540:
by 4+3=7 such parts, the Earth by 4+6=10, Mars by 4+12=16. But notice that from Mars to
Jupiter there comes a deviation from this so exact progression. From Mars there follows a space of 4+24=28 such parts, but so far no planet was sighted there. But should the Lord Architect have left that space empty? Not at all. Let us therefore assume that this space without doubt belongs to the still undiscovered satellites of Mars, let us also add that perhaps Jupiter still has around itself some smaller ones which have not been sighted yet by any telescope. Next to this for us still unexplored space there rises Jupiter's sphere of influence at 4+48=52 parts; and that of Saturn at 4+96=100 parts.
1695:
1017:
1236:
1690:{\displaystyle {\begin{aligned}\ f{\bigl (}\ \theta \ {\bigr )}\;=\;0.4594\;+\;\;&0.396\ \cos \!{\bigl (}\ \theta -27.4^{\circ }\ {\bigr )}\;+\;0.168\ \cos \!{\bigl (}\ 2\ (\ \theta -60.4^{\circ })\ {\bigr )}\;+\;0.062\ \cos \!{\bigl (}\ 3\ (\ \theta -28.1^{\circ })\ {\bigr )}\;+\;\\\;+\;\;&0.053\ \cos \!{\bigl (}\ 4\ (\ \theta -77.2^{\circ })\ {\bigr )}\;+\;0.009\ \cos \!{\bigl (}\ 5\ (\ \theta -22^{\circ })\ {\bigr )}\;+\;0.012\ \cos \!{\bigl (}\ 7\ (\ \theta -40.4^{\circ })\ {\bigr )}~.\end{aligned}}}
475:
993:"multiplier" is high for Venus and Uranus (to explain higher-than-predicted semimajor axes) but low for Mars (to explain lower-than-predicted semimajor axis). These were the extremes among planets known in 1913, and an astronomer would not have any reason to choose a range of "multiplier" values wider than the one dictated by Venus/Uranus on one end and Mars on the other. Eris, with its even lower "multiplier" value, was unknown at the time.
486:
665:
1934:
553:
4+12=16. Now comes a gap in this so orderly progression. After Mars there follows a space of 4+24=28 parts, in which no planet has yet been seen. Can one believe that the
Founder of the universe had left this space empty? Certainly not. From here we come to the distance of Jupiter by 4+48=52 parts, and finally to that of Saturn by 4+96=100 parts.
1992: are used in subsection "Comparison of the Blagg formulation with observation" (see below) where Blagg's predictions are compared to actual values; these predictions are identical to those in Nieto's paper but it's unclear how they were obtained, as they don't match any of the formulas for the function f from Blagg's paper.
1220: was not given in Blagg's 1913 paper, with Blagg noting that the empirical figures given were only for illustration. The empirical form was provided in the form of a graph (the reason that points on the curve are such a close match for empirical data, for objects discovered prior to 1913, is that they
1720:
591:– both of whose distances fit well with the law – contributed to the law's fame. Neptune's distance was very discrepant, however, and indeed Pluto – no longer considered a planet – is at a mean distance that roughly corresponds to that the Titius–Bode law predicted for the next planet out from Uranus.
3861:
Finally, raw statistics from exoplanetary orbits strongly point to a general fulfillment of Titius-Bode-like laws (with exponential increase of semi-major axes as a function of planetary index) in all the exoplanetary systems; when making a blind histogram of orbital semi-major axes for all the known
992:
At its core, the formula uses a progression ratio of 1.7275. This does not fit the data - for example, Venus and Uranus have semimajor axes higher than predicted, and Mars has a semimajor axis lower than predicted. To correct for this, the formula assigns a different "multiplier" to each planet. This
984:
A complete or partial forgery, described as Mary Adela Blagg's 1913 paper in MNRAS, is available online. The paper contains a complex formula (which includes a 7-term function) that exactly fits the data for all then-known planets in the Solar System, from
Mercury (n=-2) to Neptune (n=6; a gap at n=2
539:
Take notice of the distances of the planets from one another, and recognize that almost all are separated from one another in a proportion which matches their bodily magnitudes. Divide the distance from the Sun to Saturn into 100 parts; then
Mercury is separated by four such parts from the Sun, Venus
3543:
Nieto, who conducted the first modern comprehensive review of the Titius–Bode Law, noted that "The psychological hold of the Law on astronomy has been such that people have always tended to regard its original form as the one on which to base theories." He was emphatic that "future theories must rid
62:
and
Richardson significantly revised the original formula, and made predictions that were subsequently validated by new discoveries and observations. It is these re-formulations that offer "the best phenomenological representations of distances with which to investigate the theoretical significance
3838:
applied a generalized Titius-Bode relation to 68 exoplanet systems that contain four or more planets. They showed that 96% of these exoplanet systems adhere to a generalized Titius-Bode relation to a similar or greater extent than the Solar System does. The locations of potentially undetected
3611:
and Graner showed that power-law distance rules can be a consequence of collapsing-cloud models of planetary systems possessing two symmetries: rotational invariance (i.e., the cloud and its contents are axially symmetric) and scale invariance (i.e., the cloud and its contents look the same on all
568:(1679–1754), and the second part of the text that Titius inserted into Bonnet's work is in a book by von Wolf (1723), suggesting that Titius learned the relation from him. Twentieth-century literature about Titius–Bode law attributes authorship to von Wolf. A prior version was written by
552:
This latter point seems in particular to follow from the astonishing relation which the known six planets observe in their distances from the Sun. Let the distance from the Sun to Saturn be taken as 100, then
Mercury is separated by 4 such parts from the Sun. Venus is 4+3=7. The Earth 4+6=10. Mars
1000:
In the paper, the exact form of the 7-term function (and its bending down toward zero in the region where Eris is located) was justified by desire to fit certain moons of
Jupiter and Saturn (J3, S8) on the graph. But these moons can be put on the function graph quite arbitrarily, depending of the
2198:
Roy found that all six fitted very closely. This might have been an exaggeration: out of these six bodies, four were sharing positions with objects that were already known in 1913; concerning the two others, there was a ~6% overestimate for Pluto; and later, a 6% underestimate for
Miranda became
996:
Yet the author of the formula clearly knew about Eris, and adjusted the range of possible "multiplier" values accordingly. The formula was created so that the lower end of the range of possible "multiplier" values was Eris, nor Mars. The 7-term function (the "multiplier" being simply this 7-term
3842:
Subsequent research detected 5 candidate planets from the 97 planets predicted for the 68 planetary systems. The study showed that the actual number of planets could be larger. The occurrence rates of Mars- and
Mercury-sized planets are currently unknown, so many planets could be
3629:) cling to a regular, but non-Titius-Bode, spacing, with the four innermost satellites locked into orbital periods that are each twice that of the next inner satellite. Similarly, the large moons of Uranus have a regular but non-Titius-Bode spacing. However, according to
2150:
came across it while researching another problem. Roy noted that Blagg herself had suggested that her formula could give approximate mean distances of other bodies still undiscovered in 1913. Since then, six bodies in three systems examined by Blagg had been discovered:
3760:
1013:, an Oxford astronomer, re-visited the law. She analyzed the orbits of the planetary system and those of the satellite systems of the outer gas giants, Jupiter, Saturn and Uranus. She examined the log of the distances, trying to find the best 'average' difference.
988:
As it turns out, this formula also gives the distances of (then-unknown) objects at n=7 and n=8 as 42.00 AU and 67.07 AU, respectively. Therefore, this supposedly 1913 paper predicts the semimajor axis of Eris with uncanny accuracy, with an error of only about 1%.
531:
added two of his own paragraphs to the statement above. The insertions were placed at the bottom of page 7 and at the top of page 8. The new paragraph is not in Bonnet's original French text, nor in translations of the work into
Italian and English.
602:– with a gap between the fourth and fifth planets. Vikarius (Johann Friedrich) Wurm (1787) proposed a modified version of the Titius–Bode Law that accounted for the then-known satellites of Jupiter and Saturn, and better predicted the distance for Mercury.
605:
The Titius–Bode law was regarded as interesting, but of no great importance until the discovery of Uranus in 1781, which happens to fit into the series nearly exactly. Based on this discovery, Bode urged his contemporaries to search for a fifth planet.
3965:
Professional problem-solvers of this era invented their own clever methods for performing calculations and would do their utmost to keep these methods secret in order to maintain a reputation as the only person capable of solving a particular problem.
580:(1747) and Tomàs Cerdà (c. 1760) years before Titius's expanded translation of Bonnet's book into German (1766). Over the next two centuries, subsequent authors continued to present their own modified versions, apparently unaware of prior work.
2207:
As mentioned above, Blagg's predictions listed here apparently come from in Nieto's paper - but it's unclear how they were obtained as they don't match any of the two formulas for the function f (7-term or simplified) given in Blagg's paper.
1703:; however the price for the simpler form is that it produces a less accurate fit to the empirical data. Blagg gave it in an un-normalized form in her paper; it is shown here in normalized form (i.e. this version of the simpler form of
3620:
Only a limited number of systems are available upon which Bode's law can presently be tested; two solar planets have enough large moons that probably formed in a process similar to that which formed the planets: The four large satellites of
1181:
3581:, any stable planetary system has a high probability of satisfying a Titius–Bode-type relationship. Since it may be a mathematical coincidence rather than a "law of nature", it is sometimes referred to as a rule instead of "law".
504:"... supposing the distance of the Earth from the Sun to be divided into ten equal Parts, of these the distance of Mercury will be about four, of Venus seven, of Mars fifteen, of Jupiter fifty two, and that of Saturn ninety five."
3454:
1929:{\displaystyle \ f{\bigl (}\ \theta \ {\bigr )}\;=\;0.249\;+\;0.860\ \left({\frac {\ \cos \ \Psi \ }{\ 3-\cos \!\left(\ 2\ \Psi \ \right)\ }}\;+\;{\frac {1}{\ 6-4\ \cos \!\left(\ 2\ \Psi -60^{\circ }\right)\ }}\right)\ ,}
636:
in 1930 confounded the issue still further: Although nowhere near its predicted position according to Bode's law, it was very nearly at the position the law had designated for Neptune. The subsequent discovery of the
997:
function plus a constant) has a range of values from 0 to 1; for Eris, it reaches the value of almost exactly zero - which shows that the author knew about Eris, and adjusted the formula based on this knowledge.
