC TC νE X E YE νM RM X M YM
Deg AU AU AU AU km km/sec days days Deg AU AU Deg AU AU AU
0 0.6218 0.6218 0.0000 n/a n/a 47.860 n/a 0 48.02 0.6689 0.7434 0.000 1.3700 1.3700 0.0000
1 0.6218 0.6218 0.0109 0.011 1,623,327 47.859 0.394 0.394 48.41 0.6638 0.7479 0.206 1.3700 1.3700 0.0049
2 0.6220 0.6216 0.0217 0.011 1,622,101 47.854 0.393 0.787 48.80 0.6587 0.7524 0.412 1.3700 1.3700 0.0099
3 0.6221 0.6213 0.0325 0.011 1,619,652 47.845 0.393 1.180 49.18 0.6536 0.7568 0.618 1.3700 1.3699 0.0148
4 0.6224 0.6209 0.0433 0.011 1,615,982 47.833 0.392 1.572 49.57 0.6485 0.7612 0.824 1.3700 1.3699 0.0197
5 0.6227 0.6203 0.0541 0.011 1,611,098 47.818 0.391 1.963 49.96 0.6434 0.7655 1.029 1.3700 1.3698 0.0246
6 0.6231 0.6197 0.0648 0.011 1,605,005 47.799 0.390 2.353 50.34 0.6382 0.7698 1.233 1.3700 1.3697 0.0295
7 0.6236 0.6189 0.0754 0.011 1,597,713 47.776 0.388 2.741 50.72 0.6331 0.7741 1.436 1.3700 1.3696 0.0343
8 0.6241 0.6180 0.0860 0.011 1,589,233 47.751 0.386 3.128 51.10 0.6279 0.7783 1.639 1.3701 1.3695 0.0392
9 0.6247 0.6170 0.0965 0.011 1,579,577 47.721 0.384 3.512 51.48 0.6228 0.7824 1.840 1.3701 1.3694 0.0440
10 0.6254 0.6159 0.1070 0.010 1,568,762 47.689 0.382 3.894 51.86 0.6176 0.7865 2.040 1.3701 1.3692 0.0487
11 0.6262 0.6147 0.1173 0.010 1,556,803 47.653 0.379 4.273 52.23 0.6125 0.7905 2.239 1.3701 1.3691 0.0535
12 0.6270 0.6133 0.1275 0.010 1,543,721 47.613 0.376 4.649 52.60 0.6073 0.7944 2.436 1.3701 1.3689 0.0582
13 0.6279 0.6118 0.1376 0.010 1,529,537 47.571 0.373 5.022 52.97 0.6022 0.7983 2.632 1.3701 1.3687 0.0628
14 0.6289 0.6102 0.1476 0.010 1,514,279 47.524 0.370 5.392 53.33 0.5971 0.8021 2.826 1.3702 1.3685 0.0675
15 0.6299 0.6085 0.1575 0.010 1,497,972 47.475 0.366 5.759 53.70 0.5921 0.8059 3.017 1.3702 1.3683 0.0720
ν R(AU) X (AU) Y (AU) Δd(AU) Δd(km) V(km/s) t(dy) T(dy) νE X (AU) Y (AU) ν R(AU) X (AU) Y (AU)
16 0.6311 0.6066 0.1672 0.010 1,480,650 47.422 0.362 6.121 54.05 0.5870 0.8096 3.207 1.3702 1.3681 0.0765
17 0.6323 0.6046 0.1768 0.010 1,462,347 47.365 0.358 6.479 54.41 0.5820 0.8132 3.395 1.3702 1.3678 0.0810
18 0.6335 0.6025 0.1862 0.010 1,443,102 47.306 0.354 6.833 54.76 0.5771 0.8167 3.581 1.3702 1.3676 0.0854
19 0.6349 0.6003 0.1954 0.010 1,422,960 47.242 0.350 7.183 55.10 0.5721 0.8202 3.764 1.3703 1.3673 0.0898
20 0.6363 0.5980 0.2045 0.009 1,401,968 47.176 0.345 7.528 55.44 0.5673 0.8235 3.945 1.3703 1.3671 0.0940
21 0.6378 0.5955 0.2134 0.009 1,380,182 47.106 0.340 7.868 55.78 0.5624 0.8268 4.123 1.3703 1.3668 0.0983
22 0.6394 0.5929 0.2221 0.009 1,357,660 47.032 0.335 8.203 56.11 0.5577 0.8301 4.298 1.3704 1.3665 0.1024
23 0.6411 0.5901 0.2306 0.009 1,334,471 46.956 0.330 8.533 56.43 0.5529 0.8332 4.471 1.3704 1.3662 0.1065
24 0.6428 0.5873 0.2389 0.009 1,310,689 46.876 0.325 8.858 56.75 0.5483 0.8363 4.641 1.3704 1.3659 0.1105
25 0.6447 0.5843 0.2469 0.009 1,286,397 46.792 0.319 9.177 57.07 0.5437 0.8393 4.809 1.3704 1.3656 0.1145
26 0.6466 0.5811 0.2547 0.008 1,261,688 46.706 0.314 9.490 57.37 0.5392 0.8422 4.973 1.3705 1.3653 0.1184
27 0.6485 0.5779 0.2623 0.008 1,236,665 46.616 0.308 9.798 57.68 0.5347 0.8451 5.134 1.3705 1.3650 0.1222
28 0.6506 0.5745 0.2697 0.008 1,211,443 46.522 0.302 10.101 57.98 0.5303 0.8478 5.293 1.3705 1.3647 0.1259
29 0.6528 0.5709 0.2768 0.008 1,186,151 46.426 0.297 10.397 58.27 0.5259 0.8505 5.448 1.3706 1.3644 0.1295
30 0.6550 0.5672 0.2836 0.008 1,160,930 46.326 0.291 10.688 58.55 0.5217 0.8531 5.601 1.3706 1.3641 0.1331
ν R(AU) X (AU) Y (AU) Δd(AU) Δd(km) V(km/s) t(dy) Σt(dy) νE X (AU) Y (AU) ν R(AU) X (AU) Y (AU)
31 0.6573 0.5634 0.2902 0.008 1,135,940 46.222 0.285 10.973 58.84 0.5175 0.8557 5.750 1.3706 1.3637 0.1366
32 0.6597 0.5595 0.2965 0.007 1,111,357 46.116 0.280 11.253 59.11 0.5134 0.8582 5.897 1.3707 1.3634 0.1401
33 0.6622 0.5554 0.3025 0.007 1,087,375 46.006 0.274 11.527 59.38 0.5093 0.8606 6.040 1.3707 1.3631 0.1434
34 0.6648 0.5511 0.3082 0.007 1,064,208 45.893 0.269 11.797 59.65 0.5053 0.8629 6.181 1.3707 1.3628 0.1467
35 0.6675 0.5468 0.3136 0.007 1,042,088 45.776 0.264 12.061 59.91 0.5014 0.8652 6.320 1.3708 1.3624 0.1500
36 0.6702 0.5422 0.3187 0.007 1,021,270 45.657 0.260 12.320 60.16 0.4975 0.8675 6.456 1.3708 1.3621 0.1532
37 0.6731 0.5375 0.3235 0.007 1,002,025 45.534 0.255 12.576 60.42 0.4937 0.8696 6.590 1.3708 1.3618 0.1563
38 0.6760 0.5327 0.3280 0.007 984,642 45.408 0.252 12.828 60.66 0.4899 0.8718 6.722 1.3709 1.3614 0.1594
39 0.6790 0.5277 0.3321 0.006 969,421 45.279 0.249 13.076 60.91 0.4862 0.8738 6.852 1.3709 1.3611 0.1624
40 0.6822 0.5226 0.3359 0.006 956,670 45.146 0.246 13.322 61.15 0.4825 0.8759 6.981 1.3709 1.3608 0.1654
41 0.6854 0.5173 0.3394 0.006 946,696 45.010 0.244 13.566 61.39 0.4788 0.8779 7.109 1.3710 1.3604 0.1684
42 0.6887 0.5118 0.3425 0.006 939,798 44.872 0.243 13.809 61.63 0.4751 0.8799 7.236 1.3710 1.3601 0.1713
43 0.6921 0.5062 0.3452 0.006 936,253 44.730 0.243 14.052 61.87 0.4715 0.8819 7.363 1.3710 1.3597 0.1743
44 0.6957 0.5004 0.3476 0.006 936,311 44.584 0.244 14.296 62.11 0.4678 0.8839 7.491 1.3711 1.3594 0.1772
45 0.6993 0.4945 0.3496 0.006 940,180 44.436 0.246 14.542 62.35 0.4640 0.8858 7.620 1.3711 1.3590 0.1802
ν R(AU) X (AU) Y (AU) Δd(AU) Δd(km) V(km/s) t(dy) T(dy) νE X (AU) Y (AU) ν R(AU) X (AU) Y (AU)
46 0.7030 0.4883 0.3513 0.006 948,019 44.285 0.248 14.790 62.60 0.4602 0.8878 7.750 1.3711 1.3586 0.1832
47 0.7068 0.4820 0.3525 0.006 959,935 44.130 0.252 15.043 62.85 0.4564 0.8898 7.882 1.3712 1.3582 0.1863
48 0.7107 0.4756 0.3534 0.007 975,976 43.973 0.258 15.300 63.10 0.4524 0.8918 8.017 1.3712 1.3578 0.1894
49 0.7148 0.4689 0.3539 0.007 996,134 43.812 0.264 15.564 63.36 0.4484 0.8938 8.156 1.3713 1.3574 0.1926
