With the recent naming of 136199 Eris and its moon Dysnomia, I saw a question on a discussion list about astrologically separating their interpretations. This prompted me to dig out a few numbers to see how practical such an effort might be, not just for Eris and Dysnomia, but for any planets and moons in our solar system.
I suggest not making such an attempt because planets and their moons are always conjunct. Most are so closely conjunct that separate interpretations would be very difficult. Among the larger moons, the greatest possible separation is about 11 minutes of arc for Jupiter’s Callisto—the rest of the large moons are visually closer to their planets than that. The largest possible visual separation of any moon from its planet is about 3 degrees for Jupiter’s farthest-flung moons—most planet-moon separations are much smaller.
The main astrological technique that comes to mind immediately to allow separate interpretations would require a program that includes planets’ moons as separate points in lists of timed hits (progressions or transits). Then you would need a lot of well-timed events to check against the differing moments of planet and moon aspects. High-order harmonics are another possible technique.
I don’t know if any astrological software even offers positions of planetary moons, though it could exist (I don’t try to keep track of everything that is available). Accurate positions would certainly be a lot of work since orbital information for moons is in a variety of different forms.
You can easily make an estimate of how far apart a planet and moon could appear from Earth. (You can find most of the number you need in Wikipedia more conveniently than by hunting through reference books.) If your data sources give a mix of astronomical units and kilometers, convert all data to AU first. (1 AU = 149,597,870.7 km.)
Assume the moon’s orbit is angled so that its maximum planetocentric distance is perpendicular to the line of sight from Earth. (In most cases, the actual angle will reduce the maximum separation from the viewpoint of Earth, so this gives you an upper limit.)
Calculate the moon’s maximum planetocentric distance as moon’s semi-major axis times (1 + eccentricity).
Calculate the planet’s perihelion distance as planet’s semi-major axis times (1 - eccentricity).
Subtract the Earth’s aphelion distance from the planet’s perihelion distance to get the closest possible approach of the two planets. (This is another approximation of a limiting value. The two planets could only get this close if the Earth’s aphelion and the planets perihelion were aligned in space, which will rarely be the case.)
Calculate the circumference of a circle at the two-planet closest approach distance as distance * 2 * Pi.
