The Doubling Theory Corrects the Titius-Bode Law and Defines the Fine Structure Constant in the Solar System

Sep 21, 2026

The paper applies a “doubling theory” movement, previously developed in earlier works, as a dynamical model for the solar system. It is argued that successive embedded space-time structures at different scale levels correct and justify planetary distances described by the Titius-Bode law while also addressing its failure for distant planets. The model further predicts new planets beyond the Kuiper Belt and the Oort Cloud and links the solar-system cycle (25920 years) to the fine structure constant.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages14

Reading Time35 min

AccessFree to download

1. INTRODUCTION

1.1 Empirical Titius-Bode law and its limitations

2. THE FUNDAMENTAL MOVEMENT

2.1 Particles and Horizons

The Doubling Theory Corrects the Titius-Bode Law and Defines the Fine Structure Constant in the Solar System Jean-Pierre Garnier-Malet 28, rue Lauriston 75116 Paris (France) jpgarma@free.fr Abstract. The fundamental movement of the "doubling theory", developed in our preceding papers, is applied as a model of the dynamics ofthe solar system. It is shown that this model justifies and corrects the distances ofthe planets given by the Titius-Bode law, and predicts new planets between the Kuiper Belt and the Oort Cloud. Indeed, the empirical TitiusBode law defines in an approximate way the distances of the planets to the sun, and becomes totally false for the most distant planets (Neptune and Pluto) and does not include the Oort Cloud and Kuiper Belt. The doubling theory is based on successive embedded finite structures of space-time domain at different scale levels. The cycle of the doubling movement in the solar system corresponds to 25920 years. It is shown that this cycle defines the fine structure constant. Keywords: doubling movement, spinback, horizon, particle, radial, tangential. PACS: 95.10.Ce, 95.10.Eg, 96.12.De. 1. INTRODUCTION In the 18th century, two astronomers, Johann Titius and Johann Bode, reported a numerical sequence into which the sizes ofthe planetary orbits fit. By using the radius of the Earth orbit (AU) as a standard, astronomers recalculate the other orbital sizes in proportion to it (Table 1) . TABLE 1. The empirical Titius-Bode Law, compared to the average distance to the sun (AU) [30] | Planet name | Average distance to the Sun | n | Titius-Bode distances "a" | Absolute Error | | | --- | --- | --- | --- | --- | --- | | Sun | 0 | | | | | | Mercury | 0.387 | −∞ | 0.4 = (4+2-∞×3)/10 | 0.013 | | | Venus | 0.720 | 0 | 0.7 = (4+20×3) /10 | 0.023 | | | Earth | 1 | 1 | 1.0 = (4+21×3) /10 | 0.000 | | | Mars | 1.519 | 2 | 1.6 = (4+22×3) /10 | 0.076 | | | Asteroids | 2.770 | 3 | 2.8 = (4+23×3) /10 | 0.030 | | | Jupiter | 5.188 | 4 | 5.2 = (4+24×3) /10 | 0.003 | | | Saturn | 9.530 | 5 | 10.0 = (4+25×3) /10 | 􀒙 0.461 | | | Uranus | 19.170 | 6 | 19.6 = (4+26×3) /10 | 0.420 | | | Neptune | 30.030 | 7 | 38.8 = (4+27×3) /10 | 8.740 | | | CP839, C | omputing Anticipatory Systems: C | ASYS’0 | 5—Seventh International Confer | ence, 37.800 | | | edited by D. M. Dubois
© 2006 American Institute of Physics 0-7354-0331-7/06/$23 .00 | | | | | | 236 Downloaded 06 Nov 2009 to [95.170.46.245](95.170.46.245). Redistribution subject to AIP license or copyright; see [http://proceedings.aip.org/proceedings/cpcr.jsp](http://proceedings.aip.org/proceedings/cpcr.jsp) The modern formulation of the empirical Titius-Bode law (1766-1778), is given by the following relation: 10a = 4 + 3×2n (1) with n = − ∞, 0, 1, 2, 4, 8,… where "a" is the mean distance from the planet to the Sun, in Astronomical Units (AU) . At the time of Titius-Bode, the asteroid belt, Uranus, Neptune and Pluto were not yet discovered. With the discovery of asteroids, this rule was almost considered like a rigorous law. But, it could never explain the position of Neptune and Pluto. With the fundamental movement of the "doubling theory", it is possible to correct the Titius-Bode’s rule and to understand the explanation of this empirical law as well as the variation between the aphelion and the perihelion of the planetary orbits. It is also possible to explain the exact position of Neptune and Pluto. At last, the doubling theory gave me, ten years ago, the possibility to predict the new planets (or planetoids) between Pluto and the Oort Cloud. This prediction is now perfectly justified by the discovery of Sedna, 2003UB313,…. We’ll see that these curious planets are associated with the well-known asteroids between Mars and Jupiter. This association that connects the telluric planets to the giant planets and the asteroids belt to the planetoids belt (Kuiper Belt) can be explained by the doubling theory [8] . This

FAQs

What problem does the doubling theory address in the Titius-Bode law?

The paper argues that the empirical Titius-Bode law works approximately for many planets but becomes totally false for the most distant ones and does not include regions like the Kuiper Belt and Oort Cloud; the doubling theory is presented as a correction model.

How does the paper describe the structure underlying the doubling theory?

It states that the doubling theory is based on successive embedded finite structures of space-time domain at different scale levels, with a cycle in the solar system corresponding to 25920 years.

What new predictions does the model claim to make?

The paper claims the doubling theory predicts new planets between the Kuiper Belt and the Oort Cloud, and it asserts that these predictions are justified by later discoveries such as Sedna (2003 UB313).

How is the fine structure constant connected to the solar system cycle?

The paper claims that the cycle of the doubling movement in the solar system defines the fine structure constant, stating the value as α = 1/137.

Sep 21, 2026

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