50 0.7189 0.4621 0.3540 0.007 1,020,351 43.648 0.271 15.836 63.63 0.4442 0.8959 8.298 1.3713 1.3569 0.1958
51 0.7232 0.4551 0.3537 0.007 1,048,524 43.481 0.280 16.115 63.90 0.4399 0.8981 8.444 1.3713 1.3565 0.1992
52 0.7276 0.4479 0.3530 0.007 1,080,512 43.312 0.290 16.405 64.19 0.4354 0.9002 8.596 1.3714 1.3560 0.2027
53 0.7321 0.4406 0.3518 0.007 1,116,150 43.139 0.300 16.705 64.49 0.4307 0.9025 8.754 1.3714 1.3555 0.2063
54 0.7367 0.4330 0.3503 0.008 1,155,253 42.963 0.312 17.017 64.79 0.4259 0.9048 8.917 1.3715 1.3549 0.2100
55 0.7414 0.4252 0.3483 0.008 1,197,624 42.784 0.325 17.342 65.11 0.4208 0.9071 9.087 1.3716 1.3543 0.2139
56 0.7462 0.4173 0.3459 0.008 1,243,066 42.602 0.339 17.681 65.45 0.4155 0.9096 9.265 1.3716 1.3537 0.2179
57 0.7512 0.4091 0.3431 0.009 1,291,379 42.418 0.353 18.034 65.80 0.4100 0.9121 9.450 1.3717 1.3531 0.2222
58 0.7563 0.4008 0.3399 0.009 1,342,371 42.230 0.369 18.403 66.16 0.4042 0.9147 9.643 1.3717 1.3524 0.2265
59 0.7615 0.3922 0.3362 0.009 1,395,857 42.039 0.385 18.789 66.54 0.3981 0.9173 9.845 1.3718 1.3516 0.2311
60 0.7668 0.3834 0.3320 0.010 1,451,661 41.846 0.403 19.192 66.94 0.3918 0.9201 10.056 1.3719 1.3508 0.2359
ν R(AU) X (AU) Y (AU) Δd(AU) Δd(km) V(km/s) t(dy) Σt(dy) νE X (AU) Y (AU) ν R(AU) X (AU) Y (AU)
61 0.7723 0.3744 0.3275 0.010 1,509,620 41.650 0.421 19.612 67.35 0.3851 0.9229 10.277 1.3720 1.3500 0.2408
62 0.7779 0.3652 0.3224 0.010 1,569,577 41.450 0.440 20.052 67.78 0.3781 0.9258 10.507 1.3721 1.3491 0.2460
63 0.7836 0.3558 0.3170 0.011 1,631,390 41.248 0.459 20.511 68.24 0.3708 0.9287 10.748 1.3722 1.3481 0.2514
64 0.7895 0.3461 0.3111 0.011 1,694,923 41.044 0.479 20.990 68.71 0.3631 0.9317 10.999 1.3723 1.3471 0.2570
65 0.7955 0.3362 0.3047 0.012 1,760,052 40.836 0.500 21.491 69.20 0.3551 0.9348 11.261 1.3724 1.3460 0.2628
66 0.8017 0.3261 0.2979 0.012 1,826,660 40.626 0.522 22.012 69.72 0.3467 0.9380 11.535 1.3725 1.3448 0.2689
67 0.8080 0.3157 0.2906 0.013 1,894,638 40.412 0.544 22.557 70.25 0.3379 0.9412 11.820 1.3726 1.3435 0.2752
68 0.8144 0.3051 0.2829 0.013 1,963,886 40.197 0.567 23.124 70.81 0.3287 0.9444 12.117 1.3728 1.3422 0.2817
69 0.8210 0.2942 0.2747 0.014 2,034,308 39.978 0.591 23.714 71.39 0.3191 0.9477 12.426 1.3729 1.3407 0.2885
70 0.8278 0.2831 0.2661 0.014 2,105,813 39.757 0.615 24.329 72.00 0.3090 0.9511 12.749 1.3730 1.3392 0.2955
71 0.8347 0.2718 0.2570 0.015 2,178,318 39.533 0.640 24.969 72.63 0.2985 0.9544 13.084 1.3732 1.3376 0.3028
72 0.8418 0.2601 0.2474 0.015 2,251,742 39.306 0.665 25.634 73.29 0.2876 0.9578 13.432 1.3734 1.3358 0.3103
73 0.8490 0.2482 0.2374 0.016 2,326,007 39.077 0.691 26.325 73.97 0.2762 0.9611 13.794 1.3736 1.3340 0.3181
74 0.8564 0.2361 0.2269 0.016 2,401,041 38.845 0.717 27.042 74.67 0.2643 0.9644 14.170 1.3738 1.3320 0.3261
75 0.8640 0.2236 0.2160 0.017 2,476,773 38.611 0.745 27.787 75.41 0.2519 0.9677 14.560 1.3740 1.3298 0.3343
νR(AU) X (AU) Y (AU) Δd(AU) Δd(km) V(km/s) t(dy) Σt(dy) νE X (AU) Y (AU) νR(AU) X (AU) Y (AU)
76 0.8717 0.2109 0.2046 0.017 2,553,135 38.374 0.772 28.559 76.17 0.2391 0.9710 14.965 1.3742 1.3276 0.3428
77 0.8797 0.1979 0.1928 0.018 2,630,059 38.135 0.801 29.360 76.96 0.2257 0.9742 15.384 1.3744 1.3252 0.3516
78 0.8877 0.1846 0.1805 0.018 2,707,483 37.893 0.829 30.189 77.78 0.2117 0.9773 15.819 1.3747 1.3226 0.3605
79 0.8960 0.1710 0.1678 0.019 2,785,342 37.649 0.859 31.048 78.62 0.1973 0.9803 16.269 1.3750 1.3199 0.3698
80 0.9045 0.1571 0.1547 0.019 2,863,574 37.402 0.889 31.936 79.50 0.1823 0.9832 16.735 1.3752 1.3170 0.3792
81 0.9131 0.1428 0.1411 0.020 2,942,119 37.153 0.919 32.856 80.40 0.1667 0.9860 17.216 1.3755 1.3139 0.3889
82 0.9220 0.1283 0.1271 0.020 3,020,917 36.901 0.950 33.806 81.34 0.1506 0.9886 17.714 1.3759 1.3106 0.3988
83 0.9310 0.1135 0.1126 0.021 3,099,906 36.647 0.982 34.788 82.31 0.1338 0.9910 18.229 1.3762 1.3071 0.4089
84 0.9402 0.0983 0.0977 0.021 3,179,029 36.391 1.014 35.802 83.31 0.1165 0.9932 18.760 1.3766 1.3034 0.4192
85 0.9497 0.0828 0.0825 0.022 3,258,225 36.133 1.047 36.849 84.34 0.0986 0.9951 19.309 1.3770 1.2995 0.4297
86 0.9593 0.0669 0.0668 0.022 3,337,436 35.872 1.080 37.928 85.40 0.0801 0.9968 19.875 1.3774 1.2953 0.4404
87 0.9692 0.0507 0.0507 0.023 3,416,601 35.609 1.114 39.042 86.50 0.0610 0.9981 20.458 1.3778 1.2909 0.4512
88 0.9792 0.0342 0.0342 0.023 3,495,662 35.344 1.148 40.190 87.63 0.0413 0.9991 21.060 1.3783 1.2862 0.4622
89 0.9895 0.0173 0.0173 0.024 3,574,559 35.077 1.183 41.373 88.80 0.0209 0.9998 21.680 1.3788 1.2812 0.4733
90 1.0000 0.0000 0.0000 0.024 3,653,231 34.807 1.218 42.591 90.00 0.0000 1.0000 22.318 1.3793 1.2760 0.4845
ν R(AU) X (AU) Y (AU) Δd(AU) Δd(km) V(km/s) t(dy) Σt(dy) νE X (AU) Y (AU) ν R(AU) X (AU) Y (AU)
91 1.0107 -0.0176 -0.0176 0.025 3,731,618 34.535 1.254 43.846 91.24 -0.0216 0.9998 22.975 1.3798 1.2704 0.4959
92 1.0217 -0.0357 -0.0356 0.025 3,809,658 34.262 1.291 45.136 92.51 -0.0438 0.9990 23.651 1.3804 1.2645 0.5073
93 1.0329 -0.0541 -0.0540 0.026 3,887,291 33.986 1.328 46.464 93.82 -0.0666 0.9978 24.347 1.3810 1.2582 0.5187
94 1.0443 -0.0728 -0.0727 0.027 3,964,452 33.708 1.365 47.829 95.16 -0.0900 0.9959 25.062 1.3817 1.2516 0.5302
95 1.0560 -0.0920 -0.0917 0.027 4,041,081 33.429 1.403 49.232 96.55 -0.1140 0.9935 25.798 1.3824 1.2446 0.5416
96 1.0679 -0.1116 -0.1110 0.028 4,117,112 33.147 1.442 50.674 97.97 -0.1386 0.9903 26.553 1.3831 1.2372 0.5531
97 1.0801 -0.1316 -0.1306 0.028 4,192,481 32.864 1.481 52.155 99.43 -0.1638 0.9865 27.329 1.3839 1.2294 0.5644
98 1.0925 -0.1520 -0.1506 0.029 4,267,124 32.578 1.520 53.675 100.93 -0.1895 0.9819 28.126 1.3847 1.2212 0.5757
99 1.1051 -0.1729 -0.1708 0.029 4,340,973 32.291 1.560 55.236 102.46 -0.2158 0.9764 28.944 1.3856 1.2125 0.5868