Divide the moon’s maximum planetocentric distance by the two-planet closest approach circumference. (We are ignoring straight line vs. circle issues here as negligible in light of all the other simplifying assumptions.) This gives you the maximum angle an observer on Earth could see between the planet and the moon. Convert to degrees, minutes or seconds. Remember that this is an estimated maximum and that actual separations (which would require a LOT more calculations) will usually be less. Also remember that for some moons this separation will NOT be along the ecliptic, so the maximum separation in zodiacal longitude will be a smaller value.
Visibile separation of planets and their moons |
1 AU = 149,597,870.66 km |
|||||
Planet: |
Axis AU |
Eccentricity |
Perihelion |
Aphelion |
EarthMin AU |
Circumf AU |
Mercury |
0.3870989 |
0.2056307 |
0.3074995 |
0.4666984 |
0.5165915 |
3.2458404 |
Venus |
0.7233320 |
0.0067732 |
0.7184327 |
0.7282313 |
0.2550586 |
1.6025805 |
Earth |
1.0000001 |
0.0167102 |
0.9832899 |
1.0167103 |
n/a |
n/a |
Mars |
1.5236623 |
0.0934123 |
1.3813335 |
1.6659912 |
0.3646231 |
2.2909947 |
Jupiter |
5.2033630 |
0.0483927 |
4.9515584 |
5.4551676 |
3.9682685 |
24.9333666 |
Saturn |
9.5370703 |
0.0541506 |
9.0206322 |
10.0535084 |
8.0039219 |
50.2901245 |
Uranus |
19.1912639 |
0.0471677 |
18.2860560 |
20.0964719 |
17.2693456 |
108.5064987 |
Neptune |
30.0689635 |
0.0085859 |
29.8107953 |
30.3271317 |
28.7940849 |
180.9185714 |
Pluto |
39.4816868 |
0.2488077 |
29.6583407 |
49.3050329 |
28.6416303 |
179.9606709 |
136199 Eris |
67.6681000 |
0.4417700 |
37.7743635 |
97.5618365 |
36.7576531 |
230.9551461 |
Moon: |
Axis in km |
Axis in AU |
Eccentricity |
Peri |
Ap |
Fract. Of Circ |
AsDegrees |
AsMinutes |
AsSeconds |
1 AU Elong |
ElongSecs |
Moons of Mars |
|||||||||||
I Phobos |
9,377 |
0.0000627 |
0.0150 |
0.0000617 |
0.0000636 |
0.0000278 |
0.0100 |
0.60 |
36.0 |
||
II Deimos |
23,460 |
0.0001568 |
0.0004 |
0.0001568 |
0.0001569 |
0.0000685 |
0.0247 |
1.48 |
88.7 |
||
Moons of Jupiter |
|||||||||||
XVI Metis |
127,690 |
0.0008536 |
0.0012 |
0.0008525 |
0.0008546 |
0.0000343 |
0.0123 |
0.74 |
44.4 |
||
XV Adrastea |
128,690 |
0.0008602 |
0.0018 |
0.0008587 |
0.0008618 |
0.0000346 |
0.0124 |
0.75 |
44.8 |
||
V Amalthea |
181,170 |
0.0012110 |
0.0031 |
0.0012073 |
0.0012148 |
0.0000487 |
0.0175 |
1.05 |
63.1 |
249.55 |
62.9 |
XIV Thebe |
221,700 |
0.0014820 |
0.0177 |
0.0014557 |
0.0015082 |
0.0000605 |
0.0218 |
1.31 |
78.4 |
305.95 |
77.1 |
I Io |
421,700 |
0.0028189 |
0.0041 |
0.0028073 |
0.0028304 |
0.0001135 |
0.0409 |
2.45 |
147.1 |
||
II Europa |
671,034 |
0.0044856 |
0.0094 |
0.0044434 |
0.0045277 |
0.0001816 |
0.0654 |
3.92 |
235.3 |
||
III Ganymede |
1,070,412 |
0.0071553 |
0.0011 |
0.0071474 |
0.0071631 |
0.0002873 |
0.1034 |
6.21 |
372.3 |
||
IV Callisto |
