Stability Of The Solar System Research Articles

Numerical Studies on the Stability of the Solar System

In this paper, recent numerical and analytical results of the author and others, concerning the stability of the solar system are presented. The results indicate that the actual planetary system could possibly have stable and bounded motion.

Stability of the Solar System

This paper reviews the present status of research on the problem of stability of satellite and planetary systems in general. In addition new results concerning the stability of the solar system are described. Hill's method is generalized and related to bifurcation (or catastrophe) theory. The general and the restricted problems of three bodies are used as dynamical models. A quantitative measure of stability is introduced by establishing the differences between the actual behavior of the dynamical system as given today and its critical state. The marginal stability of the lunar orbit is discussed as well as the behavior of the Sun-Jupiter-Saturn system. Numerical values representing the measure of stability of several components of the solar system are given, indicating in the majority of cases bounded behavior.

On the stability of the solar system

On the stability of the solar system

The Stability of the Solar System and the Small Stellar Systems: Symposium Number 62 (Copernicus Symposium 1) held at Warsaw, Poland, 5–8 September, 1973

Y Kozai (ed) Dordrecht: D Reidel 1974 pp vi + 313 price Dfl 95 This book is the proceedings of a symposium bearing the same title held at Warsaw in September 1973 to commemorate the 500th anniversary of the birth of Nicolaus Copernicus. Since it is basically concerned with the stability of the orbits of gravitationally interacting sets of particles, the work is a worthy continuation of the work of Copernicus himself in establishing the heliocentric model for the planetary systems.

Stability of the solar system: Evidence from the asteroids

An analysis of the distribution of the orbital periods of the asteroids has shown that there is a preference for these periods to be near-commensurate with that of Mars. We suggest that this preference is associated with a formation process and implies that the orbital period of Mars has not changed greatly since the time of asteroid formation. We deduce from this that the solar system is highly stable and long-period gravitational perturbations have probably had little influence on the gross evolution of the solar system.

A survey of long-term observational behavior of various martian features that affect some recently proposed interpretations

In recent years an unprecedented surge of papers and articles has appeared in which various authors interpret the features and conditions on Mars. In many cases it is obvious that there was little or no personal telescopic acquaitance with the appearance of Mars under very favorable viewing conditions, nor with the complex behavior of various features and phenomena throughout all of the martian seasons. This trend can lead to a dangerous amount of misinformation and confusion. The study of Mars requires a familiarity with several different disciplines that few have met. It requires 15 years to follow Mars through one equivalent year of seasonal changes; at least two or three times 15 years is necessary to discern secular changes from the regular seasonal changes. One needs to peruse a long list of papers in the disciplines of physics, geology, meteorology, and biology to sift the evidence. A consideration of the life history of solar-type stars, the stability of the solar system, and paleoclimatology shows that Mars could never have provided an environment of other than cool to frigid temperatures and a dry climate. Consequently, the role of water on martian geology would have been very insignificant. Water denudation and the formation of marine sedimentary rocks could never have occurred. Some volcanism probably occurred. The canals and angular maria probably are features of extensive crustal faulting. The surface would be highly cratered by asteroid impacts; the round dark dots may represent impact sites. The considerable seasonal differences in maria color, polar cap phenomena, and climate between the northern and southern hemispheres appear to be related to the perihelion and aphelion positions in the orbit. Many proposed explanations of the nature of the various features are simply not supported by the complex observed phenomena. The author proposes some explanations that appear to be in accord with his experience with the planet Mars.

The Movement of Encke's Comet

IN Prof. Poincares paper on the “Stability of the Solar System”, the statement is made that “astronomers have only been able to explain the movement of Encke's comet by supposing the existence of a resisting medium.”

Book Reviews

THESE two year-books of scientific information annually increase in value by the addition of new data and revision of the old. The Annuaire of the Bureau of Longitudes has undergone several changes. In the astronomical part the tables of mean positions of stars supposed to be variable have been omitted, the tables of the elements of minor planets have been curtailed, and in the same way the number of coordinates referring to the orbits of double stars has been diminished. The table of elements of periodic comets only observed at a single apparition has been transferred to the Connaissance de Temps, but comets observed at a return are retained in the volume. The chapter on tides has been rearranged and revised, and new tables inserted. M. Moureaux contributes three new charts showing the magnetic elements in France, based on direct observations; the charts are for the epoch January 1, 1896. M. Berthelot brings up to date the tables in the section on thermo-chemistry. The articles in the Annuaire are all interesting. MM. Lœwy and Puiseux contribute a paper on recent progress in the knowledge of the lunar surface, obtained by means of photography; M. Poincaré contributes a valuable paper on the stability of the solar system; an account of Fizeau's scientific work is given by M. Cornu; and M. Janssen describes the work done at the observatory on the summit of Mont Blanc in 1897. Finally, there is an address by MM. Janssen and Lœwy, delivered on the occasion of M. Faye's jubilee last January.

On the Stability of the Solar System

On the Stability of the Solar System

III. Researches in physical astronomy

In last April I had the honour of presenting to the Society a paper containing expressions for the variations of the elliptic constants in the theory of the motions of the planets. The stability of the solar system is established by means of these expressions, if the planets move in a space absolutely devoid of any resistance*, for it results from their form that however far the ap­proximation be carried, the eccentricity, the major axis, and the tangent of the inclination of the orbit to a fixed plane, contain only periodic inequalities, each of the three other constants, namely, the longitude of the node, the longitude of the perihelion, and the longitude of the epoch, contains a term which varies with the time, and hence the line of apsides and the line of nodes revolve continually in space. The stability of the system may therefore be inferred, which would not be the case if the eccentricity, the major axis, or the tangent of the inclination of the orbit to a fixed plane contained a term varying with the time, however slowly. The problem of the precession of the equinoxes admits of a similar solution; of the six constants which determine the position of the revolving body, and the axis of instantaneous rotation at any moment, three have only periodic inequalities, while each of the other three has a term which varies with the time. From the manner in which these constants enter into the results, the equilibrium of the system may be inferred to be stable, as in the former case. Of the constants in the latter problem, the mean angular velocity of rotation may be considered analogous to the mean motion of a planet, or its major axis ; the geographical longitude, and the cosine of the geographical latitude of the pole of the axis of instantaneous rotation, to the longitude of the perihelion and the eccentricity; the longitude of the first point of Aries and the obliquity of the ecliptic, to the longitude of the node and the inclination of the orbit to a fixed plane; and the longitude of a given line in the body revolving, passing through its centre of gravity, to the longitude of the epoch. By the stability of the system I mean that the pole of the axis of rotation has always nearly the same geographical latitude, and that the angular velocity of rotation, and the obliquity of the ecliptic vary within small limits, and periodically. These questions are considered in the paper I now have the honour of submitting to the Society. It remains to investigate the effect which is produced by the action of a resisting medium; in this case the latitude of the pole of the axis of rotation, the obliquity of the ecliptic, and the angular velocity of rotation might vary considerably, although slowly, and the climates undergo a con­siderable change.