Monday, January 29, 2007

TWO YEAR CYCLER TABLE




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
0.622 0.62 0.00 n/a n/a 47.903 n/a n/a 40.16°0.76 0.64 68.60°1.461 0.53 1.36
0.622 0.62 0.01 0.0109 1,623,464 47.901 0.39 0.39 40.55°0.76 0.65 68.81°1.461 0.53 1.36
0.622 0.62 0.02 0.0109 1,623,722 47.896 0.39 0.78 40.93°0.76 0.66 69.01°1.462 0.52 1.36
0.622 0.62 0.03 0.0109 1,624,238 47.888 0.39 1.18 41.32°0.75 0.66 69.22°1.462 0.52 1.37
0.622 0.62 0.04 0.0109 1,625,012 47.876 0.39 1.57 41.71°0.75 0.67 69.42°1.462 0.51 1.37
0.623 0.62 0.05 0.0109 1,626,044 47.860 0.39 1.96 42.10°0.74 0.67 69.63°1.463 0.51 1.37
0.623 0.62 0.07 0.0109 1,627,336 47.841 0.39 2.36 42.48°0.74 0.68 69.84°1.463 0.50 1.37
0.624 0.62 0.08 0.0109 1,628,887 47.819 0.39 2.75 42.87°0.73 0.68 70.04°1.464 0.50 1.38
0.624 0.62 0.09 0.0109 1,630,699 47.793 0.39 3.15 43.26°0.73 0.69 70.25°1.464 0.49 1.38
0.625 0.62 0.10 0.0109 1,632,772 47.764 0.40 3.54 43.65°0.72 0.69 70.46°1.465 0.49 1.38
10°0.625 0.62 0.11 0.0109 1,635,107 47.732 0.40 3.94 44.04°0.72 0.70 70.67°1.465 0.49 1.38
11°0.626 0.61 0.12 0.0109 1,637,706 47.696 0.40 4.34 44.43°0.71 0.70 70.87°1.466 0.48 1.38
12°0.627 0.61 0.13 0.0110 1,640,569 47.656 0.40 4.73 44.83°0.71 0.70 71.08°1.466 0.48 1.39
13°0.628 0.61 0.14 0.0110 1,643,698 47.613 0.40 5.13 45.22°0.70 0.71 71.29°1.467 0.47 1.39
14°0.629 0.61 0.15 0.0110 1,647,095 47.567 0.40 5.53 45.61°0.70 0.71 71.50°1.467 0.47 1.39
15°0.630 0.61 0.16 0.0110 1,650,761 47.518 0.40 5.94 46.01°0.69 0.72 71.71°1.467 0.46 1.39
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°0.631 0.61 0.17 0.0111 1,654,698 47.465 0.40 6.34 46.41°0.69 0.72 71.92°1.468 0.46 1.40
17°0.632 0.60 0.18 0.0111 1,658,908 47.408 0.41 6.75 46.81°0.68 0.73 72.14°1.468 0.45 1.40
18°0.633 0.60 0.20 0.0111 1,663,393 47.348 0.41 7.15 47.21°0.68 0.73 72.35°1.469 0.45 1.40
19°0.635 0.60 0.21 0.0112 1,668,154 47.285 0.41 7.56 47.61°0.67 0.74 72.56°1.469 0.44 1.40
20°0.636 0.60 0.22 0.0112 1,673,195 47.219 0.41 7.97 48.02°0.67 0.74 72.78°1.470 0.44 1.40
21°0.638 0.60 0.23 0.0112 1,678,518 47.149 0.41 8.38 48.42°0.66 0.75 72.99°1.470 0.43 1.41
22°0.639 0.59 0.24 0.0113 1,684,126 47.076 0.41 8.80 48.83°0.66 0.75 73.21°1.471 0.42 1.41
23°0.641 0.59 0.25 0.0113 1,690,020 46.999 0.42 9.21 49.24°0.65 0.76 73.43°1.471 0.42 1.41
24°0.643 0.59 0.26 0.0113 1,696,204 46.919 0.42 9.63 49.65°0.65 0.76 73.65°1.472 0.41 1.41
25°0.645 0.58 0.27 0.0114 1,702,681 46.836 0.42 10.05 50.07°0.64 0.77 73.87°1.472 0.41 1.41
26°0.647 0.58 0.28 0.0114 1,709,455 46.749 0.42 10.47 50.48°0.64 0.77 74.09°1.473 0.40 1.42
27°0.649 0.58 0.29 0.0115 1,716,527 46.659 0.43 10.90 50.90°0.63 0.78 74.31°1.473 0.40 1.42
28°0.651 0.57 0.31 0.0115 1,723,903 46.566 0.43 11.33 51.33°0.62 0.78 74.54°1.474 0.39 1.42
29°0.653 0.57 0.32 0.0116 1,731,585 46.469 0.43 11.76 51.75°0.62 0.79 74.76°1.474 0.39 1.42
30°0.655 0.57 0.33 0.0116 1,739,577 46.369 0.43 12.19 52.18°0.61 0.79 74.99°1.475 0.38 1.42
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°0.657 0.56 0.34 0.0117 1,747,883 46.266 0.44 12.63 52.61°0.61 0.79 75.22°1.475 0.38 1.43
32°0.660 0.56 0.35 0.0117 1,756,507 46.159 0.44 13.07 53.04°0.60 0.80 75.45°1.476 0.37 1.43
33°0.662 0.56 0.36 0.0118 1,765,454 46.050 0.44 13.52 53.48°0.60 0.80 75.68°1.476 0.37 1.43
34°0.665 0.55 0.37 0.0119 1,774,728 45.937 0.45 13.96 53.92°0.59 0.81 75.92°1.477 0.36 1.43
35°0.667 0.55 0.38 0.0119 1,784,332 45.820 0.45 14.41 54.37°0.58 0.81 76.15°1.477 0.35 1.43
36°0.670 0.54 0.39 0.0120 1,794,273 45.701 0.45 14.87 54.81°0.58 0.82 76.39°1.478 0.35 1.44
37°0.673 0.54 0.41 0.0121 1,804,555 45.578 0.46 15.33 55.27°0.57 0.82 76.63°1.479 0.34 1.44
38°0.676 0.53 0.42 0.0121 1,815,182 45.452 0.46 15.79 55.72°0.56 0.83 76.88°1.479 0.34 1.44
39°0.679 0.53 0.43 0.0122 1,826,161 45.323 0.47 16.26 56.18°0.56 0.83 77.12°1.480 0.33 1.44
40°0.682 0.52 0.44 0.0123 1,837,497 45.191 0.47 16.73 56.65°0.55 0.84 77.37°1.480 0.32 1.44
41°0.685 0.52 0.45 0.0124 1,849,194 45.055 0.48 17.20 57.11°0.54 0.84 77.61°1.481 0.32 1.45
42°0.689 0.51 0.46 0.0124 1,861,260 44.916 0.48 17.68 57.59°0.54 0.84 77.87°1.481 0.31 1.45
43°0.692 0.51 0.47 0.0125 1,873,699 44.774 0.48 18.16 58.06°0.53 0.85 78.12°1.482 0.31 1.45
44°0.696 0.50 0.48 0.0126 1,886,519 44.629 0.49 18.65 58.55°0.52 0.85 78.38°1.483 0.30 1.45
45°0.699 0.49 0.49 0.0127 1,899,725 44.481 0.49 19.15 59.03°0.51 0.86 78.64°1.483 0.29 1.45
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°0.703 0.49 0.51 0.0128 1,913,324 44.330 0.50 19.65 59.53°0.51 0.86 78.90°1.484 0.29 1.46