1,882,709 |
0.0125851 |
0.0074 |
0.0124920 |
0.0126783 |
0.0005085 |
0.1831 |
10.98 |
659.0 |
||
Themisto |
7,393,200 |
0.0494205 |
0.2116 |
0.0389631 |
0.0598779 |
0.0024015 |
0.8645 |
51.87 |
3112.4 |
||
Leda |
11,097,245 |
0.0741805 |
0.1854 |
0.0604274 |
0.0879336 |
0.0035267 |
1.2696 |
76.18 |
4570.7 |
||
Himalia |
11,432,435 |
0.0764211 |
0.1443 |
0.0653935 |
0.0874487 |
0.0035073 |
1.2626 |
75.76 |
4545.5 |
||
Lysithia |
11,653,225 |
0.0778970 |
0.1132 |
0.0690791 |
0.0867149 |
0.0034779 |
1.2520 |
75.12 |
4507.3 |
||
Elara |
11,683,115 |
0.0780968 |
0.1723 |
0.0646407 |
0.0915529 |
0.0036719 |
1.3219 |
79.31 |
4758.8 |
||
Carpo |
17,144,875 |
0.1146064 |
0.2736 |
0.0832501 |
0.1459627 |
0.0058541 |
2.1075 |
126.45 |
7586.9 |
||
Euporie |
19,088,435 |
0.1275983 |
0.0960 |
0.1153489 |
0.1398477 |
0.0056089 |
2.0192 |
121.15 |
7269.1 |
||
Thelxinoe |
20,453,755 |
0.1367249 |
0.2685 |
0.1000143 |
0.1734355 |
0.0069560 |
2.5041 |
150.25 |
9014.9 |
||
Euanthe |
20,464,855 |
0.1367991 |
0.2000 |
0.1094393 |
0.1641589 |
0.0065839 |
2.3702 |
142.21 |
8532.7 |
||
Helike |
20,540,265 |
0.1373032 |
0.1375 |
0.1184240 |
0.1561824 |
0.0062640 |
2.2550 |
135.30 |
8118.1 |
||
Orthosie |
20,567,970 |
0.1374884 |
0.2433 |
0.1040375 |
0.1709393 |
0.0068558 |
2.4681 |
148.09 |
8885.2 |
||
Iocaste |
20,722,565 |
0.1385218 |
0.2874 |
0.0987106 |
0.1783330 |
0.0071524 |
2.5749 |
154.49 |
9269.5 |
||
Ananke |
20,815,225 |
0.1391412 |
0.3963 |
0.0839995 |
0.1942828 |
0.0077921 |
2.8051 |
168.31 |
10098.5 |
||
Praxidike |
20,823,950 |
0.1391995 |
0.1840 |
0.1135868 |
0.1648122 |
0.0066101 |
2.3796 |
142.78 |
8566.7 |
||
Harpalyke |
21,063,815 |
0.1408029 |
0.2441 |
0.1064329 |
0.1751729 |
0.0070256 |
2.5292 |
151.75 |
9105.2 |
||
Hermippe |
21,182,085 |
0.1415935 |
0.2290 |
0.1091686 |
0.1740184 |
0.0069793 |
2.5126 |
150.75 |
9045.2 |
||
Thyone |
21,405,570 |
0.1430874 |
0.2526 |
0.1069435 |
0.1792313 |
0.0071884 |
2.5878 |
155.27 |
9316.2 |
||
Mneme |
21,427,110 |
0.1432314 |
0.2214 |
0.1115200 |
0.1749428 |
0.0070164 |
2.5259 |
151.55 |
9093.3 |
||
Aitne |
22,285,160 |
0.1489671 |
0.3927 |
0.0904677 |
0.2074665 |
0.0083208 |
2.9955 |
179.73 |
10783.8 |
||
Kale |
22,409,210 |
0.1497963 |
0.2011 |
0.1196723 |
0.1799204 |
0.0072160 |
2.5978 |
155.87 |
9352.0 |
||
Taygete |
22,438,650 |
0.1499931 |
0.3678 |
0.0948256 |
0.2051606 |
0.0082284 |
2.9622 |
177.73 |
10663.9 |
||
Chaldene |
22,713,445 |
0.1518300 |
0.2916 |
0.1075564 |
0.1961036 |
0.0078651 |
2.8314 |
169.89 |
10193.2 |
||
Erinome |
22,986,265 |
0.1536537 |
0.2552 |
0.1144413 |
0.1928661 |
0.0077353 |
2.7847 |
167.08 |
10024.9 |
||
Aoede |
23,044,175 |
0.1540408 |
0.6012 |
0.0614315 |
0.2466501 |
0.0098924 |
3.5613 |
213.68 |
12820.5 |
||
Kallichore |
23,111,825 |
0.1544930 |
0.2042 |
0.1229455 |