100 1.1181 -0.1942 -0.1912 0.030 4,413,963 32.002 1.601 56.837 104.04 -0.2426 0.9701 29.782 1.3865 1.2033 0.5977
101 1.1313 -0.2159 -0.2119 0.030 4,486,026 31.712 1.642 58.479 105.66 -0.2699 0.9629 30.643 1.3874 1.1937 0.6084
102 1.1448 -0.2380 -0.2328 0.030 4,557,094 31.419 1.684 60.162 107.32 -0.2977 0.9547 31.525 1.3884 1.1835 0.6188
103 1.1585 -0.2606 -0.2539 0.031 4,627,099 31.125 1.726 61.888 109.02 -0.3259 0.9454 32.429 1.3895 1.1728 0.6289
104 1.1725 -0.2837 -0.2752 0.031 4,695,971 30.830 1.768 63.656 110.76 -0.3545 0.9351 33.356 1.3906 1.1615 0.6386
105 1.1868 -0.3072 -0.2967 0.032 4,763,641 30.533 1.811 65.467 112.55 -0.3835 0.9236 34.305 1.3918 1.1497 0.6479
ν R(AU) X (AU) Y (AU) Δd(AU) Δd(km) V(km/s) t(dy) T(dy) νE X (AU) Y (AU) ν R(AU) X (AU) Y (AU)
106 1.2014 -0.3312 -0.3183 0.032 4,830,039 30.234 1.854 67.321 114.38 -0.4127 0.9109 35.276 1.3930 1.1372 0.6568
107 1.2163 -0.3556 -0.3401 0.033 4,895,095 29.934 1.898 69.220 116.25 -0.4422 0.8969 36.271 1.3943 1.1241 0.6650
108 1.2314 -0.3805 -0.3619 0.033 4,958,739 29.632 1.942 71.162 118.16 -0.4720 0.8816 37.289 1.3956 1.1104 0.6727
109 1.2469 -0.4060 -0.3838 0.034 5,020,900 29.329 1.987 73.149 120.12 -0.5018 0.8650 38.330 1.3971 1.0959 0.6797
110 1.2627 -0.4319 -0.4058 0.034 5,081,509 29.025 2.032 75.181 122.12 -0.5317 0.8469 39.395 1.3985 1.0808 0.6859
111 1.2787 -0.4582 -0.4278 0.034 5,140,496 28.720 2.078 77.259 124.17 -0.5617 0.8274 40.484 1.4001 1.0649 0.6914
112 1.2951 -0.4851 -0.4498 0.035 5,197,794 28.413 2.123 79.383 126.26 -0.5915 0.8063 41.596 1.4018 1.0483 0.6959
113 1.3117 -0.5125 -0.4718 0.035 5,253,334 28.105 2.170 81.552 128.40 -0.6212 0.7837 42.733 1.4035 1.0309 0.6995
114 1.3287 -0.5404 -0.4937 0.035 5,307,051 27.796 2.216 83.768 130.59 -0.6506 0.7594 43.895 1.4053 1.0127 0.7021
115 1.3460 -0.5688 -0.5155 0.036 5,358,879 27.486 2.263 86.032 132.82 -0.6797 0.7335 45.081 1.4072 0.9936 0.7036
116 1.3635 -0.5977 -0.5372 0.036 5,408,757 27.175 2.310 88.342 135.09 -0.7083 0.7059 46.291 1.4091 0.9737 0.7038
117 1.3814 -0.6272 -0.5588 0.036 5,456,625 26.863 2.358 90.700 137.42 -0.7363 0.6766 47.527 1.4112 0.9529 0.7028
118 1.3996 -0.6571 -0.5802 0.037 5,502,426 26.550 2.406 93.105 139.79 -0.7637 0.6456 48.787 1.4133 0.9312 0.7005
119 1.4182 -0.6875 -0.6013 0.037 5,546,107 26.237 2.454 95.559 142.21 -0.7902 0.6128 50.073 1.4155 0.9085 0.6967
120 1.4370 -0.7185 -0.6222 0.037 5,587,617 25.923 2.502 98.061 144.67 -0.8159 0.5782 51.384 1.4179 0.8849 0.6914
ν R(AU) X (AU) Y (AU) Δd(AU) Δd(km) V(km/s) t(dy) Σt(dy) νE X (AU) Y (AU) ν R(AU) X (AU) Y (AU)
121 1.4561 -0.7500 -0.6428 0.038 5,626,914 25.608 2.551 100.612 147.19 -0.8405 0.5419 52.720 1.4203 0.8603 0.6845
122 1.4756 -0.7819 -0.6631 0.038 5,663,957 25.292 2.599 103.211 149.75 -0.8638 0.5038 54.083 1.4228 0.8347 0.6760
123 1.4953 -0.8144 -0.6830 0.038 5,698,714 24.976 2.648 105.860 152.36 -0.8859 0.4639 55.470 1.4255 0.8080 0.6657
124 1.5154 -0.8474 -0.7025 0.038 5,731,157 24.660 2.698 108.557 155.02 -0.9065 0.4223 56.884 1.4282 0.7803 0.6535
125 1.5357 -0.8809 -0.7216 0.039 5,761,269 24.343 2.747 111.304 157.73 -0.9254 0.3790 58.324 1.4310 0.7515 0.6395
126 1.5564 -0.9148 -0.7401 0.039 5,789,038 24.026 2.797 114.101 160.48 -0.9425 0.3341 59.789 1.4340 0.7216 0.6236
127 1.5773 -0.9493 -0.7581 0.039 5,814,463 23.709 2.847 116.948 163.29 -0.9578 0.2875 61.281 1.4371 0.6905 0.6056
128 1.5986 -0.9842 -0.7755 0.039 5,837,553 23.392 2.897 119.845 166.15 -0.9709 0.2395 62.799 1.4402 0.6584 0.5855
129 1.6201 -1.0196 -0.7923 0.039 5,858,329 23.074 2.947 122.792 169.05 -0.9818 0.1900 64.343 1.4435 0.6250 0.5634
130 1.6419 -1.0554 -0.8085 0.039 5,876,822 22.757 2.998 125.789 172.00 -0.9903 0.1391 65.914 1.4469 0.5905 0.5391
131 1.6639 -1.0916 -0.8239 0.039 5,893,078 22.441 3.048 128.838 175.01 -0.9962 0.0870 67.511 1.4505 0.5548 0.5126
132 1.6862 -1.1283 -0.8385 0.039 5,907,155 22.124 3.099 131.937 178.06 -0.9994 0.0338 69.135 1.4541 0.5179 0.4839
133 1.7088 -1.1654 -0.8523 0.040 5,919,129 21.808 3.151 135.087 181.17 -0.9998 -0.0204 70.786 1.4579 0.4798 0.4531
134 1.7316 -1.2029 -0.8653 0.040 5,929,088 21.492 3.202 138.290 184.33 -0.9972 -0.0754 72.464 1.4617 0.4404 0.4200
135 1.7546 -1.2407 -0.8773 0.040 5,937,138 21.178 3.254 141.544 187.53 -0.9914 -0.1311 74.169 1.4657 0.3999 0.3847
ν R(AU) X (AU) Y (AU) Δd(AU) Δd(km) V(km/s) t(dy) T(dy) νE X (AU) Y (AU) ν R(AU) X (AU) Y (AU)
136 1.7778 -1.2788 -0.8884 0.040 5,943,404 20.864 3.307 144.850 190.79 -0.9823 -0.1872 75.902 1.4699 0.3580 0.3473
137 1.8012 -1.3173 -0.8984 0.040 5,948,025 20.551 3.360 148.210 194.10 -0.9699 -0.2437 77.662 1.4741 0.3150 0.3077
138 1.8248 -1.3561 -0.9074 0.040 5,951,160 20.239 3.413 151.623 197.47 -0.9539 -0.3002 79.451 1.4785 0.2707 0.2661
139 1.8485 -1.3951 -0.9152 0.040 5,952,987 19.928 3.467 155.091 200.89 -0.9343 -0.3565 81.268 1.4830 0.2251 0.2225
140 1.8723 -1.4343 -0.9219 0.040 5,953,698 19.619 3.523 158.613 204.36 -0.9110 -0.4124 83.113 1.4876 0.1784 0.1771
141 1.8963 -1.4737 -0.9274 0.040 5,953,507 19.311 3.579 162.192 207.88 -0.8839 -0.4677 84.989 1.4923 0.1304 0.1299
142 1.9204 -1.5133 -0.9317 0.040 5,952,641 19.005 3.636 165.828 211.47 -0.8529 -0.5220 86.894 1.4972 0.0811 0.0810
143 1.9445 -1.5530 -0.9346 0.040 5,951,342 18.701 3.694 169.522 215.11 -0.8181 -0.5751 88.829 1.5022 0.0307 0.0307
144 1.9687 -1.5927 -0.9362 0.040 5,949,866 18.399 3.754 173.275 218.81 -0.7792 -0.6267 90.796 1.5073 -0.0209 -0.0209
145 1.9929 -1.6325 -0.9363 0.040 5,948,482 18.099 3.815 177.090 222.57 -0.7365 -0.6765 92.795 1.5125 -0.0738 -0.0737
146 2.0170 -1.6722 -0.9351 0.040 5,947,462 17.802 3.878 180.968 226.39 -0.6897 -0.7241 94.827 1.5178 -0.1277 -0.1273
