In its original form the Titius-Bode law appeared under Bonnet’s name in 1766. In 1772 Titius identified himself as the author of the law, but in the same year Bode borrowed under his own name Titius’ formulation of the law. Titius attributed the law, wholly arbitrarily, to Bonnet, Lambert, and Wolff. From 1772 until 1787 Bode was practically alone among astronomers to mention the law in its primitive, sequential form, in his various writings. The algebraic, functional form of the law was given by Wurm in 1787. The distance of Uranus, discovered in 1781, fitted well into the law which inspired the search for the missing planet between Mars and Jupiter. The discovery of Ceres in 1801 was a triumph of the law only until the discovery of Pallas in 1802, which produced the opposite effect. Most leading astronomers of the period considered the law as a mere game with numbers.
Source: The Original Formulation of the Titius-Bode Law
Source: Stamping Through Astronomy
Source: Stamping Through Astronomy
Source: Jovicentricity in the Solar System: The history of a discovery
The Titius-Bode law is simple mathematical relation describing the distances of planets from the sun. The relation comes from starting with a simple arithmetic progression of numbers:
0, 3, 6, 12, 24, 48, 96, 192, 384.
Note that each number is twice the previous. Then, by adding 4 to each number and dividing the result by 10, this yields a sequence of numbers that roughly corresponds to the spacing of planets in our solar system out to Uranus (in AU):
Mercury
Venus
Earth
Mars
Asteroid Belt
Jupiter
Saturn
Uranus
Neptune
Pluto
Predicted:
0.4
0.7
1
1.6
2.8
5.2
10
19.6
38.8
77.2
Actual:
0.39
0.72
1
1.52
2.7
5.2
9.54
19.19
30.1
39.5
When it was initially published, it was found that this law correctly predicts the distances of all known planets from Mercury to Saturn. It also correctly predicted the (then unknown) locations of the asteroid belt and Uranus, but not for Neptune or Pluto (Fig. 1). The Titius-Bode relation has been the subject of much speculation, but the so-called “law” is now largely thought to be a mathematical coincidence rather than an actual physical law since it is not well physically motivated and fails to apply to the outermost planets in our solar system. Even so, there have been suggestions that this relation is a mathematical result of orbital resonances and gravitational interactions within multi-body planetary systems.
It is difficult to say whether the Titius-Bode relation has any deeper significance just from looking in our own solar system. However, the plethora of exoplanet discoveries over the past several years allows for a larger sample of planetary systems in which we can examine this relation. In the four years that the Keplermission has been active, over 3000 extrasolar planetary systems have been discovered. About 1/5 of these planet-hosting stars are believed to host multiple planets.
In this paper, the authors use Kepler data to see if a generalized Titius-Bode relation holds for extrasolar multi-planet systems. This analysis is based on a previous paper by Bovaird & Lineweaver (hereafter BL13), in which the authors attempt to test the Titius-Bode relation on known extrasolar planetary systems. BL13 predicts that these extrasolar systems should follow a Titius-Bode relation (one that is modified and generalized from the relation that applies to the solar system), and that there may be undetected planets that fit into this relation. Specifically, the paper predicted the existence of 141 additional exoplanets in 68 multiple-exoplanet systems.
The analysis in this paper focuses on Kepler data taken over a 100 day time span. From examining the light curves from 56 exoplanet systems, the authors only managed to detect 5 of the predicted planets. That is, a majority of the planets predicted from the modified Titius-Bode relation were not found.
It is also possible that there are observational biases that prevent these “missing” planets from being detected. For example, it is assumed that most of the planets in a planetary system will lie roughly in the same orbital plane. This is not necessarily true, and any strong deviations in orbital inclination angle will reduce the number of expected observable transits. Additionally, planets could also avoid detection due to their small size and lack of observed signal in their light curves. After taking these factors into consideration, the authors predict that they should find roughly 15 planets that obey a Titius-Bode relation.
The authors ultimately only detect only 5 of the 141 predicted planets. Even after correcting for observational biases, this number is significantly smaller than expected. The authors conclude that it is questionable that a Titius-Bode relation will hold for all extrasolar planetary systems. Even if the Titius-Bode relation turns out to be a mathematical oddity, it is still insightful to see if our own solar system shares any common characteristics with any extrasolar counterparts.