0.1860405 |
0.0074615 |
2.6861 |
161.17 |
9670.1 |
||
Kalyke |
23,180,775 |
0.1549539 |
0.2140 |
0.1217938 |
0.1881140 |
0.0075447 |
2.7161 |
162.96 |
9777.9 |
||
Eurydome |
23,230,860 |
0.1552887 |
0.3770 |
0.0967449 |
0.2138326 |
0.0085762 |
3.0874 |
185.25 |
11114.7 |
||
Pasithee |
23,307,320 |
0.1557998 |
0.3289 |
0.1045573 |
0.2070424 |
0.0083038 |
2.9894 |
179.36 |
10761.8 |
||
Cyllene |
23,396,270 |
0.1563944 |
0.4116 |
0.0920225 |
0.2207663 |
0.0088543 |
3.1875 |
191.25 |
11475.1 |
||
Eukelade |
23,483,695 |
0.1569788 |
0.2829 |
0.1125695 |
0.2013881 |
0.0080771 |
2.9077 |
174.46 |
10467.9 |
||
Hegemone |
23,702,510 |
0.1584415 |
0.4077 |
0.0938449 |
0.2230381 |
0.0089454 |
3.2203 |
193.22 |
11593.2 |
||
Arche |
23,717,050 |
0.1585387 |
0.1492 |
0.1348847 |
0.1821927 |
0.0073072 |
2.6306 |
157.84 |
9470.1 |
||
Carme |
23,734,465 |
0.1586551 |
0.3122 |
0.1091230 |
0.2081872 |
0.0083497 |
3.0059 |
180.35 |
10821.3 |
||
Isonoe |
23,832,630 |
0.1593113 |
0.1665 |
0.1327860 |
0.1858366 |
0.0074533 |
2.6832 |
160.99 |
9659.5 |
||
Pasiphaë |
24,094,770 |
0.1610636 |
0.2953 |
0.1135015 |
0.2086257 |
0.0083673 |
3.0122 |
180.73 |
10844.1 |
||
Sinope |
24,214,390 |
0.1618632 |
0.2468 |
0.1219154 |
0.2018110 |
0.0080940 |
2.9138 |
174.83 |
10489.8 |
||
Sponde |
24,252,625 |
0.1621188 |
0.4432 |
0.0902677 |
0.2339698 |
0.0093838 |
3.3782 |
202.69 |
12161.4 |
||
Autonoe |
24,264,445 |
0.1621978 |
0.3690 |
0.1023468 |
0.2220488 |
0.0089057 |
3.2060 |
192.36 |
11541.8 |
||
Callirrhoe |
24,356,030 |
0.1628100 |
0.2644 |
0.1197630 |
0.2058570 |
0.0082563 |
2.9723 |
178.34 |
10700.1 |
||
Megaclite |
24,687,240 |
0.1650240 |
0.3078 |
0.1142296 |
0.2158184 |
0.0086558 |
3.1161 |
186.97 |
11217.9 |
||
Skipped several unnamed moons. |
|||||||||||
S/2003 J 2 |
30,290,845 |
0.2024818 |
0.1882 |
0.1643747 |
0.2405889 |
0.0096493 |
3.4737 |
208.42 |
12505.5 |
||
Moons of Saturn |
|||||||||||
XVIII Pan |
133,584 |
0.0008930 |
0.0000 |
0.0008929 |
0.0008930 |
0.0000178 |
0.0064 |
0.38 |
23.0 |
||
XXXV Daphnis |
136,505 |
0.0009125 |
0.0000 |
0.0009125 |
0.0009125 |
0.0000181 |
0.0065 |
0.39 |
23.5 |
||
XV Atlas |
137,670 |
0.0009203 |
0.0012 |
0.0009192 |
0.0009214 |
0.0000183 |
0.0066 |
0.40 |
23.7 |
||
XVII Prometheus |
139,380 |
0.0009317 |
0.0022 |
0.0009296 |
0.0009337 |
0.0000186 |
0.0067 |
0.40 |
24.1 |
||
XVII Pandora |
141,720 |
0.0009473 |
0.0042 |
0.0009434 |
0.0009513 |
0.0000189 |
0.0068 |
0.41 |
24.5 |
||
XI Epimetheus |
151,422 |
0.0010122 |
0.0098 |
0.0010023 |
0.0010221 |
0.0000203 |
0.0073 |
0.44 |
26.3 |
||
X Janus |
151,472 |
0.0010125 |
0.0068 |
0.0010056 |
0.0010194 |
0.0000203 |
0.0073 |
0.44 |
26.3 |
||
I Mimas |
185,404 |
0.0012393 |
0.0202 |
0.0012143 |
0.0012644 |
0.0000251 |
0.0091 |
0.54 |
32.6 |
||
XXXII Methone |
194,440 |
0.0012998 |