147 2.0411 -1.7119 -0.9323 0.040 5,947,086 17.508 3.943 184.911 230.28 -0.6391 -0.7692 96.893 1.5232 -0.1828 -0.1815
148 2.0652 -1.7514 -0.9281 0.040 5,947,634 17.216 4.010 188.921 234.23 -0.5845 -0.8114 98.995 1.5288 -0.2390 -0.2361
149 2.0891 -1.7907 -0.9223 0.040 5,949,383 16.928 4.079 193.001 238.25 -0.5262 -0.8504 101.132 1.5344 -0.2963 -0.2907
150 2.1129 -1.8298 -0.9149 0.040 5,952,599 16.643 4.152 197.152 242.34 -0.4642 -0.8857 103.308 1.5402 -0.3545 -0.3450
νR(AU) X (AU) Y (AU) Δd(AU) Δd(km) V(km/s) t(dy) Σt(dy) νE X (AU) Y (AU) ν R(AU) X (AU) Y (AU)
151 2.1365 -1.8686 -0.9059 0.040 5,957,535 16.362 4.226 201.378 246.51 -0.3986 -0.9171 105.522 1.5460 -0.4137 -0.3986
152 2.1599 -1.9071 -0.8953 0.040 5,964,424 16.086 4.304 205.682 250.75 -0.3297 -0.9441 107.778 1.5520 -0.4738 -0.4512
153 2.1830 -1.9450 -0.8830 0.040 5,973,476 15.813 4.385 210.067 255.07 -0.2576 -0.9663 110.075 1.5580 -0.5348 -0.5023
154 2.2058 -1.9825 -0.8691 0.040 5,984,866 15.545 4.469 214.536 259.48 -0.1826 -0.9832 112.417 1.5641 -0.5964 -0.5514
155 2.2282 -2.0195 -0.8535 0.040 5,998,734 15.282 4.556 219.093 263.97 -0.1051 -0.9945 114.805 1.5702 -0.6587 -0.5980
156 2.2503 -2.0558 -0.8362 0.040 6,015,181 15.024 4.647 223.740 268.55 -0.0253 -0.9997 117.240 1.5764 -0.7215 -0.6415
157 2.2720 -2.0913 -0.8172 0.040 6,034,258 14.772 4.742 228.482 273.22 0.0562 -0.9984 119.724 1.5826 -0.7847 -0.6815
158 2.2931 -2.1261 -0.7965 0.040 6,055,969 14.526 4.839 233.321 277.99 0.1391 -0.9903 122.260 1.5889 -0.8481 -0.7172
159 2.3138 -2.1601 -0.7741 0.041 6,080,264 14.287 4.940 238.261 282.86 0.2226 -0.9749 124.849 1.5951 -0.9115 -0.7480
160 2.3338 -2.1931 -0.7501 0.041 6,107,040 14.054 5.044 243.305 287.83 0.3063 -0.9519 127.492 1.6014 -0.9747 -0.7733
161 2.3533 -2.2251 -0.7244 0.041 6,136,140 13.828 5.151 248.456 292.91 0.3893 -0.9211 130.191 1.6076 -1.0374 -0.7925
162 2.3721 -2.2560 -0.6971 0.041 6,167,353 13.611 5.260 253.716 298.10 0.4709 -0.8822 132.947 1.6137 -1.0994 -0.8048
163 2.3902 -2.2858 -0.6683 0.041 6,200,418 13.401 5.371 259.086 303.39 0.5503 -0.8350 135.761 1.6197 -1.1604 -0.8096
164 2.4075 -2.3143 -0.6379 0.042 6,235,025 13.200 5.483 264.569 308.79 0.6265 -0.7794 138.634 1.6256 -1.2200 -0.8063
165 2.4241 -2.3415 -0.6060 0.042 6,270,823 13.008 5.596 270.165 314.31 0.6985 -0.7156 141.567 1.6313 -1.2778 -0.7943
ν R(AU) X (AU) Y (AU) Δd(AU) Δd(km) V(km/s) t(dy) T(dy) νE X (AU) Y (AU) ν R(AU) X (AU) Y (AU)
166 2.4398 -2.3673 -0.5727 0.042 6,307,423 12.825 5.709 275.874 319.94 0.7653 -0.6436 144.558 1.6368 -1.3335 -0.7733
167 2.4547 -2.3917 -0.5380 0.042 6,344,405 12.653 5.820 281.694 325.67 0.8258 -0.5639 147.608 1.6420 -1.3865 -0.7428
168 2.4686 -2.4146 -0.5020 0.043 6,381,327 12.491 5.930 287.624 331.52 0.8790 -0.4769 150.715 1.6470 -1.4365 -0.7027
169 2.4815 -2.4360 -0.4648 0.043 6,417,731 12.339 6.037 293.662 337.47 0.9237 -0.3832 153.879 1.6515 -1.4828 -0.6529
170 2.4935 -2.4556 -0.4264 0.043 6,453,154 12.199 6.140 299.802 343.52 0.9589 -0.2837 157.096 1.6557 -1.5252 -0.5936
171 2.5045 -2.4736 -0.3870 0.043 6,487,133 12.071 6.238 306.040 349.67 0.9838 -0.1793 160.365 1.6594 -1.5629 -0.5252
172 2.5143 -2.4899 -0.3465 0.044 6,519,216 11.956 6.330 312.369 355.91 0.9975 -0.0714 163.681 1.6627 -1.5957 -0.4484
173 2.5231 -2.5043 -0.3052 0.044 6,548,970 11.852 6.414 318.783 2.23 0.9992 0.0389 167.042 1.6654 -1.6229 -0.3639
174 2.5308 -2.5169 -0.2631 0.044 6,575,986 11.762 6.490 325.273 8.63 0.9887 0.1500 170.443 1.6675 -1.6443 -0.2730
175 2.5373 -2.5277 -0.2203 0.044 6,599,891 11.685 6.556 331.829 15.09 0.9655 0.2603 173.878 1.6690 -1.6594 -0.1770
176 2.5427 -2.5365 -0.1769 0.044 6,620,350 11.622 6.612 338.441 21.61 0.9297 0.3682 177.343 1.6698 -1.6680 -0.0773
177 2.5469 -2.5434 -0.1331 0.044 6,637,077 11.572 6.658 345.099 28.17 0.8816 0.4721 180.832 1.6700 -1.6698 0.0242
178 2.5499 -2.5484 -0.0889 0.044 6,649,834 11.536 6.691 351.790 34.76 0.8215 0.5702 184.338 1.6695 -1.6647 0.1259
179 2.5517 -2.5513 -0.0445 0.045 6,658,442 11.515 6.712 358.502 41.38 0.7504 0.6610 187.855 1.6683 -1.6526 0.2259
180 2.5523 -2.5523 0.0000 0.045 6,662,776 11.508 6.720 365.222 48.00 0.6691 0.7432 191.376 1.6664 -1.6337 0.3222
νR(AU) X (AU) Y (AU) Δd(AU) Δd(km) V(km/s) t(dy) Σt(dy) νE X (AU) Y (AU) ν R(AU) X (AU) Y (AU)
181 2.5517 -2.5513 0.0445 0.045 6,662,776 11.515 6.794 6.794 54.72 0.5776 0.8163 3.560 1.3702 1.3676 0.0849
182 2.5499 -2.5484 0.0889 0.045 6,658,442 11.536 6.777 13.571 61.40 0.4787 0.8780 7.111 1.3710 1.3604 0.1684
183 2.5469 -2.5434 0.1331 0.044 6,649,834 11.572 6.747 20.318 68.05 0.3738 0.9275 10.647 1.3721 1.3485 0.2491
184 2.5427 -2.5365 0.1769 0.044 6,637,077 11.622 6.706 27.024 74.66 0.2646 0.9644 14.161 1.3738 1.3320 0.3259
185 2.5373 -2.5277 0.2203 0.044 6,620,350 11.685 6.653 33.677 81.21 0.1527 0.9883 17.647 1.3758 1.3111 0.3974
186 2.5308 -2.5169 0.2631 0.044 6,599,891 11.762 6.589 40.265 87.71 0.0400 0.9992 21.099 1.3783 1.2859 0.4629
187 2.5231 -2.5043 0.3052 0.044 6,575,986 11.852 6.515 46.780 94.13 -0.0720 0.9974 24.513 1.3812 1.2567 0.5214
188 2.5143 -2.4899 0.3465 0.044 6,548,970 11.956 6.432 53.212 100.47 -0.1817 0.9834 27.883 1.3844 1.2237 0.5723
189 2.5045 -2.4736 0.3870 0.044 6,519,216 12.071 6.341 59.553 106.72 -0.2877 0.9577 31.206 1.3880 1.1872 0.6151
190 2.4935 -2.4556 0.4264 0.043 6,487,133 12.199 6.244 65.797 112.87 -0.3887 0.9214 34.478 1.3920 1.1475 0.6496
191 2.4815 -2.4360 0.4648 0.043 6,453,154 12.339 6.141 71.938 118.93 -0.4837 0.8752 37.696 1.3962 1.1048 0.6755
192 2.4686 -2.4146 0.5020 0.043 6,417,731 12.491 6.033 77.971 124.87 -0.5718 0.8204 40.857 1.4007 1.0594 0.6930
193 2.4547 -2.3917 0.5380 0.043 6,381,327 12.653 5.922 83.893 130.71 -0.6522 0.7580 43.960 1.4054 1.0116 0.7022