3862:
exoplanets for which this magnitude is known, and comparing it with what should be expected if planets distribute according to Titius-Bode-like laws, a significant degree of agreement (i.e., 78%) is obtained.
2211:
Bodies in parentheses were not known in 1913, when Blagg wrote her paper. Some of the calculated distances in the Saturn and Uranus systems are not very accurate. This is because the low values of constant
3843:
missed due to their small size. Other possible reasons that may account for apparent discrepancies include planets that do not transit the star or circumstances in which the predicted space is occupied by
63:
of Titius–Bode type Laws". The paper by Blagg (supposedly written in 1913) predicts the semimajor axis of Eris with an error of only about 1%, however this paper is a forgery created at a later date.
242:
1984:
3605:
that are free of long-term stable orbits. Results from simulations of planetary formation support the idea that a randomly chosen, stable planetary system will likely satisfy a Titius–Bode law.
1241:
5196:
combination history of distance measurements and development of Titius' law, notable astronomers involved, and exposition by graphs and simple ratios of modern planetary and satellite distances
3657:
361:
941:, each Titius–Bode rule distance is approximately twice the preceding value. Hence, an arbitrary planet may be found within −25% to +50% of one of the predicted positions. For small
425:
31:. The formula suggests that, extending outward, each planet should be approximately twice as far from the Sun as the one before. The hypothesis correctly anticipated the orbits of
296:
3564:
to refer theories to. But in astronomy the weight of history is heavy ... Despite the fact that the number 1.73 is much better, astronomers cling to the original number 2.
3533:
3483:
3361:
3936:
were experts in calculations of all kinds and were employed by merchants and businessmen to solve complex accounting problems. Their name derives from the Italian word
715:
150:
105:
3963:
945:, the predicted distances do not fully double, so the range of potential deviation is smaller. Note that the semi-major axis is proportional to the 2/3 power of the
3795:
3506:
3923:
Bode's footnote was initially unsourced, but in later versions credited to Titius, and in Bode’s memoir he refers to Titius, clearly recognizing Titius' priority.
3854:
named "TRAPPIST‑1i", was proposed by using the Titius–Bode law. TRAPPIST‑1i had a prediction based exclusively on the Titius–Bode law with an orbital period of
1036:
4406:
Richardson, D.E. (1945). "Distances of planets from the Sun and of satellites from their primaries in the satellite systems of Jupiter, Saturn, and Uranus".
3636:"a slight new phrasing of this law permits us to include not only planetary orbits around the Sun, but also the orbits of moons around their parent planets."
4647:
4951:
4809:. ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP Conference Proceedings. Vol. 1479. pp. 2356–2359.
5012:
4898:
4845:
4703:
4308:
3348:
magazine article, the science writer D.E. Richardson apparently independently arrived at the same conclusion as Blagg: That the progression ratio is
5189:
4358:
548:, then aged twenty-five, published an astronomical compendium, in which he included the following footnote, citing Titius (in later editions):
4718:
Dawson, Rebekah I.; Fabrycky, Daniel C. (2010). "Radial velocity planets de-aliased. A new, short period for super-Earth 55 Cnc e".
3647:
Of the recent discoveries of extrasolar planetary systems, few have enough known planets to test whether similar rules apply. An attempt with
5116:
557:
These two statements, for all their peculiar expression, and from the radii used for the orbits, seem to stem from an antique algorithm by a
244:
such that, with the exception of the first step, each value is twice the previous value. There is another representation of the formula:
3578:
5212:
4044:
434:, each planet is predicted to be roughly twice as far from the Sun as the previous object. Whereas the Titius–Bode law predicts
158:
5217:
4469:
4442:
4249:
4212:(ed.). "Verschiedene astronomische Bemerkungen und eine Abhandlung über mögliche Planeten und Kometen unsers Sonnensystems".
523:"We know seventeen planets that enter into the composition of our solar system; but we are not sure that there are no more."
4259:
3940:, meaning "thing", because they used symbols to represent an unknown quantity, similar to the way modern mathematicians use
3847:. Despite these types of allowances, the number of planets found with Titius–Bode law predictions was lower than expected.
3755:{\displaystyle ~a_{n}=0.0142\cdot \mathrm {e} ^{\left(\,0.9975\,n\,\right)}=0.0142\cdot {\bigl (}\,2.7115\,{\bigr )}^{n}~,}
1941:
535:
There are two parts to Titius's inserted text. The first part explains the succession of planetary distances from the Sun:
4424:
5049:
Ballesteros, F.J.; Fernandez-Soto, A.; Martinez, V.J. (2019). "Diving into exoplanets: Are water seas the most common?".
3612:
scales). The latter is a feature of many phenomena considered to play a role in planetary formation, such as turbulence.
4616:
3834:
Recent astronomical research suggests that planetary systems around some other stars may follow Titius-Bode-like laws.
4657:
5131:
3910:
The spacing seems to transition from the complicated Titius–series to simple equal-spacing starting at Saturn, with
5237:
3552:. It ought to be clear that the first formulation of Titius (with its asymmetric first term) should be viewed as a
621:
in a location that does not conform to the law. Simultaneously, due to the large number of asteroids discovered in
1186:
Note in particular that in Blagg's formula, the law for the Solar System was best represented by a progression in
4408:
4175:
3573:
No solid theoretical explanation underlies the Titius–Bode law – but it is possible that, given a combination of
3344:
577:
564:
Many precedents were found that predate the seventeenth century. Titius was a disciple of the German philosopher
304:
4773:
4588:; F. Graner (1994). "Titius–Bode laws in the solar system. Part II: Build your own law from disk models".
3810:
108:
72:
5227:
5153:
4781:
4157:
4021:
3876:
569:
509:
497:
379:
4558:; B. Dubrulle (1994). "Titius–Bode laws in the solar system. Part I: Scale invariance explains everything".
5007:
4695:
4139:
583:
Titius and Bode hoped that the law would lead to the discovery of new planets, and indeed the discovery of
565:
5010:(2020). "The reliability of the Titius-Bode relation and its implications for the search for exoplanets".
4353:
250:
5163:
4387:
1016:
594:
When originally published, the law was approximately satisfied by all the planets then known – i.e.,
4524:
4241:
3891:
645:, which is more massive than Pluto, yet does not fit Bode's law – further discredited the formula.
3511:
3461:
4585:
4555:
3886:
3608:
5051:
4519:
4231:
668:
Graphical plot of the eight planets, Pluto, and Ceres versus the first ten predicted distances.
626:
4459:
4235:
3991:
Nieto, Michael Martin (1970). "Conclusions about the Titius–Bode Law of Planetary Distances".
3817:
system have been greatly revised (from 2.817 days to 0.737 days and from 0.038
697:
4720:
4486:
2391:
573:
117:
77:
4601:
4571:
4004:
3943:
5183:
5060:
4970:
4917:
4864:
4810:
4739:
4597:
4567:
4511:
4367:
4354:"A review of Blagg's formula in the light of recently discovered planetary moons and rings"
4317:
4000:
3768:
3488:
2523:
2401:
2356:
2164:
2152:
813:
618:
607:
588:
528:
508:
A similar sentence, likely paraphrased from Gregory (1715), appears in a work published by
478:
48:
32:
1176:{\displaystyle \ {\mathsf {distance}}=A\cdot {\bigl }\ {\bigl (}\ 1.7275\ {\bigr )}^{n}~.}
572:(1702), in which the succession of planetary distances 4, 7, 10, 16, 52, and 100 became a
8:
2381:
642:
5064:
4974:
4921:
4868:
4814:
4743:
4515:
4371:
4321:
5094:
5021:
4988:
4960:
4907:
4854:
4755:
4729:
4674:
4537:
4501:
3881:
3844:
2180:
2156:
654:
4751:
5147:
5086:
4992:
4759:
4653:
4623:(monthly newsletter article). Gainesville, FL: Alachua Astronomy Club. Archived from
4465:
4438:
4245:
4209:
4091:
4048:
3818:
3798:
3589:
3574:
3449:{\displaystyle \ R_{n}={\bigl (}\ 1.728\ {\bigr )}^{n}\ \varrho _{n}(\theta _{n})\ ,}
2172:
950:
545:
489:
459:
451:
364:
52:
5098:
4541:
5222:
5076:
5068:
5031:
4978:
4925:
4872:
4818:
4747:
4529:
4430:
4325:
4299:
3871:
3641:
3594:
2562:
2555:
2489:
2411:
2268:
2184:
2176:
2168:
2160:
2062:
1228:
1198:
1010:
725:
595:
59:
28:
4786:(Press release). The HARPS search for southern extra-solar planets. 23 August 2010
4117:
1227:
Finding a formula that closely fit the empircal curve turned out to be difficult.
5232:
4673:
Kotliarov, Ivan (21 June 2008). "The Titius-Bode law revisited but not revived".
4263:
4256:
3626:
3200:
3193:
3039:
2875:
2868:
2833:
2783:
2670:
2654:
2580:
2455:
2433:
2192:
2114:
2088:
1206:
1202:
496:
The first mention of a series approximating Bode's law is found in a textbook by
4983:
4946:
4073:
3806:
3598:
no longer accepts papers attempting to provide improved versions of the "law".
3300:
3284:
3219:
3145:
2747:
2312:
2290:
2188:
961:) will vary in distance by (2/3) = −23.69% and +31.04% relative to one another.