47°0.707 0.48 0.52 0.0129 1,927,322 44.176 0.50 20.15 60.02°0.50 0.87 79.16°1.484 0.28 1.46
48°0.711 0.48 0.53 0.0130 1,941,727 44.018 0.51 20.66 60.53°0.49 0.87 79.43°1.485 0.27 1.46
49°0.715 0.47 0.54 0.0131 1,956,545 43.858 0.52 21.18 61.04°0.48 0.87 79.70°1.486 0.27 1.46
50°0.719 0.46 0.55 0.0132 1,971,785 43.694 0.52 21.70 61.55°0.48 0.88 79.97°1.486 0.26 1.46
51°0.723 0.46 0.56 0.0133 1,987,452 43.527 0.53 22.23 62.07°0.47 0.88 80.25°1.487 0.25 1.47
52°0.728 0.45 0.57 0.0134 2,003,556 43.358 0.53 22.77 62.60°0.46 0.89 80.53°1.488 0.24 1.47
53°0.732 0.44 0.58 0.0135 2,020,105 43.185 0.54 23.31 63.13°0.45 0.89 80.81°1.488 0.24 1.47
54°0.737 0.43 0.60 0.0136 2,037,105 43.009 0.55 23.85 63.67°0.44 0.90 81.10°1.489 0.23 1.47
55°0.741 0.43 0.61 0.0137 2,054,566 42.831 0.56 24.41 64.22°0.43 0.90 81.39°1.490 0.22 1.47
56°0.746 0.42 0.62 0.0139 2,072,496 42.649 0.56 24.97 64.77°0.43 0.90 81.69°1.490 0.22 1.47
57°0.751 0.41 0.63 0.0140 2,090,904 42.464 0.57 25.54 65.34°0.42 0.91 81.99°1.491 0.21 1.48
58°0.756 0.40 0.64 0.0141 2,109,798 42.277 0.58 26.12 65.90°0.41 0.91 82.29°1.492 0.20 1.48
59°0.761 0.39 0.65 0.0142 2,129,189 42.087 0.59 26.71 66.48°0.40 0.92 82.60°1.492 0.19 1.48
60°0.767 0.38 0.66 0.0144 2,149,085 41.893 0.59 27.30 67.07°0.39 0.92 82.91°1.493 0.18 1.48
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°0.772 0.37 0.68 0.0145 2,169,497 41.697 0.60 27.90 67.66°0.38 0.92 83.22°1.494 0.18 1.48
62°0.778 0.37 0.69 0.0146 2,190,433 41.498 0.61 28.51 68.26°0.37 0.93 83.54°1.495 0.17 1.49
63°0.784 0.36 0.70 0.0148 2,211,904 41.296 0.62 29.13 68.87°0.36 0.93 83.87°1.496 0.16 1.49
64°0.789 0.35 0.71 0.0149 2,233,921 41.092 0.63 29.76 69.49°0.35 0.94 84.20°1.496 0.15 1.49
65°0.795 0.34 0.72 0.0151 2,256,493 40.884 0.64 30.40 70.12°0.34 0.94 84.53°1.497 0.14 1.49
66°0.802 0.33 0.73 0.0152 2,279,632 40.674 0.65 31.05 70.76°0.33 0.94 84.87°1.498 0.13 1.49
67°0.808 0.32 0.74 0.0154 2,303,348 40.461 0.66 31.71 71.41°0.32 0.95 85.22°1.499 0.12 1.49
68°0.814 0.31 0.76 0.0156 2,327,653 40.246 0.67 32.38 72.07°0.31 0.95 85.57°1.500 0.12 1.50
69°0.821 0.29 0.77 0.0157 2,352,557 40.027 0.68 33.06 72.74°0.30 0.95 85.92°1.500 0.11 1.50
70°0.828 0.28 0.78 0.0159 2,378,073 39.806 0.69 33.75 73.42°0.29 0.96 86.29°1.501 0.10 1.50
71°0.835 0.27 0.79 0.0161 2,404,211 39.583 0.70 34.45 74.12°0.27 0.96 86.65°1.502 0.09 1.50
72°0.842 0.26 0.80 0.0163 2,430,984 39.356 0.71 35.17 74.82°0.26 0.97 87.03°1.503 0.08 1.50
73°0.849 0.25 0.81 0.0164 2,458,403 39.127 0.73 35.89 75.54°0.25 0.97 87.41°1.504 0.07 1.50
74°0.856 0.24 0.82 0.0166 2,486,482 38.896 0.74 36.63 76.27°0.24 0.97 87.80°1.505 0.06 1.50
75°0.864 0.22 0.83 0.0168 2,515,231 38.662 0.75 37.39 77.01°0.22 0.97 88.19°1.506 0.05 1.51
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)
76°0.872 0.21 0.85 0.0170 2,544,665 38.425 0.77 38.15 77.77°0.21 0.98 88.59°1.507 0.04 1.51
77°0.880 0.20 0.86 0.0172 2,574,794 38.186 0.78 38.93 78.53°0.20 0.98 89.00°1.508 0.03 1.51
78°0.888 0.18 0.87 0.0174 2,605,632 37.945 0.79 39.73 79.32°0.19 0.98 89.42°1.509 0.02 1.51
79°0.896 0.17 0.88 0.0176 2,637,191 37.701 0.81 40.54 80.12°0.17 0.99 89.84°1.510 0.00 1.51
80°0.904 0.16 0.89 0.0178 2,669,485 37.454 0.82 41.36 80.93°0.16 0.99 90.28°1.511 -0.01 1.51
81°0.913 0.14 0.90 0.0181 2,702,526 37.205 0.84 42.20 81.76°0.14 0.99 90.72°1.512 -0.02 1.51
82°0.922 0.13 0.91 0.0183 2,736,328 36.954 0.86 43.06 82.60°0.13 0.99 91.17°1.513 -0.03 1.51
83°0.931 0.11 0.92 0.0185 2,770,902 36.701 0.87 43.93 83.46°0.11 0.99 91.62°1.514 -0.04 1.51
84°0.940 0.10 0.94 0.0188 2,806,262 36.445 0.89 44.83 84.34°0.10 1.00 92.09°1.516 -0.06 1.51
85°0.950 0.08 0.95 0.0190 2,842,421 36.187 0.91 45.74 85.24°0.08 1.00 92.57°1.517 -0.07 1.52
86°0.959 0.07 0.96 0.0192 2,879,391 35.926 0.93 46.66 86.15°0.07 1.00 93.05°1.518 -0.08 1.52
87°0.969 0.05 0.97 0.0195 2,917,185 35.664 0.95 47.61 87.09°0.05 1.00 93.55°1.519 -0.09 1.52
88°0.979 0.03 0.98 0.0198 2,955,815 35.399 0.97 48.58 88.04°0.03 1.00 94.06°1.520 -0.11 1.52
89°0.989 0.02 0.99 0.0200 2,995,294 35.132 0.99 49.56 89.01°0.02 1.00 94.57°1.522 -0.12 1.52
90°1.000 0.00 1.00 0.0203 3,035,633 34.863 1.01 50.57 90.00°0.00 1.00 95.10°1.523 -0.14 1.52
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°1.011 -0.02 1.01 0.0206 3,076,843 34.591 1.03 51.60 91.02°-0.02 1.00 95.64°1.524 -0.15 1.52
92°1.022 -0.04 1.02 0.0208 3,118,937 34.318 1.05 52.65 92.06°-0.04 1.00 96.19°1.526 -0.16 1.52
93°1.033 -0.05 1.03 0.0211 3,161,925 34.043 1.08 53.73 93.11°-0.05 1.00 96.76°1.527 -0.18 1.52
