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Titius-Bode Rule
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Title: A Physical Interpretation of the Titius-Bode Rule
Author: Dimitris M. Christodoulou, Demosthenes Kazanas

We consider the geometric Titius-Bode rule for the semimajor axes of planetary orbits. We derive an equivalent rule for the midpoints of the segments between consecutive orbits along the radial direction and we interpret it physically in terms of the work done in the gravitational field of the Sun by particles whose orbits are perturbed around each planetary orbit. On such energetic grounds, it is not surprising that some exoplanets in multiple-planet extrasolar systems obey the same relation.

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RE: Titius-Bode Law
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Title: Exoplanet Predictions Based on the Generalised Titius-Bode Relation
Authors: Timothy Bovaird, Charles H. Lineweaver

We evaluate the extent to which newly detected exoplanetary systems containing at least four planets adhere to a generalised Titius-Bode (TB) relation. We find that the majority of exoplanet systems in our sample adhere to the TB relation to a greater extent than the Solar System does, particularly those detected by the Kepler mission. We use a generalised TB relation to make a list of predictions for the existence of 126 additional exoplanets in 64 multiple-exoplanet systems: 62 candidates from interpolation, 64 candidates from extrapolation. We predict the existence of 2 low-radius (R < 2.3 Earth Radii) exoplanets in the habitable zone of KOI-490 and that the average number of planets in the habitable zone of a star is 1-2. The usefulness of the TB relation and its validation as a tool for predicting planets will be partially tested by upcoming Kepler data releases.

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From ancient times, scientists have attempted to identify laws governing the orbits of the planets. In 1766, the physicist and mathematician Johann Daniel Titius developed a formula that can be used to derive the distances between the planets and the Sun with only a small degree of inaccuracy. It was publicised by the director of the Berlin observatory at the time, Johann Elert Bode, and is therefore called the 'Titius-Bode law'.
However, according to this empirical (that is, derived from observations) formula another planet should be present between Mars and Jupiter. This prediction was an incentive for many astronomers to try to find this as-yet unknown heavenly body.

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Title: The Titius-Bode Law Revisited But Not Revived
Authors: Ivan Kotliarov

The present article gives a detailed analysis of the new formulation of Titius-Bode law by (Poveda, Lara 2008) and of the hypothesis that this law may exist in extra-solar planetary system. A thorough study of the correspondences between the calculated distances and the observed ones in the Solar system and in 55 Cancri is given. It is shown that Poveda-Lara hypothesis contains serious mistakes (both in theory and in calculations) that makes it unacceptable.

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