946:
516:
653:
The Titius–Bode law predicts planets will be present at specific distances in
5206:
5121:
4330:
4303:
3630:
3316:
3167:
2946:
2850:
2795:
2638:
2334:
968:
622:
611:
576:
with ratio 2. This is the nearest Newtonian formula, which was also cited by
36:
4877:
4840:
4624:
4434:
5090:
4930:
4893:
4533:
3582:
3268:
3023:
2962:
2914:
2894:
2819:
2769:
2242:
2238:
2231:
2034:
964:
658:
5072:
5035:
3765:
and controversially predicts an undiscovered planet or asteroid field for
625:, Ceres was no longer a major planet. In 1898 the astronomer and logician
4894:"Testing the Titius-Bode law predictions for Kepler multi-planet systems"
4506:
2978:
638:
5081:
3601:
Orbital resonance from major orbiting bodies creates regions around the
4349:
3851:
3544:
themselves of the bias of trying to explain a progression ratio of 2":
2202:
2147:
474:
4822:
3550:
the historical bias towards a progression ratio of 2 must be abandoned
4841:"Exoplanet predictions based on the generalized Titius-Bode relation"
3814:
3648:
3615:
3585:
2930:
2622:
2216:
in the table above make them very sensitive to the exact form of the
657:, which can be compared to the observed data for the planets and two
3914:
being the first major planet that does not fit the Titius–Bode rule.
2146:
Her paper was published in 1913, and was forgotten until 1953, when
485:
27:) is a formulaic prediction of spacing between planets in any given
5026:
4965:
4696:"The exo-planetary system of 55 Cancri and the Titus–Bode law"
4426:
The Titius–Bode Law of Planetary Distances – Its History and Theory
1025: introduced in Blagg's reformulation of the Titius–Bode law.
107:
of each planet outward from the Sun in units such that the Earth's
4912:
4859:
4734:
4679:
5048:
3911:
3850:
In a 2018 paper, the idea of a hypothetical eighth planet around
3622:
1699:
After further analysis, Blagg gave the following simpler form of
1231:
of the shape resulted in the following seven term approximation:
958:
954:
901:
835:
664:
443:
44:
5134:. Plants and Planets. Archived from the original on 15 July 2014
4487:"Fitting selected random planetary systems to Titius–Bode laws"
879:
857:
599:
584:
439:
435:
431:
363:
The resulting values can be divided by 10 to convert them into
40:
5158:— mystical and speculative; ref. diagrams missing from archive
4220:. Hofbuchdrucker, Berlin: George Jacob Decker, Königl: 162–73.
923:
769:
747:
633:
447:
4045:"Where should the planets be? The law of proportionalities"
791:
4834:
4832:
4120:. Observatorio Astronomico di Palermo "Giuseppe S. Vaiana"
1216:
However, the final form of the correction function
4484:
3602:
16:
Discredited hypothesis about Solar System planets' orbits
5005:
3831:, respectively) since the publication of these studies.
237:{\displaystyle ~x=0,3,6,12,24,48,96,192,384,768\ldots ~}
4829:
1998:
Constants for Blagg's refinement of the Titius–Bode law
629:
used Bode's law as an example of fallacious reasoning.
5166:[Planetary distances and the Titius-Bode law]
458:, the actual values are closer to 10, 19, 30, 40
4774:"Section 8.2: Extrasolar Titius-Bode-like laws?"
4385:
Malcolm, Roy (1955). "Is Bode's law a coincidence?".
3946:
3771:
3660:
3535:
from an off-centered origin to points on an ellipse.
3514:
3491:
3464:
3364:
1979:{\displaystyle \ \Psi \equiv \theta -27.5^{\circ }~.}
1944:
1723:
1239:
1039:
700:
382:
307:
253:
161:
120:
80:
4584:
4554:
2203:
Comparison of the Blagg formulation with observation
617:
Bode's law was widely accepted at that point, until
4952:
Research Notes of the American Astronomical Society
4892:Huang, Chelsea X.; Bakos, Gáspár Á. (9 May 2014).
3957:
3789:
3754:
3616:Natural satellite systems and exoplanetary systems
3527:
3500:
3477:
3448:
1978:
1928:
1689:
1175:
709:
614:, was found at Bode's predicted position in 1801.
419:
355:
290:
236:
144:
99:
5013:Publications of the Astronomical Society of Japan
4899:Monthly Notices of the Royal Astronomical Society
4846:Monthly Notices of the Royal Astronomical Society
4839:Bovaird, Timothy; Lineweaver, Charles H. (2013).
4838:
4451:
4309:Monthly Notices of the Royal Astronomical Society
3835:
1873:
1812:
1707: is scaled to produce values ranging from
1625:
1559:
1493:
1415:
1349:
1298:
5204:
4224:
4144:Vernünftige Gedanken von den Wirkungen der Natur
4359:Journal of the British Astronomical Association
3548:One thing which needs to be emphasized is that
5161:
4717:
4347:
4240:. The Cambridge conferences lectures of 1898.
4096:Anleitung zur Kenntniss des gestirnten Himmels
4016:
4014:
3588:states that it is just a coincidence, and the
1988:Neither of these formulas for function
1030:Her analysis resulted in a different formula:
4807:On the structural law of exoplanetary systems
4694:Poveda, Arcadio & Lara, Patricia (2008).
4635:– via Florida Stars (floridastars.org).
4458:Carroll, Bradley W.; Ostlie, Dale A. (2007).
4457:
4068:
4066:
3735:
3722:
3400:
3383:
1748:
1732:
1672:
1628:
1606:
1562:
1540:
1496:
1462:
1418:
1396:
1352:
1330:
1301:
1268:
1252:
1156:
1139:
1129:
1082:
5188:: CS1 maint: multiple names: authors list (
5006:Lara, Patricia; Cordero-Tercero, Guadalupe;
4704:Revista Mexicana de Astronomía y Astrofísica
4485:Wayne Hayes; Scott Tremaine (October 1998).
4464:. Pearson Addison-Wesley. pp. 716–717.
4230:
4162:Astronomiae physicae et geometricae elementa
1209:, and discovered the same progression ratio
5164:Distancias planetarias y ley de Titius-Bode
4011:
3986:
3984:
3982:
3568:
356:{\displaystyle ~n=-\infty ,0,1,2,\ldots ~.}
5117:"The ghostly hand that spaced the planets"
4891:
4693:
4405:
4304:"On a suggested substitute for Bode's law"
4208:Wurm, Vikarius (Johann Friedrich) (1787).
4063:
3951:
1848:
1844:
1765:
1761:
1757:
1753:
1615:
1611:
1549:
1545:
1481:
1480:
1476:
1471:
1467:
1405:
1401:
1339:
1335:
1286:
1285:
1281:
1277:
1273:
527:In his 1766 translation of Bonnet's work,
5080:
5025:
4982:
4964:
4929:
4911:
4876:
4858:
4733:
4678:
4672:
4523:
4505:
4416:
4343:
4341:
4329:
3947:
3839:exoplanets are predicted in each system.
3731:
3727:
3703:
3699:
3695:
3337:
1021:The empirical correction function
979:
5114:
4294:
4292:
4290:
4283:. Vol. 30, no. 10. p. 70.
4279:Boss, Alan (October 2006). "Ask Astro".
4192:
4138:
4111:
4109:
3979:
1015:
663:
484:
473:
4944:
4384:
4274:
4272:
4156:
4118:"Bodes' law and the discovery of Ceres"
4020:
3625:and the biggest inner satellite (i.e.,
3485:is an oscillatory function with period
420:{\displaystyle a=0.4+0.3\times 2^{n}~.}
66:
5205:
5170:(popular astronomy essay) (in Spanish)
4645:
4461:An Introduction to Modern Astrophysics
4338:
4174:
4115:
4072:
4039:
4037:
4035:
1066:
1063:
1060:
1057:
1054:
1051:
1048:
1045:
1001:choice of A, B, α and β coefficients.
4947:"Predicting the orbit of TRAPPIST-1i"
4614:
4422:
4298:
4287:
4106:
3990:
3538:
2001:
469:
4804:
4687:
4617:"The Titius-Bode relation revisited"
4278:
4269:
4207:
4090:
974:
5162:Parés i Farràs, Ramon, Dr. (2016).
5129:
4032:
985:corresponds to the asteroid belt).
291:{\displaystyle ~a=4+3\times 2^{n}~}
13:
5132:"The law of Titius–Bode explained"
5108:
3685:
3356:. His spacing law is in the form:
1948:
1888:
1827:
1792:
1194:used by Titius, Bode, and others.
704:
430:For the far outer planets, beyond
320:
14:
5249:
5115:Matthews, Robert (9 April 1994).
4237:Reasoning and the logic of things
4102:] (in German) (2nd ed.).
4100:Manual for Knowing the Starry Sky
1190:, rather than the original value
450:at about 10, 20, 39, and 77
5213:Discoveries by Johann Elert Bode
4429:(1st ed.). Pergamon Press.
4234:; Ketner, Kenneth Laine (1992).
4116:Hoskin, Michael (26 June 1992).
949:. For example, planets in a 2:3
373:), resulting in the expression:
5042:
4999:
4938:
4885:
4798:
4766:
4711:
4666:
4639:
4608:
4578:
4548:
4478:
4412:. Vol. 53. pp. 14–26.
4399:
4378:
4201:
4186:
4168:
4150:
4132:
3836:Bovaird & Lineweaver (2013)
3813:of the innermost planet in the
641:– and in particular the object
43:, but failed as a predictor of
4423:Nieto, Michael Martin (1972).
4352:; Brown, J.C. (October 1982).
4084:
3926:
3917:
3904:
3640:The new phrasing is known as “
3437:
3424:
1664:
1642:
1598:
1576:
1532:
1510:
1454:
1432:
1388:
1366:
1004:
619:in 1846 Neptune was discovered
1:
4782:European Southern Observatory
4615:Cohen, Howard L. (May 1996).
3973:
3877:Phaeton (hypothetical planet)
3560:necessarily be viewed as the
5218:Obsolete theories in physics
4652:. Springer. pp. 27–29.
