Titius-Bode Law

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The Titius-Bode Law states that the distances of the major satellites of the Sun follow a definite exponential pattern. It was, until the discovery of Neptune, held to be a valid predictor of the positions of the planets. Neptune is perhaps the only exception to this law among the eleven planetary and dwarf planetary bodies in the solar system, but that one exception has convinced mainstream astronomers to reject the law as invalid. But a small number of contrarian astronomers, including at least one creationist, now suggest that the law ought to stand after all.

The Formula

The classical formula for the Titius-Bode Law is:

$D = \frac{A+4}{10}$

where D is the semi-major axis measured in AU (that is, multiples of Earth's semi-major axis) and

$A = 3\cdot2^{n-1}$

where n = 1 for Venus, 2 for Earth, and so on. (In the special case of Mercury, A = 0.)

Predictive value

The actual values of peri- and aphelion, semi-major axis, and the Titius-Bode predicted semi-major axis for the eleven known planets and dwarf planets are shown below:

Name	Perihelion	Aphelion	Semi-major axis	Titius-Bode prediction	Inclination	Sidereal year
Mercury (planet)	460000000000.307 AU46,000,000 km 28,583,074.843 mi	698200000000.467 AU69,820,000 km 43,384,136.642 mi	579100000000.387 AU57,910,000 km 35,983,605.742 mi	598391480000.4 AU	0.12217304763967 °0.122 rad 7.778 grad	87.9690.241 a87.969 da
Venus	1074800000000.718 AU107,480,000 km 66,784,975.742 mi	1089400000000.728 AU108,940,000 km 67,692,177.682 mi	1082100000000.723 AU108,210,000 km 67,238,576.712 mi	1047185090000.7 AU	0.0591666616426083.39 °0.0592 rad 3.767 grad	224.7010.615 a224.701 da
Earth	1470900000000.983 AU147,090,000 km 91,397,488.666 mi	1521000000001.017 AU152,100,000 km 94,510,558.339 mi	149597886455.771 AU149,597,886.456 km 92,955,817.063 mi	1495978700001 AU	8.7266462599717E-075.0e-5 °8.72665e-7 rad 5.55556e-5 grad	365.2563661 a365.256 da
Mars	2066200000001.381 AU206,620,000 km 128,387,715.74 mi	2492300000001.666 AU249,230,000 km 154,864,342.241 mi	2279200000001.524 AU227,920,000 km 141,622,922.135 mi	2393565920001.6 AU	0.0322885911618951.85 °0.0323 rad 2.056 grad	686.981.881 a686.98 da
Ceres	380982011529.112.547 AU380,982,011.529 km 236,731,246.725 mi	446827301131.842.987 AU446,827,301.132 km 277,645,612.828 mi	413904656554.872.767 AU413,904,656.555 km 257,188,429.916 mi	4188740360002.8 AU	0.184767605746310.586 °0.185 rad 11.763 grad	1680.9731634.602 a1,680.973 da
Jupiter	7405200000004.95 AU740,520,000 km 460,137,795.276 mi	8166200000005.459 AU816,620,000 km 507,424,143.005 mi	7785700000005.204 AU778,570,000 km 483,780,969.14 mi	7779089240005.2 AU	0.0227765467385261.305 °0.0228 rad 1.45 grad	4330.58662511.857 a4,330.587 da
Saturn	13525500000009.041 AU1,352,550,000 km 840,435,606.061 mi	151450000000010.124 AU1,514,500,000 km 941,066,670.643 mi	14335300000009.583 AU1,433,530,000 km 890,754,245.208 mi	149597870000010 AU	0.0433714319120592.485 °0.0434 rad 2.761 grad	10759.2229.457 a10,759.22 da
Uranus	274130000000018.324 AU2,741,300,000 km 1,703,364,849.28 mi	300362000000020.078 AU3,003,620,000 km 1,866,362,940.428 mi	287246000000019.201 AU2,872,460,000 km 1,784,863,894.854 mi	293211825200019.6 AU	0.0129852496348380.744 °0.013 rad 0.827 grad	30681.6153001584.002 a30,681.615 da
Neptune	444445000000029.709 AU4,444,450,000 km 2,761,653,195.339 mi	454567000000030.386 AU4,545,670,000 km 2,824,548,387.417 mi	449506000000030.048 AU4,495,060,000 km 2,793,100,791.378 mi	580439735600038.8 AU	0.030874874467781.769 °0.0309 rad 1.966 grad	60189.5475164.79 a60,189.548 da
Pluto	4436824591966.429.658 AU4,436,824,591.966 km 2,756,914,986.458 mi	737592789763249.305 AU7,375,927,897.632 km 4,583,189,111.608 mi	5906376244799.239.482 AU5,906,376,244.799 km 3,670,052,049.033 mi	1154895556400077.2 AU	0.2991799770537417.142 °0.299 rad 19.046 grad	90614.8725248.09 a90,614.872 da
Eris	567424720910037.93 AU5,674,247,209.1 km 3,525,813,753.368 mi	1459028026110097.53 AU14,590,280,261.1 km 9,065,979,840.917 mi	1013256293084067.732 AU10,132,562,930.84 km 6,296,082,708.756 mi	23038071980000154 AU	0.7707286710344444.16 °0.771 rad 49.066 grad	203590.35557.4 a203,590.35 da