94°1.044 -0.07 1.04 0.0214 3,205,817 33.766 1.10 54.83 94.20°-0.07 1.00 97.33°1.529 -0.20 1.52
95°1.056 -0.09 1.05 0.0217 3,250,623 33.486 1.12 55.95 95.31°-0.09 1.00 97.92°1.530 -0.21 1.52
96°1.068 -0.11 1.06 0.0220 3,296,351 33.205 1.15 57.10 96.44°-0.11 0.99 98.52°1.532 -0.23 1.51
97°1.080 -0.13 1.07 0.0223 3,343,011 32.922 1.18 58.27 97.60°-0.13 0.99 99.14°1.533 -0.24 1.51
98°1.092 -0.15 1.08 0.0227 3,390,610 32.637 1.20 59.48 98.78°-0.15 0.99 99.77°1.535 -0.26 1.51
99°1.105 -0.17 1.09 0.0230 3,439,154 32.351 1.23 60.71 99.99°-0.17 0.98 100.41°1.536 -0.28 1.51
100°1.118 -0.19 1.10 0.0233 3,488,649 32.062 1.26 61.97 101.24°-0.19 0.98 101.07°1.538 -0.30 1.51
101°1.131 -0.22 1.11 0.0237 3,539,099 31.772 1.29 63.26 102.51°-0.22 0.98 101.75°1.540 -0.31 1.51
102°1.145 -0.24 1.12 0.0240 3,590,508 31.480 1.32 64.58 103.81°-0.24 0.97 102.44°1.541 -0.33 1.51
103°1.159 -0.26 1.13 0.0244 3,642,878 31.187 1.35 65.93 105.14°-0.26 0.97 103.15°1.543 -0.35 1.50
104°1.173 -0.28 1.14 0.0247 3,696,209 30.892 1.38 67.31 106.50°-0.28 0.96 103.87°1.545 -0.37 1.50
105°1.187 -0.31 1.15 0.0251 3,750,499 30.595 1.42 68.73 107.90°-0.31 0.95 104.62°1.547 -0.39 1.50
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°1.201 -0.33 1.15 0.0254 3,805,747 30.297 1.45 70.18 109.34°-0.33 0.94 105.38°1.549 -0.41 1.49
107°1.216 -0.36 1.16 0.0258 3,861,947 29.997 1.49 71.67 110.80°-0.36 0.93 106.16°1.551 -0.43 1.49
108°1.231 -0.38 1.17 0.0262 3,919,093 29.696 1.53 73.20 112.31°-0.38 0.93 106.96°1.553 -0.45 1.49
109°1.247 -0.41 1.18 0.0266 3,977,175 29.394 1.57 74.77 113.85°-0.40 0.91 107.78°1.555 -0.47 1.48
110°1.263 -0.43 1.19 0.0270 4,036,182 29.091 1.61 76.37 115.44°-0.43 0.90 108.62°1.557 -0.50 1.48
111°1.279 -0.46 1.19 0.0274 4,096,100 28.786 1.65 78.02 117.06°-0.45 0.89 109.49°1.559 -0.52 1.47
112°1.295 -0.49 1.20 0.0278 4,156,912 28.480 1.69 79.71 118.72°-0.48 0.88 110.37°1.561 -0.54 1.46
113°1.312 -0.51 1.21 0.0282 4,218,599 28.172 1.73 81.44 120.43°-0.51 0.86 111.28°1.563 -0.57 1.46
114°1.329 -0.54 1.21 0.0286 4,281,139 27.864 1.78 83.22 122.19°-0.53 0.85 112.21°1.566 -0.59 1.45
115°1.346 -0.57 1.22 0.0290 4,344,504 27.555 1.82 85.05 123.98°-0.56 0.83 113.17°1.568 -0.62 1.44
116°1.364 -0.60 1.23 0.0295 4,408,665 27.245 1.87 86.92 125.83°-0.59 0.81 114.15°1.570 -0.64 1.43
117°1.382 -0.63 1.23 0.0299 4,473,589 26.933 1.92 88.84 127.72°-0.61 0.79 115.16°1.573 -0.67 1.42
118°1.400 -0.66 1.24 0.0303 4,539,239 26.621 1.97 90.82 129.67°-0.64 0.77 116.19°1.575 -0.70 1.41
119°1.418 -0.69 1.24 0.0308 4,605,572 26.309 2.03 92.84 131.67°-0.66 0.75 117.25°1.578 -0.72 1.40
120°1.437 -0.72 1.24 0.0312 4,672,543 25.995 2.08 94.92 133.72°-0.69 0.72 118.34°1.580 -0.75 1.39
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°1.456 -0.75 1.25 0.0317 4,740,102 25.681 2.14 97.06 135.82°-0.72 0.70 119.46°1.583 -0.78 1.38
122°1.476 -0.78 1.25 0.0321 4,808,194 25.367 2.19 99.25 137.99°-0.74 0.67 120.61°1.586 -0.81 1.36
123°1.495 -0.81 1.25 0.0326 4,876,757 25.051 2.25 101.51 140.21°-0.77 0.64 121.79°1.589 -0.84 1.35
124°1.516 -0.85 1.26 0.0331 4,945,726 24.736 2.31 103.82 142.49°-0.79 0.61 123.00°1.591 -0.87 1.33
125°1.536 -0.88 1.26 0.0335 5,015,031 24.420 2.38 106.20 144.83°-0.82 0.58 124.25°1.594 -0.90 1.32
126°1.557 -0.91 1.26 0.0340 5,084,595 24.104 2.44 108.64 147.24°-0.84 0.54 125.53°1.597 -0.93 1.30
127°1.578 -0.95 1.26 0.0345 5,154,337 23.788 2.51 111.15 149.71°-0.86 0.50 126.84°1.600 -0.96 1.28
128°1.599 -0.98 1.26 0.0349 5,224,168 23.472 2.58 113.72 152.25°-0.88 0.47 128.19°1.603 -0.99 1.26
129°1.620 -1.02 1.26 0.0354 5,293,995 23.156 2.65 116.37 154.86°-0.91 0.42 129.58°1.606 -1.02 1.24
130°1.642 -1.06 1.26 0.0359 5,363,718 22.839 2.72 119.09 157.53°-0.92 0.38 131.00°1.609 -1.06 1.21
131°1.664 -1.09 1.26 0.0363 5,433,233 22.524 2.79 121.88 160.29°-0.94 0.34 132.47°1.612 -1.09 1.19
132°1.686 -1.13 1.25 0.0368 5,502,428 22.208 2.87 124.75 163.11°-0.96 0.29 133.97°1.615 -1.12 1.16
133°1.709 -1.17 1.25 0.0372 5,571,186 21.893 2.95 127.69 166.02°-0.97 0.24 135.51°1.618 -1.15 1.13
134°1.732 -1.20 1.25 0.0377 5,639,386 21.579 3.02 130.72 169.00°-0.98 0.19 137.10°1.621 -1.19 1.10
135°1.755 -1.24 1.24 0.0381 5,706,899 21.266 3.11 133.82 172.06°-0.99 0.14 138.73°1.624 -1.22 1.07
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°1.778 -1.28 1.24 0.0386 5,773,592 20.953 3.19 137.01 175.20°-1.00 0.08 140.40°1.627 -1.25 1.04
137°1.801 -1.32 1.23 0.0390 5,839,329 20.641 3.27 140.29 178.43°-1.00 0.03 142.11°1.630 -1.29 1.00