3897:
3528:{\displaystyle \varrho _{n}}
3478:{\displaystyle \varrho _{n}}
912:
890:
868:
846:
824:
802:
780:
758:
736:
693:
673:
610:, the largest object in the
47:'s orbit. It is named after
7:
4752:10.1088/0004-637X/722/1/937
3865:
1199:satellite system of Jupiter
10:
5254:
4590:Astronomy and Astrophysics
4560:Astronomy and Astrophysics
4388:Astounding Science Fiction
4078:Contemplation de la Nature
3315:
3299:
3283:
3267:
3217:
3166:
3144:
3038:
3022:
2977:
2961:
2945:
2929:
2913:
2892:
2848:
2832:
2817:
2793:
2781:
2768:
2746:
2669:
2653:
2637:
2621:
2579:
2522:
2488:
2454:
2432:
2410:
2400:
2390:
2380:
2355:
2333:
2311:
2289:
2267:
2113:
2087:
2061:
2033:
690:Deviation from prediction
5152:: CS1 maint: unfit URL (
4662:– via Google books.
4026:The Elements of Astronomy
3508:, representing distances
2809:
2800:
2760:
2751:
2375:
2372:
2366:
2360:
23:(sometimes termed simply
4984:10.3847/2515-5172/aad6e8
4242:Harvard University Press
4193:Cerdà, Tomàs (c. 1760).
3892:Mysterium Cosmographicum
3569:Theoretical explanations
710:{\displaystyle -\infty }
5238:Astronomical hypotheses
4945:Kipping, David (2018).
4805:Lara, Patricia (2012).
4646:Harwit, Martin (1998).
4602:1994A&A...282..269D
4572:1994A&A...282..262G
4435:10.1016/C2013-0-02478-4
4214:Astronomisches Jahrbuch
4005:1970A&A.....8..105N
3887:Lennard-Jones potential
3651:suggested the equation
3556:. Certainly, it should
681:T–B rule distance (AU)
648:
145:{\displaystyle ~a=4+x~}
100:{\displaystyle ~a_{n}~}
4649:Astrophysical Concepts
4534:10.1006/icar.1998.5999
4331:10.1093/mnras/73.6.414
4262:2 January 2010 at the
4180:Philosophia Britannica
4047:. Dawn. Archived from
3959:
3958:{\displaystyle \,x\;.}
3791:
3756:
3566:
3529:
3502:
3479:
3450:
3338:Richardson formulation
2050: 112.4°
2040: 0.4162
1980:
1930:
1691:
1177:
1027:
980:Indications of forgery
711:
669:
493:
482:
421:
357:
292:
238:
146:
101:
5073:10.1089/ast.2017.1720
4878:10.1093/mnras/stt1357
4721:Astrophysical Journal
4195:Tratado de Astronomía
3960:
3792:
3790:{\displaystyle ~n=5~}
3757:
3546:
3530:
3503:
3501:{\displaystyle 2\pi }
3480:
3451:
2255:Claim by Nieto (1970)
1981:
1931:
1692:
1224:the empirical data).
1178:
1019:
712:
667:
661:in the Solar System:
574:geometric progression
488:
477:
422:
358:
293:
239:
147:
102:
5228:Ceres (dwarf planet)
5178:– via wix.com.
4931:10.1093/mnras/stu906
4627:on 28 September 2007
4244:. pp. 194–196.
3944:
3769:
3658:
3512:
3489:
3462:
3362:
1942:
1721:
1237:
1037:
963:Ceres and Pluto are
698:
687:Semimajor axis (AU)
479:Johann Daniel Titius
380:
305:
251:
159:
118:
78:
71:The law relates the
67:Original formulation
49:Johann Daniel Titius
5142:– via kpn.nl.
5065:2019AsBio..19..642B
5036:10.1093/pasj/psz146
4975:2018RNAAS...2..136K
4922:2014MNRAS.442..674H
4869:2013MNRAS.435.1126B
4815:2012AIPC.1479.2356L
4744:2010ApJ...722..937D
4516:1998Icar..135..549H
4372:1982JBAA...92..260L
4322:1913MNRAS..73..414B
4140:von Wolf, C.F.
3845:circumstellar disks
3805:. Furthermore, the
3196:
2871:
2558:
2234:
2232:Sun-orbiting bodies
2035:Sun-orbiting bodies
2005:
1197:Blagg examined the
4092:Bode, Johann Elert
3955:
3882:Logarithmic spiral
3787:
3752:
3579:degrees of freedom
3539:Historical inertia
3525:
3498:
3475:
3446:
3192:
2867:
2554:
2230:
1997:
1976:
1926:
1687:
1685:
1173:
1028:
707:
670:
655:astronomical units
566:C.F. von Wolf
494:
483:
470:Origin and history
417:
365:astronomical units
353:
288:
234:
142:
97:
4823:10.1063/1.4756667
4471:978-0-8053-0402-2
4444:978-0-08-016784-8
4409:Popular Astronomy
4251:978-0-674-74966-5
3993:Astron. Astrophys
3856:27.53 ± 0.83 days
3786:
3774:
3748:
3663:
3590:planetary science
3575:orbital resonance
3442:
3413:
3396:
3390:
3367:
3345:Popular Astronomy
3335:
3334:
3331:
3330:
3188:
3187:
2863:
2862:
2563:Jupiter satellite
2550:
2549:
2142:
2141:
1972:
1947:
1922:
1913:
1911:
1887:
1881:
1869:
1857:
1842:
1840:
1832:
1826:
1820:
1802:
1797:
1791:
1782:
1771:
1745:
1739:
1726:
1679:
1669:
1647:
1641:
1635:
1621:
1603:
1581:
1575:
1569:
1555:
1537:
1515:
1509:
1503:
1489:
1459:
1437:
1431:
1425:
1411:
1393:
1371:
1365:
1359:
1345:
1327:
1308:
1294:
1265:
1259:
1246:
1169:
1152:
1146:
1136:
1126:
1115:
1089:
1042:
975:Blagg formulation
951:orbital resonance
935:
934:
632:The discovery of
490:Johann Elert Bode
413:
349:
310:
287:
256:
233:
164:
141:
123:
96:
83:
53:Johann Elert Bode
5245:
5193:
5187:
5179:
5177:
5175:
5169:
5157:
5151:
5143:
5141:
5139:
5130:Perdijk, H.J.R.
5126:
5103:
5102:
5084:
5046:
5040:
5039:
5029:
5008:Allen, Christine
5003:
4997:
4996:
4986:
4968:
4942:
4936:
4935:
4933:
4915:
4889:
4883:
4882:
4880:
4862:
4836:
4827:
4826:
4802:
4796:
4795:
4793:
4791:
4778:
4770:
4764:
4763:
4737:
4715:
4709:
4708:
4700:
4691:
4685:
4684:
4682:
4670:
4664:
4663:
4643:
4637:
4636:
4634:
4632:
4612:
4606:
4605:
4582:
4576:
4575:
4552:
4546:
4545:
4527:
4509:
4507:astro-ph/9710116
4491:
4482:
4476:
4475:
4455:
4449:
4448:
4420:
4414:
4413:
4403:
4397:
4396:
4382:
4376:
4375:
4345:
4336:
4335:
4333:
4296:
4285:
4284:
4276:
4267:
4257:HUP catalog page
4255:
4228:
4222:
4221:
4205:
4199:
4198:
4190:
4184:
4183:
4176:Martin, Benjamin
4172:
4166:
4165:
4154:
4148:
4147:
4136:
4130:
4129:
4127:
4125:
4113:
4104:
4103:
4088:
4082:
4081:
4070:
4061:
4060:
4058:
4056:
4041:
4030:
4029:
4018:
4009:
4008:
3988:
3967:
3964:
3962:
3961:
3956:
3930:
3924:
3921:
3915:
3908:
3857:
3830:
3829:
3823:
3822:
3803:
3802:
3796:
3794:
3793:
3788:
3784:
3772:
3761:
3759:
3758:
3753:
3746:
3745:
3744:
3739:
3738:
3726:
3725:
3710:
3709:
3708:
3704:
3688:
3673:
3672:
3661:
3577:and shortage of
3554:good first guess
3534:
3532:
3531:
3526:
3524:
3523:
3507:
3505:
3504:
3499:
3484:
3482:
3481:
3476:
3474:
3473:
3455:
3453:
3452:
3447:
3440:
3436:
3435:
3423:
3422:
3411:
3410:
3409:
3404:
3403:
3394:
3388:
3387:
3386:
3377:
3376:
3365:
3355:
3351:
3263:
3255:
3243:
3234:
3207:
3201:Uranus satellite
3197:
3191:
3184:
3178:
3162:
3156:
3140:
3132:
3120:
3111:
3103:
3091:
3082:
3079:
3071:
3059:
3018:
3010:
2998:
2909:
2882:
2876:Saturn satellite
2872:
2866:
2859:
2844:
2841:
2828:
2813:
2807:
2777:
2764:
2758:
2742:
2739:
2731:
2719:
2710:
2702:
2690:
2612:
2600:
2569:
2559:
2556:Moons of Jupiter
2553:
2540:
2537:
2518:
2512:
2506:
2500:
2484:
2478:
2472:
2466:
2370:
2249:
2235:
2229:
2226:
2225:
2223:
2221:
2218:function
2215:
2137:
2125:
2122:
2108:
2096:
2082:
2073:
2063:Moons of Jupiter
2056:
2046:
2029:
2024:
2019:
2014:
2006:
2000:(as modified by
1996:
1991:
1985:
1983:
1982:
1977:
1970:
1969:
1968:
1945:
1935:
1933:
1932:
1927:
1920:
1919:
1915:
1914:
1912:
1909:
1908:
1904:
1903:
1902:
1885:
1879:
1867:
1855:
1850:
1843:
1841:
1838:
1837:
1833:
1830:
1824:
1818:
1800:
1798:
