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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.

Contents

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 0.122173047647 °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 0.05916666164263.39 °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
1495978864561 AU149,597,886.456 km
92,955,817.063 mi
1495978700001 AU 8.72664625997E-75.0e-5 °8.726646e-7 rad
5.555556e-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 0.03228859116191.85 °0.0323 rad
2.056 grad
686.981.881 a686.98 da
Ceres 3809820115292.547 AU380,982,011.529 km
236,731,246.725 mi
4468273011322.987 AU446,827,301.132 km
277,645,612.829 mi
4139046565552.767 AU413,904,656.555 km
257,188,429.916 mi
4188740360002.8 AU 0.18476760574610.586 °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 0.02277654673851.305 °0.0228 rad
1.45 grad
4330.58662511.857 a4,330.587 da
Saturn 1.35255E+129.041 AU1,352,550,000 km
840,435,606.061 mi
1.5145E+1210.124 AU1,514,500,000 km
941,066,670.643 mi
1.43353E+129.583 AU1,433,530,000 km
890,754,245.208 mi
1.4959787E+1210 AU 0.04337143191212.485 °0.0434 rad
2.761 grad
10759.2229.457 a10,759.22 da
Uranus 2.7413E+1218.324 AU2,741,300,000 km
1,703,364,849.28 mi
3.00362E+1220.078 AU3,003,620,000 km
1,866,362,940.428 mi
2.87246E+1219.201 AU2,872,460,000 km
1,784,863,894.854 mi
2.932118252E+1219.6 AU 0.01298524963480.744 °0.013 rad
0.827 grad
30681.615300284.002 a30,681.615 da
Neptune 4.44445E+1229.709 AU4,444,450,000 km
2,761,653,195.339 mi
4.54567E+1230.386 AU4,545,670,000 km
2,824,548,387.417 mi
4.49506E+1230.048 AU4,495,060,000 km
2,793,100,791.378 mi
5.804397356E+1238.8 AU 0.03087487446781.769 °0.0309 rad
1.966 grad
60189.5475164.79 a60,189.548 da
Pluto 4.436824613E+1229.658 AU4,436,824,613 km
2,756,914,999.528 mi
7.375927931E+1249.305 AU7,375,927,931 km
4,583,189,132.342 mi
5.906376272E+1239.482 AU5,906,376,272 km
3,670,052,065.935 mi
1.1548955564E+1377.2 AU 0.29917997705417.142 °0.299 rad
19.046 grad
90614.8725248.09 a90,614.873 da
Eris 5.6742472091E+1237.93 AU5,674,247,209.1 km
3,525,813,753.368 mi
1.45902802611E+1397.53 AU14,590,280,261.1 km
9,065,979,840.917 mi
1.01325629308E+1367.732 AU10,132,562,930.8 km
6,296,082,708.731 mi
2.303807198E+13154 AU 0.77072867103444.159 °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.

Reference

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