194 2.4398 -2.3673 0.5727 0.042 6,344,405 12.825 5.808 89.702 136.43 -0.7246 0.6892 47.004 1.4103 0.9618 0.7034
195 2.4241 -2.3415 0.6060 0.042 6,307,423 13.008 5.694 95.395 142.05 -0.7885 0.6150 49.987 1.4154 0.9100 0.6970
ν R(AU) X (AU) Y (AU) Δd(AU) Δd(km) V(km/s) t(dy) T(dy) νE X (AU) Y (AU) ν R(AU) X (AU) Y (AU)
196 2.4075 -2.3143 0.6379 0.042 6,270,823 13.200 5.578 100.973 147.54 -0.8438 0.5366 52.910 1.4207 0.8568 0.6834
197 2.3902 -2.2858 0.6683 0.042 6,235,025 13.401 5.463 106.437 152.93 -0.8904 0.4551 55.773 1.4260 0.8021 0.6632
198 2.3721 -2.2560 0.6971 0.041 6,200,418 13.611 5.349 111.786 158.20 -0.9285 0.3713 58.576 1.4315 0.7464 0.6369
199 2.3533 -2.2251 0.7244 0.041 6,167,353 13.828 5.237 117.022 163.36 -0.9581 0.2863 61.320 1.4371 0.6897 0.6051
200 2.3338 -2.1931 0.7501 0.041 6,136,140 14.054 5.127 122.149 168.42 -0.9796 0.2008 64.006 1.4428 0.6323 0.5684
201 2.3138 -2.1601 0.7741 0.041 6,107,040 14.287 5.019 127.168 173.36 -0.9933 0.1156 66.636 1.4485 0.5744 0.5273
202 2.2931 -2.1261 0.7965 0.041 6,080,264 14.526 4.915 132.083 178.21 -0.9995 0.0313 69.212 1.4543 0.5161 0.4825
203 2.2720 -2.0913 0.8172 0.040 6,055,969 14.772 4.814 136.897 182.95 -0.9987 -0.0515 71.734 1.4600 0.4576 0.4346
204 2.2503 -2.0558 0.8362 0.040 6,034,258 15.024 4.716 141.613 187.60 -0.9912 -0.1323 74.205 1.4658 0.3990 0.3839
205 2.2282 -2.0195 0.8535 0.040 6,015,181 15.282 4.622 146.235 192.16 -0.9776 -0.2106 76.627 1.4716 0.3404 0.3311
206 2.2058 -1.9825 0.8691 0.040 5,998,734 15.545 4.531 150.766 196.62 -0.9582 -0.2861 79.001 1.4774 0.2819 0.2767
207 2.1830 -1.9450 0.8830 0.040 5,984,866 15.813 4.444 155.210 201.00 -0.9336 -0.3584 81.330 1.4831 0.2236 0.2210
208 2.1599 -1.9071 0.8953 0.040 5,973,476 16.086 4.360 159.570 205.30 -0.9041 -0.4274 83.615 1.4889 0.1656 0.1645
209 2.1365 -1.8686 0.9059 0.040 5,964,424 16.362 4.280 163.851 209.52 -0.8702 -0.4927 85.858 1.4945 0.1080 0.1077
210 2.1129 -1.8298 0.9149 0.040 5,957,535 16.643 4.203 168.054 213.66 -0.8323 -0.5543 88.060 1.5002 0.0508 0.0508
ν R(AU) X (AU) Y (AU) Δd(AU) Δd(km) V(km/s) t(dy) Σt(dy) νE X (AU) Y (AU) ν R(AU) X (AU) Y (AU)
211 2.0891 -1.7907 0.9223 0.040 5,952,599 16.928 4.129 172.183 217.73 -0.7909 -0.6120 90.224 1.5058 -0.0059 -0.0059
212 2.0652 -1.7514 0.9281 0.040 5,949,383 17.216 4.058 176.240 221.73 -0.7463 -0.6656 92.350 1.5113 -0.0620 -0.0619
213 2.0411 -1.7119 0.9323 0.040 5,947,634 17.508 3.989 180.229 225.66 -0.6989 -0.7152 94.440 1.5168 -0.1174 -0.1171
214 2.0170 -1.6722 0.9351 0.040 5,947,086 17.802 3.923 184.152 229.53 -0.6491 -0.7607 96.495 1.5222 -0.1722 -0.1711
215 1.9929 -1.6325 0.9363 0.040 5,947,462 18.099 3.858 188.010 233.33 -0.5972 -0.8021 98.517 1.5275 -0.2262 -0.2237
216 1.9687 -1.5927 0.9362 0.040 5,948,482 18.399 3.796 191.806 237.07 -0.5436 -0.8394 100.506 1.5328 -0.2795 -0.2748
217 1.9445 -1.5530 0.9346 0.040 5,949,866 18.701 3.736 195.542 240.76 -0.4885 -0.8726 102.464 1.5380 -0.3319 -0.3241
218 1.9204 -1.5133 0.9317 0.040 5,951,342 19.005 3.677 199.219 244.38 -0.4324 -0.9017 104.391 1.5430 -0.3835 -0.3715
219 1.8963 -1.4737 0.9274 0.040 5,952,641 19.311 3.619 202.838 247.95 -0.3754 -0.9268 106.287 1.5480 -0.4342 -0.4167
220 1.8723 -1.4343 0.9219 0.040 5,953,507 19.619 3.563 206.402 251.46 -0.3180 -0.9481 108.154 1.5529 -0.4839 -0.4598
221 1.8485 -1.3951 0.9152 0.040 5,953,698 19.928 3.508 209.910 254.92 -0.2602 -0.9656 109.993 1.5578 -0.5326 -0.5005
222 1.8248 -1.3561 0.9074 0.040 5,952,987 20.239 3.454 213.363 258.32 -0.2024 -0.9793 111.802 1.5625 -0.5803 -0.5388
223 1.8012 -1.3173 0.8984 0.040 5,951,160 20.551 3.400 216.764 261.67 -0.1448 -0.9895 113.584 1.5671 -0.6270 -0.5746
224 1.7778 -1.2788 0.8884 0.040 5,948,025 20.864 3.348 220.111 264.97 -0.0876 -0.9962 115.338 1.5716 -0.6726 -0.6079
225 1.7546 -1.2407 0.8773 0.040 5,943,404 21.178 3.295 223.406 268.22 -0.0310 -0.9995 117.065 1.5760 -0.7171 -0.6385
ν R(AU) X (AU) Y (AU) Δd(AU) Δd(km) V(km/s) t(dy) T(dy) νE X (AU) Y (AU) ν R(AU) X (AU) Y (AU)
226 1.7316 -1.2029 0.8653 0.040 5,937,138 21.492 3.244 226.650 271.42 0.0248 -0.9997 118.765 1.5802 -0.7604 -0.6666
227 1.7088 -1.1654 0.8523 0.040 5,929,088 21.808 3.192 229.842 274.56 0.0796 -0.9968 120.437 1.5844 -0.8027 -0.6920
228 1.6862 -1.1283 0.8385 0.040 5,919,129 22.124 3.141 232.984 277.66 0.1333 -0.9911 122.084 1.5885 -0.8437 -0.7149
229 1.6639 -1.0916 0.8239 0.039 5,907,155 22.441 3.091 236.075 280.71 0.1858 -0.9826 123.703 1.5924 -0.8836 -0.7351
230 1.6419 -1.0554 0.8085 0.039 5,893,078 22.757 3.041 239.115 283.70 0.2369 -0.9715 125.296 1.5962 -0.9223 -0.7528
231 1.6201 -1.0196 0.7923 0.039 5,876,822 23.074 2.991 242.106 286.65 0.2866 -0.9581 126.863 1.5999 -0.9598 -0.7679
232 1.5986 -0.9842 0.7755 0.039 5,858,329 23.392 2.941 245.047 289.55 0.3346 -0.9423 128.404 1.6035 -0.9961 -0.7806
233 1.5773 -0.9493 0.7581 0.039 5,837,553 23.709 2.891 247.938 292.40 0.3811 -0.9245 129.919 1.6070 -1.0312 -0.7909
234 1.5564 -0.9148 0.7401 0.039 5,814,463 24.026 2.842 250.779 295.20 0.4258 -0.9048 131.408 1.6103 -1.0651 -0.7988
235 1.5357 -0.8809 0.7216 0.039 5,789,038 24.343 2.792 253.572 297.95 0.4688 -0.8833 132.872 1.6135 -1.0978 -0.8045
236 1.5154 -0.8474 0.7025 0.039 5,761,269 24.660 2.743 256.315 300.66 0.5099 -0.8602 134.309 1.6166 -1.1293 -0.8081
237 1.4953 -0.8144 0.6830 0.038 5,731,157 24.976 2.694 259.009 303.31 0.5492 -0.8357 135.721 1.6196 -1.1596 -0.8096
238 1.4756 -0.7819 0.6631 0.038 5,698,714 25.292 2.646 261.655 305.92 0.5867 -0.8098 137.107 1.6225 -1.1887 -0.8091
239 1.4561 -0.7500 0.6428 0.038 5,663,957 25.608 2.597 264.252 308.48 0.6223 -0.7828 138.468 1.6253 -1.2166 -0.8067
240 1.4370 -0.7185 0.6222 0.038 5,626,914 25.923 2.549 266.801 310.99 0.6560 -0.7548 139.804 1.6279 -1.2435 -0.8025
Given 2YrCy