0.0001 |
0.0012996 |
0.0012999 |
0.0000258 |
0.0093 |
0.56 |
33.5 |
||
XXXIII Pallene |
212,280 |
0.0014190 |
0.0040 |
0.0014133 |
0.0014247 |
0.0000283 |
0.0102 |
0.61 |
36.7 |
||
II Enceladus |
237,950 |
0.0015906 |
0.0047 |
0.0015831 |
0.0015981 |
0.0000318 |
0.0114 |
0.69 |
41.2 |
||
III Tethys |
294,619 |
0.0019694 |
0.0000 |
0.0019694 |
0.0019694 |
0.0000392 |
0.0141 |
0.85 |
50.8 |
||
XIII Telesto |
294,619 |
0.0019694 |
0.0000 |
0.0019694 |
0.0019694 |
0.0000392 |
0.0141 |
0.85 |
50.8 |
||
XIV Calypso |
294,619 |
0.0019694 |
0.0000 |
0.0019694 |
0.0019694 |
0.0000392 |
0.0141 |
0.85 |
50.8 |
||
IV Dione |
377,396 |
0.0025227 |
0.0022 |
0.0025172 |
0.0025283 |
0.0000503 |
0.0181 |
1.09 |
65.2 |
||
XII Helene |
377,396 |
0.0025227 |
0.0022 |
0.0025172 |
0.0025283 |
0.0000503 |
0.0181 |
1.09 |
65.2 |
||
XXXIV Polydeuces |
377,396 |
0.0025227 |
0.0192 |
0.0024743 |
0.0025712 |
0.0000511 |
0.0184 |
1.10 |
66.3 |
||
V Rhea |
527,108 |
0.0035235 |
0.0013 |
0.0035191 |
0.0035279 |
0.0000702 |
0.0253 |
1.52 |
90.9 |
||
VI Titan |
1,221,931 |
0.0081681 |
0.0289 |
0.0079322 |
0.0084040 |
0.0001671 |
0.0602 |
3.61 |
216.6 |
||
VII Hyperion |
1,481,010 |
0.0098999 |
0.1230 |
0.0086822 |
0.0111177 |
0.0002211 |
0.0796 |
4.78 |
286.5 |
||
VIII Iapetus |
3,560,820 |
0.0238026 |
0.0286 |
0.0231216 |
0.0244837 |
0.0004868 |
0.1753 |
10.52 |
631.0 |
||
XXIV Kiviuq |
11,333,200 |
0.0757578 |
0.1560 |
0.0639396 |
0.0875760 |
0.0017414 |
0.6269 |
37.61 |
2256.9 |
||
XXII Ijiraq |
11,372,000 |
0.0760171 |
0.3430 |
0.0499433 |
0.1020910 |
0.0020300 |
0.7308 |
43.85 |
2630.9 |
||
XI Pheobe |
12,955,759 |
0.0866039 |
0.1562 |
0.0730728 |
0.1001350 |
0.0019911 |
0.7168 |
43.01 |
2580.5 |
||
XX Paaliaq |
14,923,800 |
0.0997594 |
0.4330 |
0.0565636 |
0.1429553 |
0.0028426 |
1.0233 |
61.40 |
3684.0 |
||
XXVII Skathi |
15,576,200 |
0.1041205 |
0.2460 |
0.0785068 |
0.1297341 |
0.0025797 |
0.9287 |
55.72 |
3343.3 |
||
XXVI Albiorix |
16,401,600 |
0.1096379 |
0.5210 |
0.0525166 |
0.1667593 |
0.0033159 |
1.1937 |
71.62 |
4297.5 |
||
XXVIII Erriapo |
17,408,700 |
0.1163700 |
0.5340 |
0.0542284 |
0.1785115 |
0.0035496 |
1.2779 |
76.67 |
4600.3 |
||
XXIX Siarnaq |
17,905,700 |
0.1196922 |
0.4790 |
0.0623596 |
0.1770248 |
0.0035201 |
1.2672 |
76.03 |
4562.0 |
||
XXI Tarvos |
18,160,200 |
0.1213934 |
0.5470 |
0.0549912 |
0.1877957 |
0.0037342 |
1.3443 |
80.66 |
4839.6 |
||
XXV Mundilfari |
18,360,100 |
0.1227297 |
0.1980 |
0.0984292 |
0.1470302 |
0.0029236 |
1.0525 |
63.15 |
3789.0 |
||
XXXI Narvi |
19,370,700 |
0.1294851 |
0.3200 |
0.0880499 |
0.1709204 |
0.0033987 |
1.2235 |
73.41 |
4404.7 |
||
XXIII Suttungr |
19,666,700 |
0.1314638 |
0.1310 |
0.1142420 |
0.1486855 |
0.0029566 |
1.0644 |
63.86 |
3831.7 |
||
XXX Thrymr |
20,810,300 |
0.1391083 |
0.4530 |
0.0760922 |
0.2021243 |
