[astro-ph/0209276] Dynamical derivation of Bode's law

[astro-ph/0209276] Dynamical derivation of Bode's law:

"In a planetary or satellite system, idealized as n small bodies in initially coplanar, concentric orbits around a large central body, obeying Newtonian point-particle mechanics, resonant perturbations will cause dynamical evolution of the orbital radii except under highly specific mutual relationships, here derived analytically apparently for the first time. In particular, the most stable situation is achieved (in this idealized model) only when each planetary orbit is roughly twice as far from the Sun as the preceding one, as observed empirically already by Titius (1766) and Bode (1778) and used in both the discoveries of Uranus (1781) and the Asteroid Belt (1801). ETC."

'via Blog this'

Paradigm Shifts

Nevertheless the opportunity was utterly blocked by the scientific paradigm of Laplacian determinism.

From Ivan I. Shevchenko

On the Principle of Least Action Interaction (Ovenden)

Springer

The history of the Titius-Bode Law is summarized, and possible explanations for the law are examined. Numerical integrations confirm the intuition that any N-body point-mass planetary system spends most of its time in configurations where the planetary interactions are least. This result is formalized into the Principle of Least Interaction Action, viz. that such a system will most often be found in a configuration where the time-mean of the action associated with the mutual interactions of the planets is a local minimum. It is shown that this principle leads to the resonant structures predicted (by a complementary argument) by Roy and Ovenden (1955), and found in the satellite systems of Jupiter and Saturn. Time-scale estimates show that the time of relaxation from an arbitrary configuration is short compared with the time spent near such a minimum interaction configuration. These results suggest that the present distribution of planetary and satellite orbits is the result of mutual perturbations, that tidal forces need not be invoked, and that the present distribution gives no information concerning the origin of the solar system.

However, if it can be shown that processes operate within the solar system that can rearrange the planetary orbits on a su~iciently short time-scale then we must conclude that the present distribution of planetary and satellite orbits contains no information about conditions at the time of formation of the solar system. The rest of this paper will be devoted to providing evidence that such a process does exist, in the mutual gravitational perturbations of one planet or satellite upon another.

From all these integrations a general characteristic stands out clearly. A system spends a short time with the planets close together and interacting violently, and spends most of its time with the planets far apart and interacting mildly, as is indeed to be expected from the most elementary consideration. We now formalize this elementary consideration into The Principle of Planetary Claustrophobia, namely that, in any system, the planets will spend most of their time as far away from each other as possible.

On the dynamical derivation of Titius-Bode

Springer

Titius-Bode, Poveda and Rabinowitz

My friend Mario Rabinowitz just revived my interest on this relation, which the Mexican Astronomer Poveda has been studying for many years now.

Arcadio Poveda visited us at the Physics school of the University of Puebla (UAP) many years ago. Tapan Kumar Chatterjee invited him, when Dr. Chatterjee was a professor there. Poveda has been an original astronomer, and I have followed his work. Recently Dr. Poveda analyzed extra-solar planetary systems with the so-called Titius-Bode Law, which Rabinowitz told me was discovered by Johann Daniel Titius.

 I believe that they are bound to be regularities for objects moving close to a plane, because they exert forces on each other. This is a formation issue, that likely requires computer calculations to derive. The main idea though, is that a planar many body problem follows regularities, as has been observed by the hexagonal structure in Jupiter. From those hexagons to some radius relation for planetary orbits, I just see computer work directed to finding it. One planet, pulling a nearby one, competing with other planets on the other side of the orbit, could produce an orbit, not too close, and not too far, like in the Goldilocks fairy tale. Order out of Chaos.

Exoplanet Predictions Based on the Generalised Titius-Bode Relation

Timothy Bovaird, Charles H. Lineweaver

We evaluate the extent to which newly detected exoplanetary systems containing at least four planets adhere to a generalized 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 generalized TB relation to make a list of predictions for the existence of 141 additional exoplanets in 68 multiple-exoplanet systems: 73 candidates from interpolation, 68 candidates from extrapolation. We predict the existence of a low-radius (R < 2.5 Earth Radii) exoplanet within the habitable zone of KOI-812 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.

arXiv

Jonathan Swift and the Moons of Mars

They have likewise discovered two lesser stars, or satellites, which revolve about Mars; whereof the innermost is distant from the centre of the primary planet exactly three of his diameters, and the outermost, five; the former revolves in the space of ten hours, and the latter in twenty-one and a half; so that the squares of their periodical times are very near in the same proportion with the cubes of their distance from the centre of Mars; which evidently shows them to be governed by the same law of gravitation that influences the other heavenly bodies.

Gulliver's Travels