The semi-major axes of the first seven classical planets, and the dwarf planet Ceres, approximate the values that the Titius-Bode Law predicts very closely. Indeed the Titius-Bode Law aided directly in the discovery of Ceres. Furthermore, the discovery of Uranus was held to validate this law, because the formulation of this law, and its prediction of the semi-major axis of a planet beyond Saturn, anticipated the discovery of Uranus--the semi-major axis of which was very close to the value that the Titius-Bode Law predicted.

Beginning with Neptune, however, the semi-major axes fall well short of the Titius-Bode Law. Yet the table still shows an interesting pattern, in that the semi-major axes of Pluto and Eris are barely less than one-half the distances predicted by the Titius-Bode Law. Moreover the aphelion of Eris is almost double that for Pluto.

But a closer inspection of the distances for the last three planets reveals another interesting pattern: Pluto's orbit is very close to where Neptune's orbit ought to be--and Eris's orbit is less than 10 AU short of where Pluto's orbit ought to be.

Discussion

Technically, Neptune, Pluto, and Eris are in violation of the Titius-Bode Law. Remarkably, however, that law holds for all of the planets (plus the dwarf planet Ceres) inside of Neptune. And in the case of Pluto and Eris, those "violations," such as they are, are remarkably "regular." These are not the numbers of the random assortment of distances that one would expect from the nebula hypothesis of the formation of the sun and its satellites. Rather, these numbers suggest a catastrophic event in the distant past that altered the orbit of Neptune and either (a) also altered the orbits of Pluto and Eris, or else (b) injected those two dwarf planets into orbits that, while violative of the Titius-Bode Law, were nevertheless semi-regular. That the orbits of Pluto and Eris are the most steeply inclined of all the orbits of the satellites of the Sun (except for comets) is further suggestive evidence of catastrophe.

Conclusion

The Titius-Bode Law did not survive mainstream scrutiny, primarily because most astronomers regarded the more-inward position of Neptune as a fatal counterexample to it. But since that event, the scientific community has seen the discoveries, decades apart, of Pluto and Eris. These two dwarf world have vastly inclined and highly eccentric orbits that, nevertheless, have positions that would almost seem to conform to the Titius-Bode Law were Neptune not present. Findings like these cast doubt on the earlier decision to abandon this Law and suggest an alternative explanation: that God in fact set the planets in their orbits according to this Law, but a subsequent cataclysmic event or sequence significantly altered the elegant mathematical pattern of the outer reaches of the solar system.