0.0040192 |
1.4469 |
86.81 |
5208.8 |
||
XIX Ymir |
23,174,600 |
0.1549126 |
0.3580 |
0.0994539 |
0.2103714 |
0.0041832 |
1.5059 |
90.36 |
5421.4 |
||
Skipped several unnamed moons. |
|||||||||||
S/2004 S 8 |
23,608,900 |
0.1578157 |
0.1860 |
0.1284620 |
0.1871695 |
0.0037218 |
1.3398 |
80.39 |
4823.4 |
||
Moons of Uranus |
|||||||||||
VI Cordelia |
49,752 |
0.0003326 |
0.0005 |
0.0003324 |
0.0003327 |
0.0000031 |
0.0011 |
0.07 |
4.0 |
||
VII Ophelia |
53,764 |
0.0003594 |
0.0101 |
0.0003558 |
0.0003630 |
0.0000033 |
0.0012 |
0.07 |
4.3 |
||
VIII Bianca |
59,165 |
0.0003955 |
0.0009 |
0.0003951 |
0.0003958 |
0.0000036 |
0.0013 |
0.08 |
4.7 |
||
IX Cressida |
61,767 |
0.0004129 |
0.0002 |
0.0004128 |
0.0004130 |
0.0000038 |
0.0014 |
0.08 |
4.9 |
||
X Desdemona |
62,659 |
0.0004188 |
0.0002 |
0.0004188 |
0.0004189 |
0.0000039 |
0.0014 |
0.08 |
5.0 |
||
XI Juliet |
64,358 |
0.0004302 |
0.0006 |
0.0004300 |
0.0004305 |
0.0000040 |
0.0014 |
0.09 |
5.1 |
||
XII Portia |
66,097 |
0.0004418 |
0.0001 |
0.0004418 |
0.0004419 |
0.0000041 |
0.0015 |
0.09 |
5.3 |
||
XIII Rosalind |
69,927 |
0.0004674 |
0.0001 |
0.0004674 |
0.0004675 |
0.0000043 |
0.0016 |
0.09 |
5.6 |
||
XXVII Cupid |
74,392 |
0.0004973 |
0.0013 |
0.0004966 |
0.0004979 |
0.0000046 |
0.0017 |
0.10 |
5.9 |
||
XIV Belinda |
75,255 |
0.0005030 |
0.0001 |
0.0005030 |
0.0005031 |
0.0000046 |
0.0017 |
0.10 |
6.0 |
||
XXV Perdita |
76,416 |
0.0005108 |
0.0030 |
0.0005093 |
0.0005123 |
0.0000047 |
0.0017 |
0.10 |
6.1 |
||
XV Puck |
86,004 |
0.0005749 |
0.0001 |
0.0005749 |
0.0005749 |
0.0000053 |
0.0019 |
0.11 |
6.9 |
||
XXVI Mab |
97,736 |
0.0006533 |
0.0025 |
0.0006517 |
0.0006550 |
0.0000060 |
0.0022 |
0.13 |
7.8 |
||
V Miranda |
129,390 |
0.0008649 |
0.0013 |
0.0008638 |
0.0008660 |
0.0000080 |
0.0029 |
0.17 |
10.3 |
||
I Ariel |
191,020 |
0.0012769 |
0.0012 |
0.0012754 |
0.0012784 |
0.0000118 |
0.0042 |
0.25 |
15.3 |
||
II Umbriel |
266,000 |
0.0017781 |
0.0039 |
0.0017712 |
0.0017850 |
0.0000165 |
0.0059 |
0.36 |
21.3 |
||
III Titania |
435,910 |
0.0029139 |
0.0011 |
0.0029107 |
0.0029171 |
0.0000269 |
0.0097 |
0.58 |
34.8 |
||
IV Oberon |
583,520 |
0.0039006 |
0.0014 |
0.0038951 |
0.0039061 |
0.0000360 |
0.0130 |
0.78 |
46.7 |
||
XXII Francisco |
4,276,000 |
0.0285833 |
0.1459 |
0.0244130 |
0.0327536 |
0.0003019 |
0.1087 |
6.52 |
391.2 |
||
XVI Caliban |
7,231,000 |
0.0483362 |
0.1588 |
0.0406605 |
0.0560120 |
0.0005162 |
0.1858 |
11.15 |
669.0 |
||
XX Stephano |
8,004,000 |
0.0535034 |
0.2295 |
0.0412244 |
0.0657825 |
0.0006063 |
0.2183 |
13.10 |
785.7 |
||
XXI Trinculo |
8,578,000 |
0.0573404 |
0.2079 |
0.0454193 |
0.0692615 |
0.0006383 |
0.2298 |
13.79 |
827.3 |
||
XVII Sycorax |
12,179,000 |
0.0814116 |
0.5224 |
0.0388822 |
0.1239410 |
0.0011422 |
0.4112 |
24.67 |
1480.3 |
||
XXIII Margaret |