1+e×cos(ν)
Rνcos(ν) Rνsin(ν) (ΔX²+ΔY²) Δd(AU) × 
149,597,870.7km
See Vν below. Δd

Vν
Σt
t×0.9856°

day
cos(νE) sin(νE)
t×0.5240°

day
Mars

1+e×cos(ν)
RMcos(νM) RMsin(νM)
241 1.4182 -0.6875 0.6013 0.037 5,587,617 26.237 2.501 269.301 313.46 0.6878 -0.7259 141.114 1.6304 -1.2691 -0.7967
242 1.3996 -0.6571 0.5802 0.037 5,546,107 26.550 2.453 271.754 315.88 0.7178 -0.6962 142.399 1.6329 -1.2937 -0.7894
243 1.3814 -0.6272 0.5588 0.037 5,502,426 26.863 2.405 274.159 318.25 0.7460 -0.6659 143.659 1.6352 -1.3171 -0.7805
244 1.3635 -0.5977 0.5372 0.036 5,456,625 27.175 2.358 276.517 320.57 0.7724 -0.6351 144.895 1.6374 -1.3395 -0.7703
245 1.3460 -0.5688 0.5155 0.036 5,408,757 27.486 2.311 278.827 322.85 0.7970 -0.6039 146.106 1.6395 -1.3609 -0.7589
246 1.3287 -0.5404 0.4937 0.036 5,358,879 27.796 2.264 281.091 325.08 0.8199 -0.5725 147.292 1.6415 -1.3812 -0.7464
247 1.3117 -0.5125 0.4718 0.035 5,307,051 28.105 2.217 283.308 327.26 0.8412 -0.5408 148.454 1.6434 -1.4005 -0.7327
248 1.2951 -0.4851 0.4498 0.035 5,253,334 28.413 2.171 285.479 329.40 0.8608 -0.5090 149.591 1.6452 -1.4189 -0.7182
249 1.2787 -0.4582 0.4278 0.035 5,197,794 28.720 2.125 287.605 331.50 0.8788 -0.4772 150.705 1.6469 -1.4363 -0.7028
250 1.2627 -0.4319 0.4058 0.034 5,140,496 29.025 2.080 289.684 333.55 0.8953 -0.4454 151.794 1.6486 -1.4528 -0.6866
251 1.2469 -0.4060 0.3838 0.034 5,081,509 29.329 2.034 291.718 335.55 0.9103 -0.4138 152.860 1.6501 -1.4684 -0.6698
252 1.2314 -0.3805 0.3619 0.034 5,020,900 29.632 1.990 293.708 337.51 0.9240 -0.3825 153.903 1.6516 -1.4832 -0.6524
253 1.2163 -0.3556 0.3401 0.033 4,958,739 29.934 1.945 295.653 339.43 0.9363 -0.3513 154.922 1.6529 -1.4971 -0.6346
254 1.2014 -0.3312 0.3183 0.033 4,895,095 30.234 1.901 297.554 341.31 0.9472 -0.3205 155.918 1.6542 -1.5103 -0.6162
255 1.1868 -0.3072 0.2967 0.032 4,830,039 30.533 1.857 299.412 343.14 0.9570 -0.2901 156.892 1.6555 -1.5226 -0.5976
ν(deg) R(AU) X(AU) Y(AU) Δd(AU) Δd(km) V(km/s) t(day) T(day) νE(deg)  X(AU) Y(AU) ν(deg) R(AU) X(AU) Y(AU)
256 1.1725 -0.2837 0.2752 0.032 4,763,641 30.830 1.814 301.226 344.92 0.9656 -0.2601 157.842 1.6566 -1.5343 -0.5787
257 1.1585 -0.2606 0.2539 0.031 4,695,971 31.125 1.772 302.998 346.67 0.9731 -0.2306 158.771 1.6577 -1.5452 -0.5595
258 1.1448 -0.2380 0.2328 0.031 4,627,099 31.419 1.729 304.727 348.37 0.9795 -0.2015 159.677 1.6587 -1.5554 -0.5402
259 1.1313 -0.2159 0.2119 0.030 4,557,094 31.712 1.687 306.414 350.04 0.9849 -0.1730 160.561 1.6596 -1.5650 -0.5208
260 1.1181 -0.1942 0.1912 0.030 4,486,026 32.002 1.646 308.060 351.66 0.9894 -0.1450 161.423 1.6605 -1.5740 -0.5014
261 1.1051 -0.1729 0.1708 0.030 4,413,963 32.291 1.605 309.665 353.24 0.9931 -0.1177 162.265 1.6614 -1.5824 -0.4820
262 1.0925 -0.1520 0.1506 0.029 4,340,973 32.578 1.565 311.230 354.78 0.9959 -0.0909 163.084 1.6621 -1.5902 -0.4627
263 1.0801 -0.1316 0.1306 0.029 4,267,124 32.864 1.525 312.754 356.29 0.9979 -0.0648 163.883 1.6628 -1.5975 -0.4435
264 1.0679 -0.1116 0.1110 0.028 4,192,481 33.147 1.485 314.239 357.75 0.9992 -0.0392 164.661 1.6635 -1.6043 -0.4244
265 1.0560 -0.0920 0.0917 0.028 4,117,112 33.429 1.446 315.686 359.18 0.9999 -0.0144 165.419 1.6641 -1.6105 -0.4054
266 1.0443 -0.0728 0.0727 0.027 4,041,081 33.708 1.408 317.093 0.56 1.0000 0.0098 166.157 1.6647 -1.6163 -0.3867
267 1.0329 -0.0541 0.0540 0.027 3,964,452 33.986 1.370 318.463 1.91 0.9994 0.0334 166.875 1.6652 -1.6217 -0.3683
268 1.0217 -0.0357 0.0356 0.026 3,887,291 34.262 1.332 319.795 3.23 0.9984 0.0563 167.573 1.6657 -1.6267 -0.3501
269 1.0107 -0.0176 0.0176 0.025 3,809,658 34.535 1.295 321.090 4.50 0.9969 0.0785 168.251 1.6662 -1.6313 -0.3322
270 1.0000 0.0000 0.0000 0.025 3,731,618 34.807 1.259 322.349 5.74 0.9950 0.1001 168.911 1.6666 -1.6355 -0.3146
Given 2YrCy

1+e×cos(ν)
Rνcos(ν) Rνsin(ν) (ΔX²+ΔY²) Δd(AU) × 
149,597,870.7km
See Vν below. Δd