138°1.825 -1.36 1.22 0.0395 5,903,968 20.330 3.36 143.65 181.74°-1.00 -0.03 143.87°1.634 -1.32 0.96
139°1.849 -1.40 1.21 0.0399 5,967,364 20.021 3.45 147.10 185.14°-1.00 -0.09 145.68°1.637 -1.35 0.92
140°1.873 -1.43 1.20 0.0403 6,029,369 19.713 3.54 150.64 188.63°-0.99 -0.15 147.54°1.639 -1.38 0.88
141°1.897 -1.47 1.19 0.0407 6,089,832 19.407 3.63 154.27 192.21°-0.98 -0.21 149.44°1.642 -1.41 0.84
142°1.921 -1.51 1.18 0.0411 6,148,603 19.102 3.73 157.99 195.88°-0.96 -0.27 151.39°1.645 -1.44 0.79
143°1.945 -1.55 1.17 0.0415 6,205,529 18.800 3.82 161.81 199.65°-0.94 -0.34 153.39°1.648 -1.47 0.74
144°1.969 -1.59 1.16 0.0418 6,260,460 18.500 3.92 165.73 203.51°-0.92 -0.40 155.45°1.651 -1.50 0.69
145°1.993 -1.63 1.14 0.0422 6,313,247 18.201 4.01 169.74 207.46°-0.89 -0.46 157.55°1.653 -1.53 0.63
146°2.017 -1.67 1.13 0.0425 6,363,746 17.906 4.11 173.86 211.52°-0.85 -0.52 159.71°1.655 -1.55 0.57
147°2.042 -1.71 1.11 0.0429 6,411,816 17.613 4.21 178.07 215.67°-0.81 -0.58 161.91°1.657 -1.58 0.51
148°2.066 -1.75 1.09 0.0432 6,457,323 17.324 4.31 182.39 219.92°-0.77 -0.64 164.17°1.659 -1.60 0.45
149°2.090 -1.79 1.08 0.0435 6,500,142 17.037 4.42 186.80 224.28°-0.72 -0.70 166.49°1.661 -1.62 0.39
150°2.113 -1.83 1.06 0.0437 6,540,159 16.754 4.52 191.32 228.73°-0.66 -0.75 168.86°1.663 -1.63 0.32
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)
151°2.137 -1.87 1.04 0.0440 6,577,270 16.475 4.62 195.94 233.28°-0.60 -0.80 171.28°1.664 -1.64 0.25
152°2.160 -1.91 1.01 0.0442 6,611,386 16.200 4.72 200.66 237.94°-0.53 -0.85 173.75°1.665 -1.65 0.18
153°2.183 -1.95 0.99 0.0444 6,642,434 15.929 4.83 205.49 242.70°-0.46 -0.89 176.28°1.666 -1.66 0.11
154°2.206 -1.98 0.97 0.0446 6,670,358 15.663 4.93 210.42 247.55°-0.38 -0.92 178.86°1.666 -1.67 0.03
155°2.229 -2.02 0.94 0.0448 6,695,123 15.402 5.03 215.45 252.51°-0.30 -0.95 181.50°1.666 -1.67 -0.04
156°2.251 -2.06 0.92 0.0449 6,716,714 15.146 5.13 220.58 257.57°-0.22 -0.98 184.19°1.665 -1.66 -0.12
157°2.272 -2.09 0.89 0.0450 6,735,142 14.896 5.23 225.82 262.73°-0.13 -0.99 186.93°1.665 -1.65 -0.20
158°2.294 -2.13 0.86 0.0451 6,750,440 14.652 5.33 231.15 267.99°-0.04 -1.00 189.73°1.663 -1.64 -0.28
159°2.314 -2.16 0.83 0.0452 6,762,669 14.415 5.43 236.58 273.34°0.06 -1.00 192.57°1.662 -1.62 -0.36
160°2.334 -2.19 0.80 0.0453 6,771,917 14.184 5.53 242.10 278.78°0.15 -0.99 195.47°1.660 -1.60 -0.44
161°2.354 -2.23 0.77 0.0453 6,778,299 13.961 5.62 247.72 284.32°0.25 -0.97 198.41°1.657 -1.57 -0.52
162°2.373 -2.26 0.73 0.0453 6,781,959 13.745 5.71 253.43 289.95°0.34 -0.94 201.41°1.654 -1.54 -0.60
163°2.391 -2.29 0.70 0.0453 6,783,068 13.538 5.80 259.23 295.67°0.43 -0.90 204.44°1.651 -1.50 -0.68
164°2.408 -2.31 0.66 0.0453 6,781,827 13.338 5.88 265.12 301.47°0.52 -0.85 207.53°1.647 -1.46 -0.76
165°2.425 -2.34 0.63 0.0453 6,778,459 13.148 5.97 271.08 307.35°0.61 -0.79 210.65°1.642 -1.41 -0.84
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°2.440 -2.37 0.59 0.0453 6,773,214 12.968 6.05 277.13 313.31°0.69 -0.73 213.82°1.637 -1.36 -0.91
167°2.455 -2.39 0.55 0.0452 6,766,362 12.797 6.12 283.25 319.34°0.76 -0.65 217.03°1.632 -1.30 -0.98
168°2.469 -2.42 0.51 0.0452 6,758,192 12.637 6.19 289.44 325.44°0.82 -0.57 220.27°1.626 -1.24 -1.05
169°2.482 -2.44 0.47 0.0451 6,749,006 12.487 6.26 295.69 331.60°0.88 -0.48 223.55°1.620 -1.17 -1.12
170°2.494 -2.46 0.43 0.0450 6,739,115 12.349 6.32 302.01 337.83°0.93 -0.38 226.86°1.613 -1.10 -1.18
171°2.505 -2.47 0.39 0.0450 6,728,836 12.223 6.37 308.38 344.11°0.96 -0.27 230.20°1.606 -1.03 -1.23
172°2.515 -2.49 0.35 0.0449 6,718,484 12.108 6.42 314.80 350.44°0.99 -0.17 233.56°1.599 -0.95 -1.29
173°2.524 -2.51 0.31 0.0448 6,708,367 12.006 6.47 321.27 356.81°1.00 -0.06 236.95°1.591 -0.87 -1.33
174°2.531 -2.52 0.26 0.0448 6,698,780 11.917 6.51 327.78 3.23°1.00 0.06 240.36°1.583 -0.78 -1.38
175°2.538 -2.53 0.22 0.0447 6,689,996 11.841 6.54 334.32 9.67°0.99 0.17 243.79°1.575 -0.70 -1.41
176°2.543 -2.54 0.18 0.0447 6,682,265 11.779 6.57 340.88 16.14°0.96 0.28 247.23°1.567 -0.61 -1.44
177°2.548 -2.54 0.13 0.0446 6,675,804 11.730 6.59 347.47 22.64°0.92 0.38 250.68°1.559 -0.52 -1.47
178°2.551 -2.55 0.09 0.0446 6,670,793 11.695 6.60 354.07 29.14°0.87 0.49 254.14°1.550 -0.42 -1.49
179°2.552 -2.55 0.04 0.0446 6,667,374 11.673 6.61 360.68 35.66°0.81 0.58 257.61°1.541 -0.33 -1.51
180°2.553 -2.55 0.00 0.0446 6,665,640 11.666 6.61 367.30 42.18°0.74 0.67 261.07°1.533 -0.24 -1.51
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)
181°2.552 -2.55 -0.04 0.0446 6,665,640 11.673 6.61 373.90 48.69°0.66 0.75 264.53°1.524 -0.15 -1.52
