Michael W. Ovenden

On the Principle of Least Interaction Action and the Laplacean satellites of Jupiter and Uranus

The Principle of Least Interaction Action, which explains the observed preference in the Solar System for two-satellite resonant configurations, is shown to apply also to the Laplacean satellites of Jupiter and Uranus, in the sense that these triplet resonant structures lie close to configurations for which the time-mean of the action associated with the mutual interaction of the satellites is an overall minimum. Far from the minimum configuration, significant changes take place in the major semi-axes on time-scales ∼106-107y. Both systems require times ∼108 y to come close to the minimum configuration; to approach resonance to the observed precision of the Laplace relationship (3×10−4 for the Uranian case, 2×10−7 for the Jovian case) requires, for both systems, a time closely comparable with the age of the solar system.

9.1. Bode's law—truth or consequences?

Abstract 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.

On the reflection effect in spectroscopic binary stars

Abstract It is shown that both spectroscopic observations and observations of reddening during eclipses of close binary stars indicate the existence of “hot spot” conditions over an area of a “reflecting” star that cannot be explained by a simple geometrical model of reflection. It is also shown that circulating currents must be generated in the atmosphere of a reflecting star which could bring to the surface material of a higher temperature, but that the decay of ionization appears to be too rapid to explain the spectroscopic observations.

Comets and the Missing Planet

Integrating backwards in time in the circular restricted three-body problem Galaxy-Sun-Comet, for both the real long-period comets and fictitious random sets of orbital elements, we have confirmed van Flandern’s conclusion that there is a statistically-significant clustering of the orbits of real long-period comets, in heliocentric direction, some 5×106 years ago. The clustering is also significant in heliocentric distance, and is more marked if it is assumed that the comets have gone round the Sun more than once since the epoch of maximum clustering. We suggest that the “event” discovered by van Flandern is not the explosive disruption of a planet formerly in the asteroid belt, but the latest in a series of minor catastrophies, such as the collisional break-up of a pair of large asteroids.

Disseminated storage of information with sequential coding

The paper demonstrates that it is possible to construct memory models where the information inserted is stored in disseminated form, using sequential coding, the changes in the units forming the models being determined by their geometrical connections and by the incoming stream of information. The models are shown to have large storage capacity and their efficiency can be made insensitive to loss of or damage to a large fraction of their units. The satisfactory verification by computer simulation of the analysis and results described in the present paper will be the subject of a future paper.

Photometric effects of gaseous envelopes in close eclipsing binaries

Abstract A brief discussion is given of observations of short-period eclipsing binaries, which indicate that variations from a mean curve may be attributed to absorption by gaseous envelopes. An analysis is made of the deviations from a mean curve in the authors two-colour photoelectric observations of GO Cygni, by a method which utilizes the stability of the response of the photoelectric cell. The deviations are shown to be correlated with the asymmetric terms in the variation of light between eclipses, and it is suggested that such asymmetric terms are due to photometric effects of gaseous envelopes.

Kinematics of Carbon Stars in the Large Magellanic Cloud

Published radial velocities of HII regions, luminous early- and late-type stars, and planetary nebulae, are consistent with a rotation law for the Large Magellanic Cloud V ∞ C R for R< 5.5°. New radial velocities for some of the carbon stars in the WORC Catalogue extend the determination of rotation velocities to R ≃ 7°. These observations are consistent with V ∞R for R <5.5°, with a rapid decrease of V for greater distances. If these results are interpreted as indicating solid-body rotation of a finite disc, and if a true distance modulus of 18.6 is assumed for the LMC, the mass of the LMC is found to be ~2.6 × l010 solar masses.