14,345,000 |
0.0958904 |
0.6608 |
0.0325260 |
0.1592548 |
0.0014677 |
0.5284 |
31.70 |
1902.1 |
||
XVIII Prospero |
16,243,000 |
0.1085777 |
0.4431 |
0.0604669 |
0.1566885 |
0.0014440 |
0.5199 |
31.19 |
1871.5 |
||
XIX Setebos |
17,501,000 |
0.1169870 |
0.5843 |
0.0486315 |
0.1853424 |
0.0017081 |
0.6149 |
36.90 |
2213.7 |
||
XXIV Ferdinand |
20,901,000 |
0.1397146 |
0.3682 |
0.0882717 |
0.1911575 |
0.0017617 |
0.6342 |
38.05 |
2283.2 |
||
Moons of Neptune |
|||||||||||
III Naiad |
48,227 |
0.0003224 |
0.0004 |
0.0003222 |
0.0003225 |
0.0000018 |
0.0006 |
0.04 |
2.3 |
||
IV Thalassa |
50,075 |
0.0003347 |
0.0002 |
0.0003347 |
0.0003348 |
0.0000019 |
0.0007 |
0.04 |
2.4 |
||
V Despina |
52,526 |
0.0003511 |
0.0002 |
0.0003510 |
0.0003512 |
0.0000019 |
0.0007 |
0.04 |
2.5 |
||
VI Galatea |
61,953 |
0.0004141 |
0.0000 |
0.0004141 |
0.0004141 |
0.0000023 |
0.0008 |
0.05 |
3.0 |
||
VII Larissa |
73,548 |
0.0004916 |
0.0014 |
0.0004910 |
0.0004923 |
0.0000027 |
0.0010 |
0.06 |
3.5 |
||
VIII Proteus |
117,647 |
0.0007864 |
0.0005 |
0.0007860 |
0.0007868 |
0.0000043 |
0.0016 |
0.09 |
5.6 |
||
I Triton |
354,800 |
0.0023717 |
0.0000 |
0.0023717 |
0.0023717 |
0.0000131 |
0.0047 |
0.28 |
17.0 |
488.49 |
17.0 |
II Nereid |
5,513,400 |
0.0368548 |
0.7512 |
0.0091695 |
0.0645401 |
0.0003567 |
0.1284 |
7.71 |
462.3 |
||
S/2002 N 1 |
15,728,000 |
0.1051352 |
0.5711 |
0.0450925 |
0.1651779 |
0.0009130 |
0.3287 |
19.72 |
1183.2 |
||
S/2002 N 2 |
22,422,000 |
0.1498818 |
0.2931 |
0.1059515 |
0.1938122 |
0.0010713 |
0.3857 |
23.14 |
1388.4 |
||
S/2002 N 3 |
23,571,000 |
0.1575624 |
0.4237 |
0.0908032 |
0.2243216 |
0.0012399 |
0.4464 |
26.78 |
1606.9 |
||
X Psamathe |
46,695,000 |
0.3121368 |
0.4499 |
0.1717065 |
0.4525671 |
0.0025015 |
0.9005 |
54.03 |
3241.9 |
||
S/2002 N 4 |
48,387,000 |
0.3234471 |
0.4945 |
0.1635025 |
0.4833917 |
0.0026719 |
0.9619 |
57.71 |
3462.7 |
||
Moons of Pluto |
|||||||||||
I Charon |
19,571 |
0.0001308 |
0.0000 |
0.0001308 |
0.0001308 |
0.0000007 |
0.0003 |
0.02 |
0.9 |
0 |
0.000004 |
II Nix |
48,675 |
0.0003254 |
0.0020 |
0.0003247 |
0.0003260 |
0.0000018 |
0.0007 |
0.04 |
2.3 |
||
III Hydra |
64,780 |
0.0004330 |
0.0050 |
0.0004309 |
0.0004352 |
0.0000024 |
0.0009 |
0.05 |
3.1 |
||
Moons of Eris |
|||||||||||
Dysnomia |
36,000 |
0.0002406 |
0.0000 |
0.0002406 |
0.0002406 |
0.0000010 |
0.0004 |
0.02 |
1.4 |
Most of the columns in the above table should be self-explanatory. AsDegrees, AsMinutes and AsSeconds are the answers to look at (mostly AsSeconds). “1 AU Elong” is a value I found in the Explanatory Supplement for a few moons and “ElongSecs” is that value converted to seconds of arc at the planet’s minimum distance from Earth. I included it as a cross-check of the calculations described (with all their simplifying assumptions).