182°2.551 -2.55 -0.09 0.0446 6,667,374 11.695 6.60 380.50 55.19°0.57 0.82 267.99°1.515 -0.05 -1.51
183°2.548 -2.54 -0.13 0.0446 6,670,793 11.730 6.58 387.09 61.68°0.47 0.88 271.44°1.507 0.04 -1.51
184°2.543 -2.54 -0.18 0.0446 6,675,804 11.779 6.56 393.65 68.15°0.37 0.93 274.88°1.499 0.13 -1.49
185°2.538 -2.53 -0.22 0.0447 6,682,265 11.841 6.53 400.18 74.59°0.27 0.96 278.30°1.490 0.22 -1.47
186°2.531 -2.52 -0.26 0.0447 6,689,996 11.917 6.50 406.67 80.99°0.16 0.99 281.71°1.482 0.30 -1.45
187°2.524 -2.51 -0.31 0.0448 6,698,780 12.006 6.46 413.13 87.35°0.05 1.00 285.09°1.475 0.38 -1.42
188°2.515 -2.49 -0.35 0.0448 6,708,367 12.108 6.41 419.54 93.67°-0.06 1.00 288.45°1.467 0.46 -1.39
189°2.505 -2.47 -0.39 0.0449 6,718,484 12.223 6.36 425.91 99.94°-0.17 0.98 291.78°1.460 0.54 -1.36
190°2.494 -2.46 -0.43 0.0450 6,728,836 12.349 6.31 432.21 106.16°-0.28 0.96 295.09°1.453 0.62 -1.32
191°2.482 -2.44 -0.47 0.0450 6,739,115 12.487 6.25 438.46 112.32°-0.38 0.93 298.36°1.446 0.69 -1.27
192°2.469 -2.42 -0.51 0.0451 6,749,006 12.637 6.18 444.64 118.41°-0.48 0.88 301.60°1.440 0.75 -1.23
193°2.455 -2.39 -0.55 0.0452 6,758,192 12.797 6.11 450.75 124.43°-0.57 0.82 304.80°1.434 0.82 -1.18
194°2.440 -2.37 -0.59 0.0452 6,766,362 12.968 6.04 456.79 130.39°-0.65 0.76 307.97°1.428 0.88 -1.13
195°2.425 -2.34 -0.63 0.0453 6,773,214 13.148 5.96 462.75 136.26°-0.72 0.69 311.09°1.423 0.94 -1.07
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°2.408 -2.31 -0.66 0.0453 6,778,459 13.338 5.88 468.64 142.06°-0.79 0.61 314.18°1.418 0.99 -1.02
197°2.391 -2.29 -0.70 0.0453 6,781,827 13.538 5.80 474.43 147.78°-0.85 0.53 317.21°1.414 1.04 -0.96
198°2.373 -2.26 -0.73 0.0453 6,783,068 13.745 5.71 480.15 153.40°-0.89 0.45 320.21°1.409 1.08 -0.90
199°2.354 -2.23 -0.77 0.0453 6,781,959 13.961 5.62 485.77 158.95°-0.93 0.36 323.15°1.405 1.12 -0.84
200°2.334 -2.19 -0.80 0.0453 6,778,299 14.184 5.53 491.30 164.40°-0.96 0.27 326.05°1.402 1.16 -0.78
201°2.314 -2.16 -0.83 0.0453 6,771,917 14.415 5.44 496.74 169.76°-0.98 0.18 328.90°1.399 1.20 -0.72
202°2.294 -2.13 -0.86 0.0452 6,762,669 14.652 5.34 502.08 175.02°-1.00 0.09 331.70°1.396 1.23 -0.66
203°2.272 -2.09 -0.89 0.0451 6,750,440 14.896 5.24 507.32 180.19°-1.00 0.00 334.45°1.393 1.26 -0.60
204°2.251 -2.06 -0.92 0.0450 6,735,142 15.146 5.15 512.47 185.26°-1.00 -0.09 337.14°1.391 1.28 -0.54
205°2.229 -2.02 -0.94 0.0449 6,716,714 15.402 5.05 517.52 190.24°-0.98 -0.18 339.79°1.389 1.30 -0.48
206°2.206 -1.98 -0.97 0.0448 6,695,123 15.663 4.95 522.46 195.12°-0.97 -0.26 342.38°1.387 1.32 -0.42
207°2.183 -1.95 -0.99 0.0446 6,670,358 15.929 4.85 527.31 199.89°-0.94 -0.34 344.92°1.386 1.34 -0.36
208°2.160 -1.91 -1.01 0.0444 6,642,434 16.200 4.75 532.06 204.57°-0.91 -0.42 347.41°1.384 1.35 -0.30
209°2.137 -1.87 -1.04 0.0442 6,611,386 16.475 4.64 536.70 209.15°-0.87 -0.49 349.84°1.383 1.36 -0.24
210°2.113 -1.83 -1.06 0.0440 6,577,270 16.754 4.54 541.25 213.63°-0.83 -0.55 352.22°1.383 1.37 -0.19
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°2.090 -1.79 -1.08 0.0437 6,540,159 17.037 4.44 545.69 218.00°-0.79 -0.62 354.55°1.382 1.38 -0.13
212°2.066 -1.75 -1.09 0.0435 6,500,142 17.324 4.34 550.03 222.29°-0.74 -0.67 356.83°1.382 1.38 -0.08
213°2.042 -1.71 -1.11 0.0432 6,457,323 17.613 4.24 554.27 226.47°-0.69 -0.72 359.05°1.382 1.38 -0.02
214°2.017 -1.67 -1.13 0.0429 6,411,816 17.906 4.14 558.42 230.55°-0.64 -0.77 1.22°1.382 1.38 0.03
215°1.993 -1.63 -1.14 0.0425 6,363,746 18.201 4.05 562.47 234.54°-0.58 -0.81 3.34°1.382 1.38 0.08
216°1.969 -1.59 -1.16 0.0422 6,313,247 18.500 3.95 566.42 238.43°-0.52 -0.85 5.41°1.382 1.38 0.13
217°1.945 -1.55 -1.17 0.0418 6,260,460 18.800 3.85 570.27 242.23°-0.47 -0.88 7.43°1.382 1.37 0.18
218°1.921 -1.51 -1.18 0.0415 6,205,529 19.102 3.76 574.03 245.94°-0.41 -0.91 9.40°1.383 1.36 0.23
219°1.897 -1.47 -1.19 0.0411 6,148,603 19.407 3.67 577.70 249.55°-0.35 -0.94 11.32°1.384 1.36 0.27
220°1.873 -1.43 -1.20 0.0407 6,089,832 19.713 3.58 581.27 253.08°-0.29 -0.96 13.20°1.385 1.35 0.32
221°1.849 -1.40 -1.21 0.0403 6,029,369 20.021 3.49 584.76 256.51°-0.23 -0.97 15.02°1.386 1.34 0.36
222°1.825 -1.36 -1.22 0.0399 5,967,364 20.330 3.40 588.15 259.86°-0.18 -0.98 16.80°1.387 1.33 0.40
223°1.801 -1.32 -1.23 0.0395 5,903,968 20.641 3.31 591.47 263.12°-0.12 -0.99 18.54°1.388 1.32 0.44
224°1.778 -1.28 -1.24 0.0390 5,839,329 20.953 3.23 594.69 266.30°-0.06 -1.00 20.23°1.389 1.30 0.48
225°1.755 -1.24 -1.24 0.0386 5,773,592 21.266 3.14 597.83 269.40°-0.01 -1.00 21.88°1.390 1.29 0.52