About the Author
About Anson Lam
I am a graduate student at UCLA, where I am working with Steve Furlanetto on models of galaxy clustering and their applications to the reionization era. My main interests involve high redshift cosmology, dark matter, and structure formation. Previously, I was an undergraduate at Caltech, where I did my BS in astrophysics. When I’m not doing astronomy, I enjoy engaging in some linear combination of swimming/biking/running.
Source: The complex planetary synchronization structure of the solar system
Source: Solar System Dynamics
Source: Solar System Dynamics
Source: Solar System Dynamics
Source: Solar System Dynamics
Source: Solar System Dynamics
Source: Solar System Dynamics
Source: Solar System Dynamics
Source: Solar System Dynamics
Source: Solar System Dynamics
Source: Solar System Dynamics
Source: Solar System Dynamics
Source: Solar System Dynamics
Source: The Titius-Bode Law of Planetary Distances Its History and Theory
Source: The Titius-Bode Law of Planetary Distances Its History and Theory
Source: The Titius-Bode Law of Planetary Distances Its History and Theory
Source: Scaling, Mirror Symmetries and Musical Consonances Among the Distances of the Planets of the Solar System
Source: Scaling, Mirror Symmetries and Musical Consonances Among the Distances of the Planets of the Solar System
Source: Scaling, Mirror Symmetries and Musical Consonances Among the Distances of the Planets of the Solar System
Source: Scaling, Mirror Symmetries and Musical Consonances Among the Distances of the Planets of the Solar System
Source: Scaling, Mirror Symmetries and Musical Consonances Among the Distances of the Planets of the Solar System
Source: Scaling, Mirror Symmetries and Musical Consonances Among the Distances of the Planets of the Solar System
Source: Scaling, Mirror Symmetries and Musical Consonances Among the Distances of the Planets of the Solar System
The HARPS search for southern extra-solar planets⋆
XXVII. Up to seven planets orbiting HD 10180: probing the architecture of low-mass planetary systems
C. Lovis1, D. Se ́gransan1, M. Mayor1, S. Udry1, W. Benz2, J.-L. Bertaux3, F. Bouchy4, A. C. M. Correia5, J. Laskar6, G. Lo Curto7, C. Mordasini8,2, F. Pepe1, D. Queloz1, and N. C. Santos9,1
Astronomy & Astrophysics manuscript no. HD10180 August 13, 2010
Scaling, Mirror Symmetries and Musical Consonances Among the Distances of the Planets of the Solar System
Michael J. Bank1†
Nicola Scafetta2*†
1Danbury Music Centre, Danbury, CT, United States 2Department of Earth Sciences, Environment and Georesources, University of Naples Federico II, Complesso Universitario di Monte S. Angelo, Naples, Italy
Exoplanet Predictions Based on Harmonic Orbit Resonances
by Markus J. Aschwanden 1 and Felix Scholkmann 2,*
1 Lockheed Martin, Solar and Astrophysics Laboratory, Org. A021S, Bldg. 252, 3251 Hanover St., Palo Alto, CA 94304, USA 2 Research Office for Complex Physical and Biological Systems, Mutschellenstr. 179, 8038 Zürich, Switzerland *Author to whom correspondence should be addressed.
The Planetary Theory of Solar Activity Variability: A Review
Nicola Scafetta1*
Antonio Bianchini2* 1Department of Earth Sciences, Environment and Georesources, Complesso Universitario di Monte S. Angelo, University of Naples Federico II, Naples, Italy 2INAF, Astronomical Observatory of Padua, Padua, Italy
Overview of the Spectral Coherence between Planetary Resonances and Solar and Climate Oscillations
by Nicola Scafetta 1,* and Antonio Bianchini 2
1 Department of Earth Sciences, Environment and Georesources, University of Naples Federico II, Complesso Universitario di Monte S. Angelo, via Cinthia, 21, 80126 Napoli, Italy 2 INAF, Astronomical Observatory of Padua, Vicolo Osservatorio 5, 35122 Padova, Italy * Author to whom correspondence should be addressed.
Climate 2023, 11(4), 77; https://doi.org/10.3390/cli11040077 Received: 8 March 2023 / Revised: 23 March 2023 / Accepted: 25 March 2023 / Published: 27 March 2023 (This article belongs to the Special Issue Natural Drivers of Climate Change: Emerging Research)
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Viewpoints which Matter 