1795:
1789:
1780:
1778:
1769:
1752:
1751:
1743:
1737:
1736:
1735:
1724:
1714:
1710:
1706:
1702:
1696:
1694:
1693:
1688:
1686:
1677:
1676:
1675:
1667:
1663:
1662:
1645:
1639:
1633:
1632:
1631:
1619:
1610:
1609:
1601:
1597:
1596:
1579:
1573:
1567:
1566:
1565:
1553:
1544:
1543:
1535:
1531:
1530:
1513:
1507:
1501:
1500:
1499:
1487:
1466:
1465:
1457:
1453:
1452:
1435:
1429:
1423:
1422:
1421:
1409:
1400:
1399:
1391:
1387:
1386:
1369:
1363:
1357:
1356:
1355:
1343:
1334:
1333:
1325:
1324:
1323:
1306:
1305:
1304:
1292:
1272:
1271:
1263:
1257:
1256:
1255:
1244:
1229:Fourier analysis
1219:
1212:
1193:
1189:
1182:
1180:
1179:
1174:
1167:
1166:
1165:
1160:
1159:
1150:
1144:
1143:
1142:
1134:
1133:
1132:
1124:
1123:
1119:
1113:
1087:
1086:
1085:
1070:
1069:
1040:
1024:
716:
714:
713:
708:
672:
671:
627:C.S. Peirce
464:
463:
456:
455:
426:
424:
423:
418:
411:
410:
409:
372:
371:
362:
360:
359:
354:
347:
308:
297:
295:
294:
289:
285:
284:
283:
254:
243:
241:
240:
235:
231:
162:
151:
149:
148:
143:
139:
121:
111:is equal to 10:
106:
104:
103:
98:
94:
93:
92:
81:
29:planetary system
5253:
5252:
5248:
5247:
5246:
5244:
5243:
5242:
5203:
5202:
5181:
5180:
5173:
5171:
5167:
5145:
5144:
5137:
5135:
5111:
5109:Further reading
5106:
5047:
5043:
5004:
5000:
4943:
4939:
4890:
4886:
4837:
4830:
4803:
4799:
4789:
4787:
4776:
4772:
4771:
4767:
4716:
4712:
4698:
4692:
4688:
4671:
4667:
4660:
4644:
4640:
4630:
4628:
4613:
4609:
4583:
4579:
4553:
4549:
4489:
4483:
4479:
4472:
4456:
4452:
4445:
4421:
4417:
4404:
4400:
4383:
4379:
4346:
4339:
4297:
4288:
4277:
4270:
4264:Wayback Machine
4252:
4229:
4225:
4206:
4202:
4191:
4187:
4173:
4169:
4155:
4151:
4137:
4133:
4123:
4121:
4114:
4107:
4089:
4085:
4071:
4064:
4054:
4052:
4051:on 7 March 2016
4043:
4042:
4033:
4019:
4012:
3989:
3980:
3976:
3971:
3970:
3945:
3942:
3941:
3931:
3927:
3922:
3918:
3909:
3905:
3900:
3868:
3855:
3827:
3826:
3820:
3819:
3811:semi-major axis
3800:
3799:
3770:
3767:
3766:
3740:
3734:
3733:
3732:
3721:
3720:
3694:
3690:
3689:
3684:
3683:
3668:
3664:
3659:
3656:
3655:
3618:
3571:
3541:
3519:
3515:
3513:
3510:
3509:
3490:
3487:
3486:
3469:
3465:
3463:
3460:
3459:
3431:
3427:
3418:
3414:
3405:
3399:
3398:
3397:
3382:
3381:
3372:
3368:
3363:
3360:
3359:
3353:
3349:
3340:
3261:
3257:
3253:
3245:
3241:
3232:
3205:
3194:Moons of Uranus
3182:
3176:
3160:
3154:
3138:
3134:
3130:
3122:
3118:
3109:
3105:
3101:
3093:
3089:
3080:
3077:
3073:
3069:
3061:
3057:
3016:
3012:
3008:
3000:
2996:
2907:
2880:
2869:Moons of Saturn
2857:
2842:
2839:
2826:
2811:
2805:
2775:
2762:
2756:
2740:
2737:
2733:
2729:
2721:
2717:
2708:
2704:
2700:
2692:
2688:
2614:
2610:
2602:
2598:
2567:
2538:
2535:
2516:
2510:
2504:
2498:
2482:
2476:
2470:
2464:
2368:
2262:
2247:
2219:
2217:
2213:
2205:
2161:Jupiter IX
2135:
2131: 125.7°
2128: 0.0805
2123:
2120:
2115:Moons of Uranus
2106:
2102: 118.0°
2099: 0.0071
2094:
2089:Moons of Saturn
2080:
2076: 113.0°
2071:
2067: 0.4523
2054:
2044:
2027:
2022:
2017:
2012:
1999:
1989:
1964:
1960:
1943:
1940:
1939:
1898:
1894:
1878:
1874:
1854:
1849:
1817:
1813:
1799:
1779:
1777:
1776:
1772:
1747:
1746:
1731:
1730:
1722:
1719:
1718:
1712:
1708:
1704:
1700:
1684:
1683:
1671:
1670:
1658:
1654:
1627:
1626:
1605:
1604:
1592:
1588:
1561:
1560:
1539:
1538:
1526:
1522:
1495:
1494:
1482:
1473:
1472:
1461:
1460:
1448:
1444:
1417:
1416:
1395:
1394:
1382:
1378:
1351:
1350:
1329:
1328:
1319:
1315:
1300:
1299:
1287:
1267:
1266:
1251:
1250:
1240:
1238:
1235:
1234:
1217:
1210:
1191:
1187:
1161:
1155:
1154:
1153:
1138:
1137:
1128:
1127:
1103:
1099:
1081:
1080:
1044:
1043:
1038:
1035:
1034:
1026:
1022:
1007:
982:
977:
972:
962:
699:
696:
695:
651:
578:Benjamin Martin
570:D. Gregory
472:
461:
460:
453:
452:
405:
401:
381:
378:
377:
369:
368:
306:
303:
302:
279:
275:
252:
249:
248:
160:
157:
156:
119:
116:
115:
109:semi-major axis
88:
84:
79:
76:
75:
73:semi-major axis
69:
21:Titius–Bode law
17:
12:
11:
5:
5251:
5241:
5240:
5235:
5230:
5225:
5220:
5215:
5199:
5198:
5159:
5127:
5110:
5107:
5105:
5104:
5059:(5): 642–654.
5041:
4998:
4937:
4906:(1): 674–681.
4884:
4828:
4797:
4765:
4728:(1): 937–953.
4710:
4707:(44): 243–246.
4686:
4665:
4658:
4638:
4607:
4596:(1): 269–276.
4577:
4566:(1): 262–268.
4547:
4525:10.1.1.27.8254
4477:
4470:
4450:
4443:
4415:
4398:
4377:
4366:(6): 260–263.
4348:Lobban, G.G.;
4337:
4286:
4268:
4250:
4223:
4200:
4185:
4167:
4158:Gregory, David
4149:
4131:
4105:
4083:
4062:
4031:
4010:
3977:
3975:
3972:
3969:
3968:
3954:
3950:
3925:
3916:
3902:
3901:
3899:
3896:
3895:
3894:
3889:
3884:
3879:
3874:
3867:
3864:
3825:to 0.016
3815:55 Cancri
3807:orbital period
3783:
3780:
3777:
3763:
3762:
3751:
3743:
3737:
3730:
3724:
3719:
3716:
3713:
3707:
3702:
3698:
3693:
3687:
3682:
3679:
3676:
3671:
3667:
3638:
3637:
3617:
3614:
3583:Astrophysicist
3570:
3567:
3540:
3537:
3522:
3518:
3497:
3494:
3472:
3468:
3445:
3439:
3434:
3430:
3426:
3421:
3417:
3408:
3402:
3393:
3385:
3380:
3375:
3371:
3339:
3336:
3333:
3332:
3329:
3328:
3325:
3322:
3319:
3313:
3312:
3309:
3306:
3303:
3297:
3296:
3293:
3290:
3287:
3281:
3280:
3277:
3274:
3271:
3265:
3264:
3258:
3251:
3249:
3246:
3239:
3236:
3235:
3229:
3226:
3223:
3215:
3214:
3211:
3208:
3203:
3189:
3186:
3185:
3179:
3173:
3170:
3164:
3163:
3157:
3151:
3148:
3142:
3141:
3135:
3128:
3126:
3123:
3116:
3113:
3112:
3106:
3099:
3097:
3094:
3087:
3084:
3083:
3074:
3067:
3065:
3062:
3055:
3052:
3051:
3048:
3045:
3042:
3036:
3035:
3032:
3029:
3026:
3020:
3019:
3013:
3006:
3004:
3001:
2994:
2991:
2990:
2987:
2984:
2981:
2975:
2974:
2971:
2968:
2965:
2959:
2958:
2955:
2952:
2949:
2943:
2942:
2939:
2936:
2933:
2927:
2926:
2923:
2920:
2917:
2911:
2910:
2904:
2901:
2898:
2890:
2889:
2886:
2883:
2878:
2864:
2861:
2860:
2854:
2846:
2845:
2836:
2830:
2829:
2823:
2815:
2814:
2808:
2802:
2799:
2791:
2790:
2787:
2779:
2778:
2772:
2766:
2765:
2759:
2753:
2750:
2744:
2743:
2734:
2727:
2725:
2722:
2715:
2712:
2711:
2705:
2698:
2696:
2693:
2686:
2683:
2682:
2679:
2676:
2673:
2667:
2666:
2663:
2660:
2657:
2651:
2650:
2647:
2644:
2641:
2635:
2634:
2631:
2628:
2625:
2619:
2618:
2615:
2608:
2606:
2603:
2596:
2593:
2592:
2589:
2586:
2583:
2577:
2576:
2573:
2570:
2565:
2551:
2548:
2547:
2544:
2541:
2532:
2529:
2526:
2520:
2519:
2513:
2507:
2501:
2495:
2492:
2486:
2485:
2479:
2473:
2467:
2461:
2458:
2452:
2451:
2448:
2445:
2442:
2439:
2436:
2430:
2429:
2426:
2423:
2420:
2417:
2414:
2408:
2407:
2404:
2398:
2397:
2394:
2388:
2387:
2384:
2378:
2377:
2374:
2371:
2365:
2362:
2359:
2353:
2352:
2349:
2346:
2343:
2340:
2337:
2331:
2330:
2327:
2324:
2321:
2318:
2315:
2309:
2308:
2305:
2302:
2299:
2296:
2293:
2287:
2286:
2283:
2280:
2277:
2274:
2271:
2265:
2264:
2261:Blagg, simpli-
2259:
2256:
2253:
2250:
2245:
2243:minor pl.