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°1.732 -1.20 -1.25 0.0381 5,706,899 21.579 3.06 600.89 272.42°0.04 -1.00 23.48°1.391 1.28 0.55
227°1.709 -1.17 -1.25 0.0377 5,639,386 21.893 2.98 603.88 275.36°0.09 -1.00 25.04°1.393 1.26 0.59
228°1.686 -1.13 -1.25 0.0372 5,571,186 22.208 2.90 606.78 278.22°0.14 -0.99 26.56°1.394 1.25 0.62
229°1.664 -1.09 -1.26 0.0368 5,502,428 22.524 2.83 609.61 281.00°0.19 -0.98 28.05°1.395 1.23 0.66
230°1.642 -1.06 -1.26 0.0363 5,433,233 22.839 2.75 612.36 283.72°0.24 -0.97 29.49°1.397 1.22 0.69
231°1.620 -1.02 -1.26 0.0359 5,363,718 23.156 2.68 615.04 286.36°0.28 -0.96 30.89°1.398 1.20 0.72
232°1.599 -0.98 -1.26 0.0354 5,293,995 23.472 2.61 617.65 288.93°0.32 -0.95 32.26°1.400 1.18 0.75
233°1.578 -0.95 -1.26 0.0349 5,224,168 23.788 2.54 620.19 291.44°0.37 -0.93 33.59°1.401 1.17 0.78
234°1.557 -0.91 -1.26 0.0345 5,154,337 24.104 2.47 622.67 293.88°0.40 -0.91 34.89°1.403 1.15 0.80
235°1.536 -0.88 -1.26 0.0340 5,084,595 24.420 2.41 625.08 296.25°0.44 -0.90 36.15°1.405 1.13 0.83
236°1.516 -0.85 -1.26 0.0335 5,015,031 24.736 2.35 627.42 298.57°0.48 -0.88 37.38°1.406 1.12 0.85
237°1.495 -0.81 -1.25 0.0331 4,945,726 25.051 2.28 629.71 300.82°0.51 -0.86 38.58°1.408 1.10 0.88
238°1.476 -0.78 -1.25 0.0326 4,876,757 25.367 2.23 631.93 303.01°0.54 -0.84 39.75°1.409 1.08 0.90
239°1.456 -0.75 -1.25 0.0321 4,808,194 25.681 2.17 634.10 305.15°0.58 -0.82 40.88°1.411 1.07 0.92
240°1.437 -0.72 -1.24 0.0317 4,740,102 25.995 2.11 636.21 307.23°0.60 -0.80 41.99°1.412 1.05 0.94
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°1.418 -0.69 -1.24 0.0312 4,672,543 26.309 2.06 638.27 309.25°0.63 -0.77 43.06°1.414 1.03 0.97
242°1.400 -0.66 -1.24 0.0308 4,605,572 26.621 2.00 640.27 311.23°0.66 -0.75 44.11°1.416 1.02 0.99
243°1.382 -0.63 -1.23 0.0303 4,539,239 26.933 1.95 642.22 313.15°0.68 -0.73 45.14°1.417 1.00 1.00
244°1.364 -0.60 -1.23 0.0299 4,473,589 27.245 1.90 644.12 315.02°0.71 -0.71 46.13°1.419 0.98 1.02
245°1.346 -0.57 -1.22 0.0295 4,408,665 27.555 1.85 645.97 316.85°0.73 -0.68 47.10°1.420 0.97 1.04
246°1.329 -0.54 -1.21 0.0290 4,344,504 27.864 1.80 647.78 318.63°0.75 -0.66 48.05°1.422 0.95 1.06
247°1.312 -0.51 -1.21 0.0286 4,281,139 28.172 1.76 649.54 320.36°0.77 -0.64 48.97°1.423 0.93 1.07
248°1.295 -0.49 -1.20 0.0282 4,218,599 28.480 1.71 651.25 322.05°0.79 -0.61 49.87°1.425 0.92 1.09
249°1.279 -0.46 -1.19 0.0278 4,156,912 28.786 1.67 652.92 323.70°0.81 -0.59 50.74°1.426 0.90 1.10
250°1.263 -0.43 -1.19 0.0274 4,096,100 29.091 1.63 654.55 325.30°0.82 -0.57 51.60°1.428 0.89 1.12
251°1.247 -0.41 -1.18 0.0270 4,036,182 29.394 1.59 656.14 326.87°0.84 -0.55 52.43°1.429 0.87 1.13
252°1.231 -0.38 -1.17 0.0266 3,977,175 29.696 1.55 657.69 328.40°0.85 -0.52 53.24°1.431 0.86 1.15
253°1.216 -0.36 -1.16 0.0262 3,919,093 29.997 1.51 659.20 329.89°0.87 -0.50 54.04°1.432 0.84 1.16
254°1.201 -0.33 -1.15 0.0258 3,861,947 30.297 1.48 660.68 331.34°0.88 -0.48 54.81°1.433 0.83 1.17
255°1.187 -0.31 -1.15 0.0254 3,805,747 30.595 1.44 662.12 332.76°0.89 -0.46 55.56°1.435 0.81 1.18
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°1.173 -0.28 -1.14 0.0251 3,750,499 30.892 1.41 663.52 334.15°0.90 -0.44 56.30°1.436 0.80 1.19
257°1.159 -0.26 -1.13 0.0247 3,696,209 31.187 1.37 664.90 335.50°0.91 -0.41 57.02°1.437 0.78 1.21
258°1.145 -0.24 -1.12 0.0244 3,642,878 31.480 1.34 666.23 336.82°0.92 -0.39 57.72°1.439 0.77 1.22
259°1.131 -0.22 -1.11 0.0240 3,590,508 31.772 1.31 667.54 338.11°0.93 -0.37 58.41°1.440 0.75 1.23
260°1.118 -0.19 -1.10 0.0237 3,539,099 32.062 1.28 668.82 339.37°0.94 -0.35 59.07°1.441 0.74 1.24
261°1.105 -0.17 -1.09 0.0233 3,488,649 32.351 1.25 670.07 340.60°0.94 -0.33 59.73°1.443 0.73 1.25
262°1.092 -0.15 -1.08 0.0230 3,439,154 32.637 1.22 671.29 341.80°0.95 -0.31 60.37°1.444 0.71 1.25
263°1.080 -0.13 -1.07 0.0227 3,390,610 32.922 1.19 672.48 342.97°0.96 -0.29 60.99°1.445 0.70 1.26
264°1.068 -0.11 -1.06 0.0223 3,343,011 33.205 1.17 673.65 344.12°0.96 -0.27 61.60°1.446 0.69 1.27
265°1.056 -0.09 -1.05 0.0220 3,296,351 33.486 1.14 674.78 345.25°0.97 -0.25 62.20°1.447 0.68 1.28
266°1.044 -0.07 -1.04 0.0217 3,250,623 33.766 1.11 675.90 346.34°0.97 -0.24 62.78°1.449 0.66 1.29
267°1.033 -0.05 -1.03 0.0214 3,205,817 34.043 1.09 676.99 347.42°0.98 -0.22 63.36°1.450 0.65 1.30
268°1.022 -0.04 -1.02 0.0211 3,161,925 34.318 1.07 678.06 348.47°0.98 -0.20 63.91°1.451 0.64 1.30
269°1.011 -0.02 -1.01 0.0208 3,118,937 34.591 1.04 679.10 349.50°0.98 -0.18 64.46°1.452 0.63 1.31
270°1.000 0.00 -1.00 0.0206 3,076,843 34.863 1.02 680.12 350.50°0.99 -0.16 65.00°1.453 0.61 1.32