Vν
Σt
t×0.9856°

day
cos(νE) sin(νE)
t×0.5240°

day
Mars

1+e×cos(ν)
RMcos(νM) RMsin(νM)
271 0.9895 0.0173 -0.0173 0.024 3,653,231 35.077 1.223 323.572 6.95 0.9927 0.1210 169.552 1.6670 -1.6393 -0.2973
272 0.9792 0.0342 -0.0342 0.024 3,574,559 35.344 1.188 324.760 8.12 0.9900 0.1413 170.174 1.6673 -1.6429 -0.2804
273 0.9692 0.0507 -0.0507 0.023 3,495,662 35.609 1.153 325.912 9.26 0.9870 0.1609 170.778 1.6676 -1.6461 -0.2638
274 0.9593 0.0669 -0.0668 0.023 3,416,601 35.872 1.118 327.031 10.36 0.9837 0.1798 171.364 1.6679 -1.6490 -0.2476
275 0.9497 0.0828 -0.0825 0.022 3,337,436 36.133 1.085 328.115 11.43 0.9802 0.1981 171.932 1.6682 -1.6517 -0.2318
276 0.9402 0.0983 -0.0977 0.022 3,258,225 36.391 1.051 329.167 12.46 0.9764 0.2158 172.483 1.6684 -1.6541 -0.2164
277 0.9310 0.1135 -0.1126 0.021 3,179,029 36.647 1.019 330.185 13.47 0.9725 0.2329 173.017 1.6686 -1.6563 -0.2014
278 0.9220 0.1283 -0.1271 0.021 3,099,906 36.901 0.986 331.172 14.44 0.9684 0.2494 173.534 1.6688 -1.6582 -0.1867
279 0.9131 0.1428 -0.1411 0.020 3,020,917 37.153 0.955 332.126 15.38 0.9642 0.2652 174.034 1.6690 -1.6600 -0.1725
280 0.9045 0.1571 -0.1547 0.020 2,942,119 37.402 0.924 333.050 16.29 0.9598 0.2805 174.518 1.6692 -1.6615 -0.1587
281 0.8960 0.1710 -0.1678 0.019 2,863,574 37.649 0.893 333.943 17.17 0.9554 0.2952 174.986 1.6693 -1.6629 -0.1453
282 0.8877 0.1846 -0.1805 0.019 2,785,342 37.893 0.863 334.806 18.02 0.9509 0.3094 175.438 1.6694 -1.6641 -0.1324
283 0.8797 0.1979 -0.1928 0.018 2,707,483 38.135 0.834 335.640 18.84 0.9464 0.3230 175.875 1.6695 -1.6652 -0.1198
284 0.8717 0.2109 -0.2046 0.018 2,630,059 38.374 0.805 336.444 19.64 0.9418 0.3361 176.297 1.6696 -1.6661 -0.1076
285 0.8640 0.2236 -0.2160 0.017 2,553,135 38.611 0.776 337.221 20.40 0.9373 0.3486 176.704 1.6697 -1.6669 -0.0958
ν(deg) R(AU) X(AU) Y(AU) Δd(AU) Δd(km) V(km/s) t(day) T(day) νE(deg)  X(AU) Y(AU) ν(deg) R(AU) X(AU) Y(AU)
286 0.8564 0.2361 -0.2269 0.017 2,476,773 38.845 0.749 337.970 21.14 0.9327 0.3607 177.096 1.6698 -1.6676 -0.0845
287 0.8490 0.2482 -0.2374 0.016 2,401,041 39.077 0.721 338.691 21.85 0.9281 0.3722 177.474 1.6698 -1.6682 -0.0735
288 0.8418 0.2601 -0.2474 0.016 2,326,007 39.306 0.695 339.386 22.54 0.9236 0.3833 177.838 1.6699 -1.6687 -0.0629
289 0.8347 0.2718 -0.2570 0.015 2,251,742 39.533 0.669 340.055 23.20 0.9192 0.3939 178.189 1.6699 -1.6691 -0.0528
290 0.8278 0.2831 -0.2661 0.015 2,178,318 39.757 0.643 340.698 23.83 0.9147 0.4040 178.526 1.6699 -1.6694 -0.0429
291 0.8210 0.2942 -0.2747 0.014 2,105,813 39.978 0.618 341.317 24.44 0.9104 0.4137 178.850 1.6700 -1.6696 -0.0335
292 0.8144 0.3051 -0.2829 0.014 2,034,308 40.197 0.594 341.911 25.03 0.9061 0.4230 179.161 1.6700 -1.6698 -0.0244
293 0.8080 0.3157 -0.2906 0.013 1,963,886 40.412 0.571 342.481 25.59 0.9019 0.4319 179.460 1.6700 -1.6699 -0.0157
294 0.8017 0.3261 -0.2979 0.013 1,894,638 40.626 0.548 343.029 26.13 0.8978 0.4404 179.747 1.6700 -1.6700 -0.0074
295 0.7955 0.3362 -0.3047 0.012 1,826,660 40.836 0.525 343.554 26.65 0.8938 0.4485 180.022 1.6700 -1.6700 0.0007
296 0.7895 0.3461 -0.3111 0.012 1,760,052 41.044 0.504 344.058 27.14 0.8899 0.4562 180.286 1.6700 -1.6700 0.0083
297 0.7836 0.3558 -0.3170 0.011 1,694,923 41.248 0.482 344.540 27.62 0.8861 0.4636 180.539 1.6700 -1.6699 0.0157
298 0.7779 0.3652 -0.3224 0.011 1,631,390 41.450 0.462 345.002 28.07 0.8824 0.4706 180.781 1.6700 -1.6698 0.0228
299 0.7723 0.3744 -0.3275 0.010 1,569,577 41.650 0.442 345.445 28.51 0.8787 0.4773 181.013 1.6700 -1.6697 0.0295
300 0.7668 0.3834 -0.3320 0.010 1,509,620 41.846 0.424 345.868 28.93 0.8752 0.4837 181.235 1.6700 -1.6696 0.0360
Given 2YrCy

1+e×cos(ν)
Rνcos(ν) Rνsin(ν) (ΔX²+ΔY²) Δd(AU) × 
149,597,870.7km
See Vν below. Δd

Vν
Σt
t×0.9856°

day
cos(νE) sin(νE)
t×0.5240°

day
Mars

1+e×cos(ν)
RMcos(νM) RMsin(νM)
301 0.7615 0.3922 -0.3362 0.010 1,451,661 42.039 0.405 346.274 29.33 0.8718 0.4898 181.448 1.6699 -1.6694 0.0422
302 0.7563 0.4008 -0.3399 0.009 1,395,857 42.230 0.388 346.662 29.71 0.8686 0.4956 181.651 1.6699 -1.6692 0.0481
303 0.7512 0.4091 -0.3431 0.009 1,342,371 42.418 0.372 347.034 30.07 0.8654 0.5011 181.846 1.6699 -1.6690 0.0538
304 0.7462 0.4173 -0.3459 0.009 1,291,379 42.602 0.356 347.390 30.43 0.8623 0.5064 182.032 1.6699 -1.6688 0.0592
305 0.7414 0.4252 -0.3483 0.008 1,243,066 42.784 0.341 347.731 30.76 0.8593 0.5115 182.211 1.6699 -1.6686 0.0644
306 0.7367 0.4330 -0.3503 0.008 1,197,624 42.963 0.327 348.058 31.08 0.8564 0.5163 182.382 1.6698 -1.6684 0.0694
307 0.7321 0.4406 -0.3518 0.008 1,155,253 43.139 0.314 348.372 31.39 0.8536 0.5209 182.547 1.6698 -1.6682 0.0741
308 0.7276 0.4479 -0.3530 0.007 1,116,150 43.312 0.303 348.675 31.69 0.8509 0.5254 182.706 1.6698 -1.6679 0.0787
309 0.7232 0.4551 -0.3537 0.007 1,080,512 43.481 0.292 348.967 31.98 0.8482 0.5296 182.859 1.6698 -1.6677 0.0832
310 0.7189 0.4621 -0.3540 0.007 1,048,524 43.648 0.282 349.249 32.26 0.8457 0.5337 183.006 1.6697 -1.6674 0.0875
311 0.7148 0.4689 -0.3539 0.007 1,020,351 43.812 0.273 349.522 32.53 0.8431 0.5377 183.150 1.6697 -1.6672 0.0916
312 0.7107 0.4756 -0.3534 0.007 996,134 43.973 0.266 349.788 32.79 0.8407 0.5416 183.289 1.6697 -1.6669 0.0956
313 0.7068 0.4820 -0.3525 0.007 975,976 44.130 0.260 350.048 33.05 0.8382 0.5453 183.425 1.6697 -1.6667 0.0996
314 0.7030 0.4883 -0.3513 0.006 959,935 44.285 0.255 350.303 33.30 0.8358 0.5490 183.559 1.6696 -1.6664 0.1034
315 0.6993 0.4945 -0.3496 0.006 948,019 44.436 0.251 350.553 33.54 0.8335 0.5526 183.690 1.6696 -1.6662 0.1072
ν(deg) R(AU) X(AU) Y(AU) Δd(AU) Δd(km) V(km/s) t(day) T(day) νE(deg)  X(AU) Y(AU) ν(deg) R(AU) X(AU) Y(AU)
316 0.6957 0.5004 -0.3476 0.006 940,180 44.584 0.248 350.801 33.79 0.8311 0.5561 183.820 1.6696 -1.6659 0.1110
317 0.6921 0.5062 -0.3452 0.006 936,311 44.730 0.246 351.046 34.03 0.8287 0.5596 183.948 1.6696 -1.6656 0.1147
318 0.6887 0.5118 -0.3425 0.006 936,253 44.872 0.245 351.291 34.27 0.8264 0.5631 184.077 1.6695 -1.6653 0.1184
319 0.6854 0.5173 -0.3394 0.006 939,798 45.010 0.245 351.537 34.51 0.8240 0.5666 184.205 1.6695 -1.6650 0.1221
320 0.6822 0.5226 -0.3359 0.006 946,696 45.146 0.246 351.783 34.76 0.8216 0.5701 184.334 1.6695 -1.6647 0.1258
321 0.6790 0.5277 -0.3321 0.006 956,670 45.279 0.248 352.031 35.00 0.8191 0.5736 184.464 1.6694 -1.6644 0.1295
322 0.6760 0.5327 -0.3280 0.006 969,421 45.408 0.251 352.282 35.25 0.8167 0.5771 184.596 1.6694 -1.6640 0.1333
323 0.6731 0.5375 -0.3235 0.007 984,642 45.534 0.254 352.536 35.50 0.8141 0.5807 184.729 1.6694 -1.6637 0.1371
324 0.6702 0.5422 -0.3187 0.007 1,002,025 45.657 0.258 352.793 35.75 0.8116 0.5843 184.864 1.6693 -1.6633 0.1410
325 0.6675 0.5468 -0.3136 0.007 1,021,270 45.776 0.262 353.055 36.01 0.8089 0.5879 185.001 1.6693 -1.6629 0.1450
326 0.6648 0.5511 -0.3082 0.007 1,042,088 45.893 0.267 353.322 36.27 0.8062 0.5916 185.141 1.6693 -1.6625 0.1490
327 0.6622 0.5554 -0.3025 0.007 1,064,208 46.006 0.272 353.593 36.54 0.8034 0.5954 185.283 1.6692 -1.6621 0.1530
328 0.6597 0.5595 -0.2965 0.007 1,087,375 46.116 0.277 353.870 36.81 0.8006 0.5992 185.428 1.6692 -1.6617 0.1572
329 0.6573 0.5634 -0.2902 0.007 1,111,357 46.222 0.282 354.153 37.09 0.7977 0.6031 185.576 1.6691 -1.6612 0.1614
330 0.6550 0.5672 -0.2836 0.008 1,135,940 46.326 0.288 354.441 37.38 0.7947 0.6070 185.727 1.6691 -1.6608 0.1657
Given 2YrCy