For anyone who wants to plug in other values, here are two sample lines showing the calculations in the spreadsheet:
Mars 1.52366231 0.09341233 =B6*(1-C6) =B6*(1+C6) =D6-E5 =F6*2*3.14159265358979
I Phobos 9377 =B16/G1 0.015 =C16*(1-D16) =C16*(1+D16) =F16/G6 =G16*360 =H16*60 =I16*60
As you can see from the tables, the maximum possible separation between 136199 Eris and Dysnomia is only 1.4 seconds of arc. Given the angles and the current uncertainty of the Dysnomia data, the actual ecliptic separation is almost certainly less. This is EXTREMELY close for any astrological work. It is more than the mean error in tests of my Eris ephemeris against observations but less than my maximum error, so even if the orbital elements needed to calculate Dysnomia were available I would be VERY skeptical of any positions I could produce.
Pluto and Charon are a special case—really a double planet. The barycenter of the Pluto-Charon orbit is NOT below the surface of Pluto the way the Earth-Moon barycenter is below the surface of the Earth. If I read one value right in an astronomical reference book, the maximum visual separation of Pluto and Charon can’t exceed 0.000004 seconds of arc, so the point called Pluto in charts is really Pluto-Charon.
For practical purposes, if one is going to think about planetary moons at all, one should think of the astrological interpretation of the planet as actually interpreting the planet plus its moons. Thus, what astrologers really work with is:
Mars + Phobos + Deimos
Jupiter + Metis + Adrastea + Amalthea + Thebe + Io + Europa + Ganymede + Callisto + Themisto + Leda + Himalia + Lysithia + Elara + Carpo + Euporie + Thelxinoe + Euanthe + Helike + Orthosie + Iocaste + Ananke + Praxidike + Harpalyke + Hermippe + Thyone + Mneme + Aitne + Kale + Taygete + Chaldene + Erinome + Aoede + Kallichore + Kalyke + Eurydome + Pasithee + Cyllene + Eukelade + Hegemone + Arche + Carme + Isonoe + Pasiphaë + Sinope + Sponde + Autonoe + Callirrhoe + Megaclite + moons yet to be named
Saturn + Pan + Daphnis + Atlas + Prometheus + Pandora + Epimetheus + Janus + Mimas + Methone + Pallene + Enceladus + Tethys + Telesto + Calypso + Dione + Helene + Polydeuces + Rhea + Titan + Hyperion + Iapetus + Kiviuq + Ijiraq + Pheobe + Paaliaq + Skathi + Albiorix + Erriapo + Siarnaq + Tarvos + Mundilfari + Narvi + Suttungr + Thrymr + Ymir + moons yet to be named
Uranus + Cordelia + Ophelia + Bianca + Cressida + Desdemona + Juliet + Portia + Rosalind + Cupid + Belinda + Perdita + Puck + Mab + Miranda + Ariel + Umbriel + Titania + Oberon + Francisco + Caliban + Stephano + Trinculo + Sycorax + Margaret + Prospero + Setebos + Ferdinand
Neptune + Naiad + Thalassa + Despina + Galatea + Larissa + Proteus + Triton + Nereid + Psamathe + moons yet to be named
Pluto + Charon + Nix + Hydra
Eris + Dysnomia
2019 note: more moons have been discovered and/or named since I wrote this, but I won't expand the 2006 list, since the basic point won't be changed by more examples.