2204:
2201:
2144:
2143:
2140:
2139:
2132:
2129:
2126:
2117:
2111:
2110:
2103:
2100:
2097:
2093: 3.074
2091:
2085:
2084:
2077:
2074:
2070: 1.852
2068:
2065:
2059:
2058:
2057:56.6°
2051:
2048:
2041:
2038:
2031:
2030:
2025:
2020:
2015:
2010:
1975:
1967:
1963:
1959:
1956:
1953:
1950:
1925:
1918:
1907:
1901:
1897:
1893:
1890:
1884:
1877:
1872:
1866:
1863:
1860:
1853:
1847:
1836:
1829:
1823:
1816:
1811:
1808:
1805:
1794:
1788:
1785:
1775:
1768:
1764:
1760:
1756:
1750:
1742:
1734:
1729:
1715:, inclusive):
1682:
1674:
1666:
1661:
1657:
1653:
1650:
1644:
1638:
1630:
1624:
1618:
1614:
1608:
1600:
1595:
1591:
1587:
1584:
1578:
1572:
1564:
1558:
1552:
1548:
1542:
1534:
1529:
1525:
1521:
1518:
1512:
1506:
1498:
1492:
1486:
1483:
1479:
1475:
1474:
1470:
1464:
1456:
1451:
1447:
1443:
1440:
1434:
1428:
1420:
1414:
1408:
1404:
1398:
1390:
1385:
1381:
1377:
1374:
1368:
1362:
1354:
1348:
1342:
1338:
1332:
1322:
1318:
1314:
1311:
1303:
1297:
1291:
1288:
1284:
1280:
1276:
1270:
1262:
1254:
1249:
1243:
1242:
1184:
1183:
1172:
1164:
1158:
1149:
1141:
1131:
1122:
1118:
1112:
1109:
1106:
1102:
1098:
1095:
1092:
1084:
1079:
1076:
1073:
1068:
1065:
1062:
1059:
1056:
1053:
1050:
1047:
1020:
1006:
1003:
981:
978:
976:
973:
947:orbital period
936:
933:
932:
929:
926:
921:
918:
915:
911:
910:
907:
904:
899:
896:
893:
889:
888:
885:
882:
877:
874:
871:
867:
866:
863:
860:
855:
852:
849:
845:
844:
841:
838:
833:
830:
827:
823:
822:
819:
816:
811:
808:
805:
801:
800:
797:
794:
789:
786:
783:
779:
778:
775:
772:
767:
764:
761:
757:
756:
753:
750:
745:
742:
739:
735:
734:
731:
728:
723:
720:
717:
706:
703:
692:
691:
688:
685:
682:
679:
676:
650:
647:
555:
554:
542:
541:
525:
524:
506:
505:
471:
468:
428:
427:
416:
408:
404:
400:
397:
394:
391:
388:
385:
352:
346:
343:
340:
337:
334:
331:
328:
325:
322:
319:
316:
313:
299:
298:
282:
278:
274:
271:
268:
265:
262:
259:
230:
227:
224:
221:
218:
215:
212:
209:
206:
203:
200:
197:
194:
191:
188:
185:
182:
179:
176:
173:
170:
167:
153:
152:
138:
135:
132:
129:
126:
91:
87:
68:
65:
58:Later work by
15:
9:
6:
4:
3:
2:
5250:
5239:
5236:
5234:
5231:
5229:
5226:
5224:
5221:
5219:
5216:
5214:
5211:
5210:
5208:
5201:
5197:
5191:
5185:
5165:
5160:
5155:
5149:
5133:
5128:
5125:. p. 13.
5124:
5123:
5122:New Scientist
5118:
5113:
5112:
5100:
5096:
5092:
5088:
5083:
5078:
5074:
5070:
5066:
5062:
5058:
5054:
5053:
5045:
5037:
5033:
5028:
5023:
5019:
5015:
5014:
5009:
5002:
4994:
4990:
4985:
4980:
4976:
4972:
4967:
4962:
4958:
4954:
4953:
4948:
4941:
4932:
4927:
4923:
4919:
4914:
4909:
4905:
4901:
4900:
4895:
4888:
4879:
4874:
4870:
4866:
4861:
4856:
4852:
4848:
4847:
4842:
4835:
4833:
4824:
4820:
4816:
4812:
4808:
4801:
4785:
4783:
4775:
4769:
4761:
4757:
4753:
4749:
4745:
4741:
4736:
4731:
4727:
4723:
4722:
4714:
4706:
4705:
4697:
4690:
4681:
4676:
4669:
4661:
4659:9780387949437
4655:
4651:
4650:
4642:
4626:
4622:
4618:
4611:
4603:
4599:
4595:
4591:
4587:
4581:
4573:
4569:
4565:
4561:
4557:
4551:
4543:
4539:
4535:
4531:
4526:
4521:
4517:
4513:
4508:
4503:
4499:
4495:
4488:
4481:
4473:
4467:
4463:
4462:
4454:
4446:
4440:
4436:
4432:
4428:
4427:
4419:
4411:
4410:
4402:
4394:
4390:
4389:
4381:
4373:
4369:
4365:
4361:
4360:
4355:
4351:
4344:
4342:
4332:
4327:
4323:
4319:
4315:
4311:
4310:
4305:
4301:
4295:
4293:
4291:
4282:
4275:
4273:
4265:
4261:
4258:
4253:
4247:
4243:
4239:
4238:
4233:
4227:
4219:
4215:
4211:
4204:
4197:(in Spanish).
4196:
4189:
4181:
4177:
4171:
4163:
4159:
4153:
4145:
4141:
4135:
4119:
4112:
4110:
4101:
4097:
4093:
4087:
4079:
4075:
4069:
4067:
4050:
4046:
4040:
4038:
4036:
4027:
4023:
4017:
4015:
4006:
4002:
3998:
3994:
3987:
3985:
3983:
3978:
3952:
3948:
3939:
3935:
3929:
3920:
3913:
3907:
3903:
3893:
3890:
3888:
3885:
3883:
3880:
3878:
3875:
3873:
3872:Dermott's law
3870:
3869:
3863:
3859:
3853:
3848:
3846:
3840:
3837:
3832:
3824:
3816:
3812:
3808:
3804:
3781:
3778:
3775:
3749:
3741:
3728:
3717:
3714:
3711:
3705:
3700:
3696:
3691:
3680:
3677:
3674:
3669:
3665:
3654:
3653:
3652:
3650:
3645:
3643:
3642:Dermott's law
3635:
3634:
3633:
3632:
3631:Martin Harwit
3628:
3624:
3613:
3610:
3606:
3604:
3599:
3597:
3596:
3591:
3587:
3584:
3580:
3576:
3565:
3563:
3559:
3555:
3551:
3545:
3536:
3520:
3516:
3495:
3492:
3470:
3466:
3456:
3443:
3432:
3428:
3419:
3415:
3406:
3391:
3378:
3373:
3369:
3357:
3347:
3346:
3326:
3323:
3320:
3318:
3314:
3310:
3307:
3304:
3302:
3298:
3294:
3291:
3288:
3286:
3282:
3278:
3275:
3272:
3270:
3266:
3259:
3256:
3250:
3247:
3244:
3238:
3237:
3230:
3227:
3224:
3221:
3216:
3212:
3209:
3204:
3202:
3199:
3198:
3195:
3190:
3180:
3174:
3171:
3169:
3165:
3158:
3152:
3149:
3147:
3143:
3136:
3133:
3127:
3124:
3121:
3115:
3114:
3107:
3104:
3098:
3095:
3092:
3086:
3085:
3075:
3072:
3066:
3063:
3060:
3054:
3053:
3049:
3046:
3043:
3041:
3037:
3033:
3030:
3027:
3025:
3021:
3014:
3011:
3005:
3002:
2999:
2993:
2992:
2988:
2985:
2982:
2980:
2976:
2972:
2969:
2966:
2964:
2960:
2956:
2953:
2950:
2948:
2944:
2940:
2937:
2934:
2932:
2928:
2924:
2921:
2918:
2916:
2912:
2905:
2902:
2899:
2896:
2891:
2887:
2884:
2879:
2877:
2874:
2873:
2870:
2865:
2855:
2852:
2847:
2837:
2835:
2831:
2824:
2821:
2816:
2803:
2797:
2792:
2788:
2785:
2780:
2773:
2771:
2767:
2754:
2749:
2745:
2735:
2732:
2726:
2723:
2720:
2714:
2713:
2706:
2703:
2697:
2694:
2691:
2685:
2684:
2680:
2677:
2674:
2672:
2668:
2664:
2661:
2658:
2656:
2652:
2648:
2645:
2642:
2640:
2636:
2632:
2629:
2626:
2624:
2620:
2616:
2613:
2607:
2604:
2601:
2595:
2594:
2590:
2587:
2584:
2582:
2578:
2574:
2571:
2566:
2564:
2561:
2560:
2557:
2552:
2545:
2542:
2533:
2530:
2527:
2525:
2521:
2514:
2508:
2502:
2496:
2493:
2491:
2487:
2480:
2474:
2468:
2462:
2459:
2457:
2453:
2449:
2446:
2443:
2440:
2437:
2435:
2431:
2427:
2424:
2421:
2418:
2415:
2413:
2409:
2405:
2403:
2399:
2395:
2393:
2389:
2385:
2383:
2379:
2363:
2358:
2354:
2350:
2347:
2344:
2341:
2338:
2336:
2332:
2328:
2325:
2322:
2319:
2316:
2314:
2310:
2306:
2303:
2300:
2297:
2294:
2292:
2288:
2284:
2281:
2278:
2275:
2272:
2270:
2266:
2260:
2258:Blagg, 7-term
2257:
2254:
2251:
2246:
2244:
2240:
2237:
2236:
2233:
2228:
2227:
2224:
2209:
2200:
2196:
2194:
2193:Uranus V
2190:
2186:
2182:
2178:
2174:
2170:
2166:
2162:
2158:
2154:
2149:
2133:
2130:
2127:
2119: 2.98
2118:
2116:
2112:
2104:
2101:
2098:
2092:
2090:
2086:
2078:
2075:
2069:
2066:
2064:
2060:
2052:
2049:
2043: 2.025
2042:
2039:
2036:
2032:
2026:
2021:
2016:
2011:
2008:
2007:
2003:
1995:
1994:
1993:
1986:
1973:
1965:
1961:
1957:
1954:
1951:
1936:
1923:
1916:
1905:
1899:
1895:
1891:
1882:
1875:
1870:
1864:
1861:
1858:
1851:
1845:
1834:
1821:
1814:
1809:
1806:
1803:
1786:
1783:
1773:
1766:
1762:
1758:
1754:
1740:
1727:
1716:
1697:
1680:
1659:
1655:
1651:
1648:
1636:
1622:
1616:
1612:
1593:
1589:
1585:
1582:
1570:
1556:
1550:
1546:
1527:
1523:
1519:
1516:
1504:
1490:
1484:
1477:
1468:
1449:
1445:
1441:
1438:
1426:
1412:
1406:
1402:
1383:
1379:
1375:
1372:
1360:
1346:
1340:
1336:
1320:
1316:
1312:
1309:
1295:
1289:
1282:
1278:
1274:
1260:
1247:
1232:
1230:
1225:
1223:
1214:
1208:
1204:
1200:
1195:
1170:
1162:
1147:
1120:
1116:
1110:
1107:
1104:
1100:
1096:
1093:
1090:
1077:
1074:
1071:
1033:
1032:
1031:
1018:
1014:
1012:
1002:
998:
994:
990:
986:
970:
969:major planets
966:
965:dwarf planets
960:
956:
952:
948:
944:
940:
930:
927:
925:
922:
919:
916:
913:
908:
905:
903:
900:
897:
894:
891:
886:
883:
881:
878:
875:
872:
869:
864:
861:
859:
856:
853:
850:
847:
842:
839:
837:
834:
831:
828:
825:
820:
817:
815:
812:
809:
806:
803:
798:
795:
793:
790:
787:
784:
781:
776:
773:
771:
768:
765:
762:
759:
754:
751:
749:
746:
743:
740:
737:
732:
729:
727:
724:
721:
718:
701:
694:
689:
686:
683:
680:
677:
674:
666:
662:
660:
659:dwarf planets
656:
646:
644:
640:
635:
630:
628:
624:
620:
615:
613:
612:asteroid belt
609:
603:
601:
597:
592:
590:
586:
581:
579:
575:
571:
567:
562:
560:
551:
550:
549:
547:
538:
537:
536:
533:
530:
522:
521:
520:
518:
513:
511:
503:
502:
501:
499:
491:
487:
480:
476:
467:
465:
457:
449:
445:
441:
437:
433:
414:
406:
402:
398:
395:
392:
389:
386:
383:
376:
375:
374:
366:
350:
344:
341:
338:
335:
332:
329:
326:
323:
317:
314:
311:
280:
276:
272:
269:
266:
263:
260:
257:
247:
246:
245:
228:
225:
222:
219:
216:
213:
210:
207:
204:
201:
198:
195:
192:
189:
186:
183:
180:
177:
174:
171:
168:
165:
136:
133:
130:
127:
124:
114:
113:
112:
110:
89:
85:
74:
64:
61:
56:
54:
50:
46:
42:
38:
37:asteroid belt
34:
30:
26:
22:
5200:
5195:
5172:. Retrieved
5136:. Retrieved
5120:
5082:10261/213115
5056:
5052:Astrobiology
5050:
5044:
5017:
5011:
5001:
4956:
4950:
4940:
4903:
4897:
4887:
4850:
4844:
4806:
4800:
4788:. Retrieved
4780:
4768:
4725:
4719:
4713:
4702:
4689:
4668:
4648:
4641:
4629:. Retrieved
4625:the original
4620:
4610:
4593:
4589:
4580:
4563:
4559:
4550:
4497:
4493:
4480:
4460:
4453:
4425:
4418:
4407:
4401:
4392:
4386:
4380:
4363:
4357:
4313:
4307:
4280:
4236:
4232:Peirce, C.S.
4226:
4217:
4213:
4203:
4194:
4188:
4179:
4170:
4161:
4152:
4146:(in German).
4143:
4134:
4122:. Retrieved
4099:
4095:
4086:
4080:(in French).
4077:
4053:. Retrieved
4049:the original
4025:
3996:
3992:
3937:
3933:
3928:
3919:
3906:
3860:
3849:
3841:
3833:
3764:
3646:
3639:
3619:
3607:
3600:
3593:
3572:
3561:
3557:
3553:
3549:
3547:
3542:
3457:
3358:
3352:rather than
3343:
3341:
3252:
3240:
3213:Blagg pred.
3129:
3117:
3100:
3088:
3068:
3056:
3007:
2995:
2888:Blagg pred.
2728:
2716:
2699:
2687:
2609:
2597:
2575:Blagg pred.
2210:
2206:
2197:
2145:
1987:
1937:
1717:
1698:
1233:
1226:
1221:
1215:
1196:
1185:
1029:
1008:
999:
995:
991:
987:
983:
967:rather than
957:relative to
942:
938:
652:
631:
616:
604:
593:
582:
563:
558:
556:
543:
534:
526:
514:
507:
495:
481:(1729–1796)
429:
300:
154:
70:
57:
24:
20:
18:
5184:cite report
4853:(2): 1126.
4631:24 February
4586:B. Dubrulle
4300:Blagg, M.A.
4164:(in Latin).
4022:Gregory, D.
3999:: 105–111.
1213:, in each.
1005:Description
639:Kuiper belt
529:J.D. Titius
492:(1747–1826)
5207:Categories
5174:26 January
5138:26 January
5027:2003.05121
4966:1807.10835
4959:(3): 136.
4621:FirstLight
4500:(2): 549.
4316:: 414–22.
4210:Bode, J.E.
4074:Bonnet, C.
3974:References
3852:TRAPPIST-1
3797:at 2
3562:best guess
3342:In a 1945
3210:obs. dist.
2885:obs. dist.
2572:obs. dist.
2252:obs. dist.
2199:apparent.
2185:J XII
2002:Nieto 1970
1011:M.A. Blagg
937:For large
498:D. Gregory
25:Bode's law
4993:119005201
4913:1405.2259
4860:1304.3341
4790:24 August
4784:(ESO.org)
4760:118592734
4735:1005.4050
4680:0806.3532
4556:F. Graner
4520:CiteSeerX
4350:Roy, A.E.
4281:Astronomy
3898:Footnotes
3718:⋅
3681:⋅
3649:55 Cancri
3586:Alan Boss
3517:ϱ
3496:π
3467:ϱ
3429:θ
3416:ϱ
2931:Enceladus
2222: .
2177:J XI
2134:
2105:
2079:
1966:∘
1958:−
1955:θ
1952:≡
1949:Ψ
1900:∘
1892:−
1889:Ψ
1862:−
1828:Ψ
1807:−
1793:Ψ
1787:
1741:θ
1660:∘
1652:−
1649:θ
1594:∘
1586:−
1583:θ
1528:∘
1520:−
1517:θ
1450:∘
1442:−
1439:θ
1384:∘
1376:−
1373:θ
1321:∘
1313:−
1310:θ
1261:θ
1117:β
1105:α
1078:⋅
1009:In 1913,
953:(such as
705:∞
702:−
546:J.E. Bode
544:In 1772,
517:C. Bonnet
515:In 1764,
512:in 1724.
399:×
345:…
321:∞
318:−
273:×
229:…
5148:cite web
5099:73498809
5091:30789285
4542:15015134
4302:(1913).
4260:Archived
4178:(1747).
4160:(1702).
4142:(1723).
4094:(1772).
4076:(1764).
4055:16 March
4024:(1715).
3934:cossists
3866:See also
3627:Amalthea
3609:Dubrulle
3592:journal
3040:Hyperion
2834:Pasiphae
2789:(27.85)
2784:Lysithea
2671:Callisto
2655:Ganymede
2581:Amalthea
2169:J X
2165:Lysithea
2148:A.E. Roy
2053:
955:plutinos
623:the belt
598:through
510:C. Wolff
500:(1715):
35:(in the
5223:Planets
5061:Bibcode
4971:Bibcode
4918:Bibcode
4865:Bibcode
4811:Bibcode
4740:Bibcode
4598:Bibcode
4568:Bibcode
4512:Bibcode
4368:Bibcode
4318:Bibcode
4001:Bibcode
3912:Neptune
3623:Jupiter
3301:Titania
3285:Umbriel
3228:(0.678)
3220:Miranda
3146:Iapetus
2903:(0.538)
2748:Himalia
2531:(39.48)
2524:(Pluto)
2490:Neptune
2412:Jupiter
2269:Mercury
2189:Miranda
2187:), and
2047:
2037:
959:Neptune
931:+1.02%
902:Neptune
887:−1.95%
865:−4.42%
843:+0.05%
836:Jupiter
821:−1.16%
799:−4.77%
755:+3.33%
733:−3.23%
726:Mercury
684:Planet
596:Mercury
559:cossist
519:wrote:
444:Neptune
45:Neptune
5233:Uranus
5097:
5089:
4991:
4758:
4656:
4540:
4522:
4494:Icarus
4468:
4441:
4248:
4124:5 July
3785:
3773:
3747:
3729:2.7115
3715:0.0142
3697:0.9975
3678:0.0142
3662:
3595:Icarus
3458:where
3441:
3412:
3395:
3389:
3366:
3327:3.055
3317:Oberon
3311:2.286
3295:1.393
3279:1.000
3168:Phoebe
3050:5.023
3034:4.140
2989:1.786
2973:1.279
2957:1.000
2947:Tethys
2941:0.807
2925:0.629
2856:(56.2)
2851:Sinope
2825:(53.3)
2804:(49.8)
2796:Ananke
2681:4.467
2665:2.541
2649:1.592
2639:Europa
2633:1.000
2617:0.708
2591:0.429
2546:42.65
2456:Uranus
2450:9.430
2434:Saturn
2428:5.063
2406:2.769
2396:2.774
2392:Pallas
2386:2.670
2376:2.818
2351:1.530
2307:0.726
2285:0.376
2239:Planet
2181:Ananke
2157:Sinope
2138:12.5°
2109:10.0°
2083:36.0°
2028:β
2023:α
2009:System
1971:
1946:
1938:where
1921:
1910:
1886:
1880:
1868:
1856:
1839:
1831:
1825:
1819:
1801:
1796:
1790:
1781:
1770:
1744:
1738:
1725:
1678:
1668:
1646:
1640:
1634:
1620:
1602:
1580:
1574:
1568:
1554:
1536:
1514:
1508:
1502:
1488:
1458:
1436:
1430:
1424:
1410:
1392:
1370:
1364:
1358:
1344:
1326:
1307:
1293:
1279:0.4594
1264:
1258:
1245:
1211:1.7275
1207:Uranus
1205:, and
1203:Saturn
1188:1.7275
1168:
1151:
1148:1.7275
1145:
1135:
1125:
1114:
1088:
1041:
928:39.48
906:30.07
884:19.22
880:Uranus
858:Saturn
777:0.00%
600:Saturn
585:Uranus
446:, and
440:Uranus
436:Saturn
432:Saturn
412:
348:
309:
301:where
286:
255:
232:
163:
155:where
140:
122:
95:
82:
41:Uranus
39:) and
5168:(PDF)
5095:S2CID
5022:arXiv
5020:(2).