1+e×cos(ν)
Rνcos(ν) Rνsin(ν) (ΔX²+ΔY²) Convert to km. See Vν below. Δd

Vν
Σt
t×0.9856°

day
cos(νE) sin(νE)
t×0.5240°

day
Mars

1+e×cos(ν)
RMcos(νM) RMsin(νM)
331 0.6528 0.5709 -0.2768 0.008 1,160,930 46.426 0.294 354.734 37.66 0.7916 0.6110 185.881 1.6690 -1.6603 0.1701
332 0.6506 0.5745 -0.2697 0.008 1,186,151 46.522 0.299 355.034 37.96 0.7884 0.6151 186.038 1.6690 -1.6597 0.1746
333 0.6485 0.5779 -0.2623 0.008 1,211,443 46.616 0.305 355.339 38.26 0.7852 0.6192 186.197 1.6689 -1.6592 0.1791
334 0.6466 0.5811 -0.2547 0.008 1,236,665 46.706 0.311 355.650 38.57 0.7819 0.6234 186.360 1.6689 -1.6586 0.1837
335 0.6447 0.5843 -0.2469 0.008 1,261,688 46.792 0.317 355.966 38.88 0.7785 0.6277 186.526 1.6688 -1.6580 0.1884
336 0.6428 0.5873 -0.2389 0.009 1,286,397 46.876 0.322 356.288 39.20 0.7750 0.6320 186.695 1.6687 -1.6574 0.1932
337 0.6411 0.5901 -0.2306 0.009 1,310,689 46.956 0.328 356.616 39.52 0.7714 0.6363 186.867 1.6687 -1.6567 0.1981
338 0.6394 0.5929 -0.2221 0.009 1,334,471 47.032 0.333 356.949 39.85 0.7677 0.6408 187.041 1.6686 -1.6560 0.2030
339 0.6378 0.5955 -0.2134 0.009 1,357,660 47.106 0.338 357.288 40.18 0.7640 0.6452 187.219 1.6685 -1.6553 0.2080
340 0.6363 0.5980 -0.2045 0.009 1,380,182 47.176 0.344 357.631 40.52 0.7602 0.6497 187.399 1.6685 -1.6546 0.2131
341 0.6349 0.6003 -0.1954 0.009 1,401,968 47.242 0.348 357.980 40.86 0.7563 0.6543 187.581 1.6684 -1.6538 0.2182
342 0.6335 0.6025 -0.1862 0.010 1,422,960 47.306 0.353 358.333 41.21 0.7523 0.6588 187.766 1.6683 -1.6530 0.2234
343 0.6323 0.6046 -0.1768 0.010 1,443,102 47.365 0.358 358.691 41.56 0.7482 0.6635 187.954 1.6682 -1.6522 0.2286
344 0.6311 0.6066 -0.1672 0.010 1,462,347 47.422 0.362 359.053 41.92 0.7441 0.6681 188.144 1.6682 -1.6513 0.2339
345 0.6299 0.6085 -0.1575 0.010 1,480,650 47.475 0.366 359.419 42.28 0.7398 0.6728 188.336 1.6681 -1.6504 0.2393
ν(deg) R(AU) X(AU) Y(AU) Δd(AU) Δd(km) V(km/s) t(day) T(day) νE(deg)  X(AU) Y(AU) ν(deg) R(AU) X(AU) Y(AU)
346 0.6289 0.6102 -0.1476 0.010 1,497,972 47.524 0.370 359.789 42.65 0.7355 0.6775 188.529 1.6680 -1.6495 0.2447
347 0.6279 0.6118 -0.1376 0.010 1,514,279 47.571 0.374 360.163 43.02 0.7312 0.6822 188.725 1.6679 -1.6486 0.2501
348 0.6270 0.6133 -0.1275 0.010 1,529,537 47.613 0.377 360.540 43.39 0.7267 0.6869 188.923 1.6678 -1.6476 0.2556
349 0.6262 0.6147 -0.1173 0.010 1,543,721 47.653 0.380 360.920 43.76 0.7222 0.6917 189.122 1.6677 -1.6466 0.2611
350 0.6254 0.6159 -0.1070 0.010 1,556,803 47.689 0.383 361.304 44.14 0.7176 0.6964 189.323 1.6676 -1.6456 0.2666
351 0.6247 0.6170 -0.0965 0.010 1,568,762 47.721 0.386 361.690 44.52 0.7130 0.7012 189.525 1.6675 -1.6445 0.2721
352 0.6241 0.6180 -0.0860 0.011 1,579,577 47.751 0.388 362.078 44.90 0.7083 0.7059 189.729 1.6674 -1.6434 0.2777
353 0.6236 0.6189 -0.0754 0.011 1,589,233 47.776 0.391 362.469 45.29 0.7035 0.7107 189.934 1.6673 -1.6423 0.2833
354 0.6231 0.6197 -0.0648 0.011 1,597,713 47.799 0.392 362.861 45.68 0.6987 0.7154 190.139 1.6671 -1.6411 0.2889
355 0.6227 0.6203 -0.0541 0.011 1,605,005 47.818 0.394 363.255 46.06 0.6939 0.7201 190.346 1.6670 -1.6399 0.2945
356 0.6224 0.6209 -0.0433 0.011 1,611,098 47.833 0.395 363.651 46.45 0.6889 0.7248 190.553 1.6669 -1.6387 0.3001
357 0.6221 0.6213 -0.0325 0.011 1,615,982 47.845 0.397 364.047 46.84 0.6840 0.7295 190.761 1.6668 -1.6375 0.3057
358 0.6220 0.6216 -0.0217 0.011 1,619,652 47.854 0.397 364.445 47.24 0.6790 0.7342 190.969 1.6667 -1.6362 0.3113
359 0.6218 0.6218 -0.0109 0.011 1,622,101 47.859 0.398 364.843 47.63 0.6739 0.7388 191.178 1.6665 -1.6349 0.3169
360 0.6218 0.6218 0.0000 0.011 1,623,327 47.860 0.398 365.241 48.02 0.6689 0.7434 191.386 1.6664 -1.6336 0.3225
Given 2YrCy

1+e×cos(ν)
Rνcos(ν) Rνsin(ν) (ΔX²+ΔY²) Δd(AU) × 
149,597,870.7km
See Vν below. Δd

Vν
Σt
t×0.9856°

day
cos(νE) sin(νE)
t×0.5240°

day
Mars

1+e×cos(ν)
RMcos(νM) RMsin(νM)
For this example of a resonant cycler, let T, orbital period, equal 2.0 years ( ≈ 730.5 days)
Thus, a, semimajor axis, = T2/3 = 1.587 AU 
An orbit's semi latis rectum, C, is distance from focus (i.e. Sol) to cycler at ν = 90°.
In this case, let C = 1.0 AU =149,597,870.7 km  (deliberately chosen to be same distance as from Sol to Terra).
Then, b, semiminor axis, = (a×C) = (1.587AU×1.0AU) = 1.26 AU
Then, c, focus, = (a2-b2) = .965 AU.
Then, e, eccentricity, = c/a = .608
Rν(c

1 + ec×cos(ν)
)
Δd=
√((ΔX)²+(ΔY)²)
(
(X2-X1
+ (Y2-Y1)
Vν=(

Rν
-μ

aC
)
μ, Solar standard gravitational parameter, = 132,712,440,018 km3s−2
ALSO, can convert: μ  = 888.888 AU-km2s−2
Assume zero inclination for both orbit of Mars and orbit of Cycler.
Thus, computed positions of Earth and Mars are approximate.
t=Δd

Vν
×day

86,400 sec




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