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°0.989 0.02 -0.99 0.0203 3,035,633 35.132 1.00 681.12 351.49°0.99 -0.15 65.52°1.454 0.60 1.32
272°0.979 0.03 -0.98 0.0200 2,995,294 35.399 0.98 682.10 352.46°0.99 -0.13 66.03°1.455 0.59 1.33
273°0.969 0.05 -0.97 0.0198 2,955,815 35.664 0.96 683.06 353.40°0.99 -0.11 66.54°1.456 0.58 1.34
274°0.959 0.07 -0.96 0.0195 2,917,185 35.926 0.94 684.00 354.33°1.00 -0.10 67.03°1.457 0.57 1.34
275°0.950 0.08 -0.95 0.0192 2,879,391 36.187 0.92 684.92 355.23°1.00 -0.08 67.51°1.458 0.56 1.35
276°0.940 0.10 -0.94 0.0190 2,842,421 36.445 0.90 685.82 356.12°1.00 -0.07 67.98°1.459 0.55 1.35
277°0.931 0.11 -0.92 0.0188 2,806,262 36.701 0.88 686.71 357.00°1.00 -0.05 68.45°1.460 0.54 1.36
278°0.922 0.13 -0.91 0.0185 2,770,902 36.954 0.87 687.58 357.85°1.00 -0.04 68.90°1.461 0.53 1.36
279°0.913 0.14 -0.90 0.0183 2,736,328 37.205 0.85 688.43 358.69°1.00 -0.02 69.35°1.462 0.52 1.37
280°0.904 0.16 -0.89 0.0181 2,702,526 37.454 0.84 689.26 359.51°1.00 -0.01 69.79°1.463 0.51 1.37
281°0.896 0.17 -0.88 0.0178 2,669,485 37.701 0.82 690.08 0.32°1.00 0.01 70.22°1.464 0.50 1.38
282°0.888 0.18 -0.87 0.0176 2,637,191 37.945 0.80 690.89 1.11°1.00 0.02 70.64°1.465 0.49 1.38
283°0.880 0.20 -0.86 0.0174 2,605,632 38.186 0.79 691.68 1.89°1.00 0.03 71.05°1.466 0.48 1.39
284°0.872 0.21 -0.85 0.0172 2,574,794 38.425 0.78 692.45 2.66°1.00 0.05 71.46°1.467 0.47 1.39
285°0.864 0.22 -0.83 0.0170 2,544,665 38.662 0.76 693.21 3.41°1.00 0.06 71.86°1.468 0.46 1.39
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°0.856 0.24 -0.82 0.0168 2,515,231 38.896 0.75 693.96 4.15°1.00 0.07 72.25°1.469 0.45 1.40
287°0.849 0.25 -0.81 0.0166 2,486,482 39.127 0.74 694.70 4.87°1.00 0.08 72.63°1.469 0.44 1.40
288°0.842 0.26 -0.80 0.0164 2,458,403 39.356 0.72 695.42 5.58°1.00 0.10 73.01°1.470 0.43 1.41
289°0.835 0.27 -0.79 0.0163 2,430,984 39.583 0.71 696.13 6.28°0.99 0.11 73.39°1.471 0.42 1.41
290°0.828 0.28 -0.78 0.0161 2,404,211 39.806 0.70 696.83 6.97°0.99 0.12 73.75°1.472 0.41 1.41
291°0.821 0.29 -0.77 0.0159 2,378,073 40.027 0.69 697.52 7.65°0.99 0.13 74.11°1.473 0.40 1.42
292°0.814 0.31 -0.76 0.0157 2,352,557 40.246 0.68 698.19 8.32°0.99 0.14 74.47°1.474 0.39 1.42
293°0.808 0.32 -0.74 0.0156 2,327,653 40.461 0.67 698.86 8.97°0.99 0.16 74.82°1.474 0.39 1.42
294°0.802 0.33 -0.73 0.0154 2,303,348 40.674 0.66 699.51 9.62°0.99 0.17 75.16°1.475 0.38 1.43
295°0.795 0.34 -0.72 0.0152 2,279,632 40.884 0.65 700.16 10.26°0.98 0.18 75.50°1.476 0.37 1.43
296°0.789 0.35 -0.71 0.0151 2,256,493 41.092 0.64 700.80 10.88°0.98 0.19 75.83°1.477 0.36 1.43
297°0.784 0.36 -0.70 0.0149 2,233,921 41.296 0.63 701.42 11.50°0.98 0.20 76.16°1.477 0.35 1.43
298°0.778 0.37 -0.69 0.0148 2,211,904 41.498 0.62 702.04 12.11°0.98 0.21 76.48°1.478 0.35 1.44
299°0.772 0.37 -0.68 0.0146 2,190,433 41.697 0.61 702.65 12.71°0.98 0.22 76.80°1.479 0.34 1.44
300°0.767 0.38 -0.66 0.0145 2,169,497 41.893 0.60 703.25 13.30°0.97 0.23 77.11°1.480 0.33 1.44
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°0.761 0.39 -0.65 0.0144 2,149,085 42.087 0.59 703.84 13.88°0.97 0.24 77.42°1.480 0.32 1.44
302°0.756 0.40 -0.64 0.0142 2,129,189 42.277 0.58 704.42 14.45°0.97 0.25 77.73°1.481 0.31 1.45
303°0.751 0.41 -0.63 0.0141 2,109,798 42.464 0.58 705.00 15.02°0.97 0.26 78.03°1.482 0.31 1.45
304°0.746 0.42 -0.62 0.0140 2,090,904 42.649 0.57 705.56 15.58°0.96 0.27 78.33°1.482 0.30 1.45
305°0.741 0.43 -0.61 0.0139 2,072,496 42.831 0.56 706.12 16.13°0.96 0.28 78.62°1.483 0.29 1.45
306°0.737 0.43 -0.60 0.0137 2,054,566 43.009 0.55 706.68 16.68°0.96 0.29 78.91°1.484 0.29 1.46
307°0.732 0.44 -0.58 0.0136 2,037,105 43.185 0.55 707.22 17.22°0.96 0.30 79.20°1.484 0.28 1.46
308°0.728 0.45 -0.57 0.0135 2,020,105 43.358 0.54 707.76 17.75°0.95 0.30 79.48°1.485 0.27 1.46
309°0.723 0.46 -0.56 0.0134 2,003,556 43.527 0.53 708.29 18.27°0.95 0.31 79.76°1.486 0.26 1.46
310°0.719 0.46 -0.55 0.0133 1,987,452 43.694 0.53 708.82 18.79°0.95 0.32 80.04°1.486 0.26 1.46
311°0.715 0.47 -0.54 0.0132 1,971,785 43.858 0.52 709.34 19.30°0.94 0.33 80.31°1.487 0.25 1.47
312°0.711 0.48 -0.53 0.0131 1,956,545 44.018 0.51 709.85 19.81°0.94 0.34 80.58°1.488 0.24 1.47
313°0.707 0.48 -0.52 0.0130 1,941,727 44.176 0.51 710.36 20.31°0.94 0.35 80.84°1.488 0.24 1.47
314°0.703 0.49 -0.51 0.0129 1,927,322 44.330 0.50 710.87 20.81°0.93 0.36 81.11°1.489 0.23 1.47
315°0.699 0.49 -0.49 0.0128 1,913,324 44.481 0.50 711.36 21.30°0.93 0.36 81.37°1.490 0.22 1.47