4989:S2CID
4961:arXiv
4908:arXiv
4855:arXiv
4777:(PDF)
4756:S2CID
4730:arXiv
4699:(PDF)
4675:arXiv
4538:S2CID
4502:arXiv
4490:(PDF)
4098:[
3392:1.728
3350:1.728
3324:3.058
3308:2.293
3292:1.394
3276:1.000
3269:Ariel
3181:43.85
3175:43.92
3159:12.11
3153:12.09
3047:5.034
3031:4.149
3024:Titan
2986:1.789
2970:1.281
2963:Dione
2954:1.000
2938:0.808
2922:0.630
2915:Mimas
2895:Janus
2820:Carme
2810:55.46
2774:27.85
2770:Elara
2761:27.54
2755:27.25
2678:4.467
2662:2.539
2646:1.592
2630:1.000
2588:0.429
2543:42.00
2515:28.37
2509:30.06
2503:30.13
2497:30.07
2481:19.00
2475:19.23
2469:19.23
2463:19.22
2447:9.539
2444:9.550
2441:9.583
2425:5.204
2422:5.200
2419:5.204
2402:Ceres
2373:2.707
2364:2.362
2357:Vesta
2348:1.523
2345:1.524
2342:1.524
2329:1.00
2323:1.000
2320:1.000
2313:Earth
2304:0.722
2301:0.723
2298:0.723
2291:Venus
2282:0.388
2279:0.387
2276:0.387
2263:fied
2173:Carme
2153:Pluto
1767:0.860
1759:0.249
1617:0.012
1551:0.009
1485:0.053
1407:0.062
1341:0.168
1290:0.396
924:Pluto
920:38.8
876:19.6
862:9.58
854:10.0
840:5.20
818:2.77
814:Ceres
796:1.52
774:1.00
770:Earth
752:0.72
748:Venus
730:0.39
634:Pluto
608:Ceres
589:Ceres
448:Pluto
60:Blagg
33:Ceres
5190:link
5176:2024
5154:link
5140:2024
5087:PMID
4792:2010
4654:ISBN
4633:2008
4466:ISBN
4439:ISBN
4395:(5).
4246:ISBN
4126:2007
4057:2018
3938:cosa
3932:The
3809:and
3260:0.77
3231:0.64
3137:7.00
3108:6.65
3015:2.97
2979:Rhea
2906:0.54
2838:55.7
2736:15.4
2707:9.26
2534:41.8
2382:Juno
2367:2.67
2335:Mars
2326:1.00
1962:27.5
1656:40.4
1524:77.2
1446:28.1
1380:60.4
1317:27.4
917:128
832:5.2
810:2.8
792:Mars
788:1.6
766:1.0
744:0.7
722:0.4
649:Data
643:Eris
587:and
51:and
19:The
5077:hdl
5069:doi
5032:doi
4979:doi
4926:doi
4904:442
4873:doi
4851:435
4819:doi
4748:doi
4726:722
4594:282
4564:282
4530:doi
4498:135
4431:doi
4326:doi
3644:”.
3603:Sun
3558:not
3076:6.3
2195:).
2179:),
2171:),
2163:),
1871:cos
1810:cos
1784:cos
1711:to
1623:cos
1557:cos
1491:cos
1413:cos
1347:cos
1296:cos
1222:are
873:64
851:32
829:16
396:0.3
390:0.4
226:768
220:384
214:192
5209::
5194:—
5186:}}
5182:{{
5150:}}
5146:{{
5119:.
5093:.
5085:.
5075:.
5067:.
5057:19
5055:.
5030:.
5018:72
5016:.
4987:.
4977:.
4969:.
4955:.
4949:.
4924:.
4916:.
4902:.
4896:.
4871:.
4863:.
4849:.
4843:.
4831:^
4817:.
4779:.
4754:.
4746:.
4738:.
4724:.
4701:.
4619:.
4592:.
4562:.
4536:.
4528:.
4518:.
4510:.
4496:.
4492:.
4437:.
4393:LV
4391:.
4364:92
4362:.
4356:.
4340:^
4324:.
4314:73
4312:.
4306:.
4289:^
4271:^
4218:15
4216:.
4108:^
4065:^
4034:^
4013:^
3995:.
3981:^
3858:.
3828:AU
3821:AU
3801:AU
3248:−1
3225:−2
3172:10
2935:−1
2919:−2
2900:−3
2623:Io
2605:−1
2585:−2
2295:−1
2273:−2
2241:/
2155:,
2004:)
1896:60
1590:22
1201:,
914:7
909:–
898:–
895:–
892:–
870:6
848:5
826:4
807:8
804:3
785:4
782:2
763:2
760:1
741:1
738:0
719:0
678:k
675:m
561:.
466:.
462:AU
454:AU
442:,
438:,
370:AU
208:96
202:48
196:24
190:12
55:.
5192:)
5156:)
5101:.
5079::
5071::
5063::
5038:.
5034::
5024::
4995:.
4981::
4973::
4963::
4957:2
4934:.
4928::
4920::
4910::
4881:.
4875::
4867::
4857::
4825:.
4821::
4813::
4794:.
4762:.
4750::
4742::
4732::
4683:.
4677::
4604:.
4600::
4574:.
4570::
4544:.
4532::
4514::
4504::
4474:.
4447:.
4433::
4374:.
4370::
4334:.
4328::
4320::
4266:.
4254:.
4182:.
4128:.
4059:.
4028:.
4007:.
4003::
3997:8
3953:.
3949:x
3782:5
3779:=
3776:n
3750:,
3742:n
3736:)
3723:(
3712:=
3706:)
3701:n
3692:(
3686:e
3675:=
3670:n
3666:a
3521:n
3493:2
3471:n
3444:,
3438:)
3433:n
3425:(
3420:n
3407:n
3401:)
3384:(
3379:=
3374:n
3370:R
3354:2
3321:3
3305:2
3289:1
3273:0
3262:0
3254:—
3242:—
3233:0
3222:)
3218:(
3206:n
3183:0
3177:0
3161:0
3155:0
3150:9
3139:0
3131:—
3125:8
3119:—
3110:0
3102:—
3096:7
3090:—
3081:0
3078:0
3070:—
3064:6
3058:—
3044:5
3028:4
3017:0
3009:—
3003:3
2997:—
2983:2
2967:1
2951:0
2908:0
2897:)
2893:(
2881:n
2858:0
2853:)
2849:(
2843:0
2840:0
2827:0
2822:)
2818:(
2812:0
2806:0
2801:7
2798:)
2794:(
2786:)
2782:(
2776:0
2763:0
2757:0
2752:6
2741:0
2738:0
2730:—
2724:5
2718:—
2709:0
2701:—
2695:4
2689:—
2675:3
2659:2
2643:1
2627:0
2611:—
2599:—
2568:n
2539:0
2536:0
2528:7
2517:0
2511:0
2505:0
2499:0
2494:6
2483:0
2477:0
2471:0
2465:0
2460:5
2438:4
2416:3
2369:0
2361:2
2339:1
2317:0
2248:n
2220:f
2214:B
2191:(
2183:(
2175:(
2167:(
2159:(
2136:0
2124:0
2121:0
2107:0
2095:0
2081:0
2072:0
2055:0
2045:0
2018:B
2013:A
1990:f
1974:.
1924:,
1917:)
1906:)
1883:2
1876:(
1865:4
1859:6
1852:1
1846:+
1835:)
1822:2
1815:(
1804:3
1774:(
1763:+
1755:=
1749:)
1733:(
1728:f
1713:1
1709:0
1705:f
1701:f
1681:.
1673:)
1665:)
1643:(
1637:7
1629:(
1613:+
1607:)
1599:)
1577:(
1571:5
1563:(
1547:+
1541:)
1533:)
1511:(
1505:4
1497:(
1478:+
1469:+
1463:)
1455:)
1433:(
1427:3
1419:(
1403:+
1397:)
1389:)
1367:(
1361:2
1353:(
1337:+
1331:)
1302:(
1283:+
1275:=
1269:)
1253:(
1248:f
1218:f
1192:2
1171:.
1163:n
1157:)
1140:(
1130:]
1121:)
1111:n
1108:+
1101:(
1097:f
1094:+
1091:B
1083:[
1075:A
1072:=
1067:e
1064:c
1061:n
1058:a
1055:t
1052:s
1049:i
1046:d
1023:f
971:.
943:k
939:k
415:.
407:n
403:2
393:+
387:=
384:a
367:(
351:.
342:,
339:2
336:,
333:1
330:,
327:0
324:,
315:=
312:n
281:n
277:2
270:3
267:+
264:4
261:=
258:a
223:,
217:,
211:,
205:,
199:,
193:,
187:,
184:6
181:,
178:3
175:,
172:0
169:=
166:x
137:x
134:+
131:4
128:=
125:a
90:n
86:a
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