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°0.696 0.50 -0.48 0.0127 1,899,725 44.629 0.49 711.86 21.79°0.93 0.37 81.63°1.490 0.22 1.47
317°0.692 0.51 -0.47 0.0126 1,886,519 44.774 0.49 712.34 22.27°0.93 0.38 81.88°1.491 0.21 1.48
318°0.689 0.51 -0.46 0.0125 1,873,699 44.916 0.48 712.83 22.74°0.92 0.39 82.14°1.491 0.20 1.48
319°0.685 0.52 -0.45 0.0124 1,861,260 45.055 0.48 713.31 23.21°0.92 0.39 82.39°1.492 0.20 1.48
320°0.682 0.52 -0.44 0.0124 1,849,194 45.191 0.47 713.78 23.68°0.92 0.40 82.63°1.493 0.19 1.48
321°0.679 0.53 -0.43 0.0123 1,837,497 45.323 0.47 714.25 24.14°0.91 0.41 82.88°1.493 0.19 1.48
322°0.676 0.53 -0.42 0.0122 1,826,161 45.452 0.47 714.71 24.60°0.91 0.42 83.12°1.494 0.18 1.48
323°0.673 0.54 -0.41 0.0121 1,815,182 45.578 0.46 715.17 25.05°0.91 0.42 83.37°1.494 0.17 1.48
324°0.670 0.54 -0.39 0.0121 1,804,555 45.701 0.46 715.63 25.51°0.90 0.43 83.61°1.495 0.17 1.49
325°0.667 0.55 -0.38 0.0120 1,794,273 45.820 0.45 716.08 25.95°0.90 0.44 83.84°1.495 0.16 1.49
326°0.665 0.55 -0.37 0.0119 1,784,332 45.937 0.45 716.53 26.40°0.90 0.44 84.08°1.496 0.15 1.49
327°0.662 0.56 -0.36 0.0119 1,774,728 46.050 0.45 716.98 26.83°0.89 0.45 84.31°1.497 0.15 1.49
328°0.660 0.56 -0.35 0.0118 1,765,454 46.159 0.44 717.42 27.27°0.89 0.46 84.54°1.497 0.14 1.49
329°0.657 0.56 -0.34 0.0117 1,756,507 46.266 0.44 717.86 27.70°0.89 0.46 84.77°1.498 0.14 1.49
330°0.655 0.57 -0.33 0.0117 1,747,883 46.369 0.44 718.30 28.13°0.88 0.47 85.00°1.498 0.13 1.49
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°0.653 0.57 -0.32 0.0116 1,739,577 46.469 0.43 718.73 28.56°0.88 0.48 85.23°1.499 0.12 1.49
332°0.651 0.57 -0.31 0.0116 1,731,585 46.566 0.43 719.16 28.99°0.87 0.48 85.46°1.499 0.12 1.49
333°0.649 0.58 -0.29 0.0115 1,723,903 46.659 0.43 719.59 29.41°0.87 0.49 85.68°1.500 0.11 1.50
334°0.647 0.58 -0.28 0.0115 1,716,527 46.749 0.42 720.02 29.83°0.87 0.50 85.90°1.500 0.11 1.50
335°0.645 0.58 -0.27 0.0114 1,709,455 46.836 0.42 720.44 30.24°0.86 0.50 86.12°1.501 0.10 1.50
336°0.643 0.59 -0.26 0.0114 1,702,681 46.919 0.42 720.86 30.66°0.86 0.51 86.34°1.501 0.10 1.50
337°0.641 0.59 -0.25 0.0113 1,696,204 46.999 0.42 721.28 31.07°0.86 0.52 86.56°1.502 0.09 1.50
338°0.639 0.59 -0.24 0.0113 1,690,020 47.076 0.42 721.69 31.48°0.85 0.52 86.78°1.503 0.08 1.50
339°0.638 0.60 -0.23 0.0113 1,684,126 47.149 0.41 722.10 31.88°0.85 0.53 87.00°1.503 0.08 1.50
340°0.636 0.60 -0.22 0.0112 1,678,518 47.219 0.41 722.52 32.29°0.85 0.53 87.21°1.504 0.07 1.50
341°0.635 0.60 -0.21 0.0112 1,673,195 47.285 0.41 722.93 32.69°0.84 0.54 87.43°1.504 0.07 1.50
342°0.633 0.60 -0.20 0.0112 1,668,154 47.348 0.41 723.33 33.10°0.84 0.55 87.64°1.505 0.06 1.50
343°0.632 0.60 -0.18 0.0111 1,663,393 47.408 0.41 723.74 33.50°0.83 0.55 87.85°1.505 0.06 1.50
344°0.631 0.61 -0.17 0.0111 1,658,908 47.465 0.40 724.14 33.90°0.83 0.56 88.07°1.506 0.05 1.50
345°0.630 0.61 -0.16 0.0111 1,654,698 47.518 0.40 724.55 34.29°0.83 0.56 88.28°1.506 0.05 1.51
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°0.629 0.61 -0.15 0.0110 1,650,761 47.567 0.40 724.95 34.69°0.82 0.57 88.49°1.507 0.04 1.51
347°0.628 0.61 -0.14 0.0110 1,647,095 47.613 0.40 725.35 35.08°0.82 0.57 88.70°1.507 0.03 1.51
348°0.627 0.61 -0.13 0.0110 1,643,698 47.656 0.40 725.75 35.48°0.81 0.58 88.91°1.508 0.03 1.51
349°0.626 0.61 -0.12 0.0110 1,640,569 47.696 0.40 726.15 35.87°0.81 0.59 89.11°1.508 0.02 1.51
350°0.625 0.62 -0.11 0.0109 1,637,706 47.732 0.40 726.54 36.26°0.81 0.59 89.32°1.509 0.02 1.51
351°0.625 0.62 -0.10 0.0109 1,635,107 47.764 0.40 726.94 36.65°0.80 0.60 89.53°1.509 0.01 1.51
352°0.624 0.62 -0.09 0.0109 1,632,772 47.793 0.40 727.33 37.04°0.80 0.60 89.74°1.510 0.01 1.51
353°0.624 0.62 -0.08 0.0109 1,630,699 47.819 0.39 727.73 37.43°0.79 0.61 89.94°1.510 0.00 1.51
354°0.623 0.62 -0.07 0.0109 1,628,887 47.841 0.39 728.12 37.82°0.79 0.61 90.15°1.511 0.00 1.51
355°0.623 0.62 -0.05 0.0109 1,627,336 47.860 0.39 728.52 38.21°0.79 0.62 90.36°1.511 -0.01 1.51
356°0.622 0.62 -0.04 0.0109 1,626,044 47.876 0.39 728.91 38.59°0.78 0.62 90.56°1.512 -0.01 1.51
357°0.622 0.62 -0.03 0.0109 1,625,012 47.888 0.39 729.30 38.98°0.78 0.63 90.77°1.512 -0.02 1.51
358°0.622 0.62 -0.02 0.0109 1,624,238 47.896 0.39 729.70 39.37°0.77 0.63 90.97°1.513 -0.03 1.51
359°0.622 0.62 -0.01 0.0109 1,623,722 47.901 0.39 730.09 39.75°0.77 0.64 91.18°1.513 -0.03 1.51
360°0.622 0.62 0.00 0.0109 1,623,464 47.903 0.39 730.48 40.14°0.76 0.64 91.39°1.514 -0.04 1.51
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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