A numerical method for determining the temperature structure of planetary atmospheres

A numerical method for calculating the time-average, vertical temperature structure of planetary atmospheres is presented. It is assumed that the atmospheres are in radiative-convective equilibrium, which is a good first approximation to many situations. Numerical tests of the rate of convergence and accuracy of the answer are presented. The method can readily handle molecular sources of opacity. Accurate results can be obtained with a minimum of computer time, because the number of iterations needed (～ 4) is small and the number of pressure levels at which the net flux needs to be evaluated (～ 10) is small. As an application of this procedure, we have calculated some model atmospheres of Jupiter.     

Planetary nebulae in the Galaxy

It is shown that the planetary nebulae can be divided into three types according to the values of the mass of shell and a central star. The criteria are given using which one can determine the mass type of the nebula. The distance scale of each mass-type planetary nebulae is given. The distribution of planetary nebulae in the Galaxy, their formation rate, scale-height and other physical and kinematic characteristics are investigated. A catalogue of planetary nebulae emitting in the radio range is given.     

Planetary theories with the aid of the expansions of elliptic functions

For coplanar circular orbits, the mutual perturbations between two bodies can be expressed in term of the argument of Jacobian elliptic functions instead of the difference of the mean longitudes. For a given pair of planets, such a change of time variable improves the convergence of the developments. At the first order of planetary masses an integration of Lagrange's equations for the osculating elements is performed. When compared to classical developments the results are reduced by an important factor. The method is then extended to the mutual perturbations of Jupiter and Saturn, at any order of planetary masses, either with Fourier series with two arguments, or with one argument solely, taking advantage of the close commensurability of the mean motions.     

Chinese records on the correlation of heliocentric planetary alignments and earthquake activities

A short account of the correlation of heliocentric planetary alignments and the earthquake activities in Northern China is given. It appears that such arrangement of planetary orbital positions has no effect on the triggering of earthquakes.     

Ancient Chinese observations of planetary positions and a table of planetary occultations

Ancient Chinese records of observations of planetary positions are introduced and classified. A table which includes 66 records of planetary occultations is given in this paper. Those ancient records are valuable for research on the secular motions of planets.     

Emission from an Inhomogeneous Plasma: Line Intensities and Determination of Elemental Abundances in Gaseous Nebulae with Fluctuations of Te and ne

A method is proposed for determining the abundances of chemical elements in planetary nebulae based on allowance for the actual distribution functions of errors in measuring line intensities. Fluctuations both in temperature and in mass density of a nebula are taken into account in the proposed method. The results of a determination of C and O abundances and of the amplitudes of temperature and density fluctuations are given.     

Eclipses of natural planetary satellites

A general method is given for predicting eclipse events for natural planetary satellites suitable for use on a large scale digital computer. The precision is sufficient to process photometric eclipse observations to improve natural satellite ephemerides. Expected accuracy improvement for Saturn's satellites should be an order of magnitude or better. Predicted eclipse times of satellites by Saturn and the Rings are given for the next decade.Presented at IAU Colloquium No. 28, Ithaca, New York, August, 1974.     

Numerical Instruments for the Analysis of Secular Dynamics of Exoplanetary Systems

A review is given of modern numerical methods for the analysis of resonant and chaotic dynamics: calculation of the Lyapunov characteristic exponents, the MEGNO method, and the maximum eccentricity method. These methods are used to construct stability diagrams for the planetary systems γ Cep, HD 196885, and HD 41004. The diagrams are analyzed to determine the most probable values taken by the orbital parameters of the exoplanets and obtain estimates for the Lyapunov time of their orbital dynamics. The stability diagrams constructed using the different methods are compared to analyze their effectiveness in the study of secular dynamics of exoplanetary systems.     

Origin of the atmospheres of the terrestrial planets

The monotonic decrease in the atmospheric abundance of ³⁶Ar per gram of planet in the sequence, Venus, Earth, and Mars has been assumed to reflect some conditions in the primitive solar nebula at the time of formation of the planetary atmospheres, having to do either with the composition of the nebula itself or the composition of the trapped gases in small solid bodies in the nebula. Behind such hypotheses lies the assumption that planetary atmospheres steadily gain components. However, not only can gases enter atmospheres; they may also be lost from atmospheres both by adsorption into the planetary interior and by loss into space as a result of collisions with minor and major planetesimals. In this paper a necessarily qualitative discussion is given of the problem of collisions with minor planetesimals, a process called atmospheric cratering or atmospheric erosion, and a discussion is given of atmospheric loss accompanying collision of a planet with a major planetesimal, such as may have produced the Earth's Moon.     

Averaging the Equations of a Planetary Problem in an Astrocentric Reference Frame

A system of averaged equations of planetary motion around a central star is constructed. An astrocentric coordinate system is used. The two-planet problem is considered, but all constructions are easily generalized to an arbitrary number N of planets. The motion is investigated in modified (complex) Poincarécanonical elements. The averaging is performed by the Hori–Deprit method over the fast mean longitudes to the second order relative to the planetary masses. An expansion of the disturbing function is constructed using the Laplace coefficients. Some terms of the expansion of the disturbing function and the first terms of the expansion of the averaged Hamiltonian are given. The results of this paper can be used to investigate the evolution of orbits with moderate eccentricities and inclinations in various planetary systems.     

Stability of outer planetary systems

The conditions for stability in the Liapunov-Hill sense of outer planetary systems are given in terms of radii of planetary orbits. The outer planets of the solar system are found stable and the possible existence of other than the presently known planets between Jupiter and Pluto are indicated. The existence of other planetary systems with arbitrary mass ratios of the primaries is suggested, and the stability conditions for such systems are derived.Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August, 1978.     

Multiple scattering in the atmosphere with a rough surface

In the present paper, the intensity of radiation emergent from the atmosphere bounded by a rough surface is discussed with the aid of the superposition method derived by Mukai (1973). The merit of this method is to express the laws of diffuse reflection and transmission for the planetary problem with a rough surface in terms of a scattering and a transmission function for the standard problem.Here the bottom surface is assumed to reflect light in accordance with the slope distribution given by Cox and Munk (1954a, b). The results are discussed in terms of the optical properties and roughness of the bottom surface.     

Alternative representation of planetary perturbations

An attempt is made to find a representation of planetary perturbations which does not require a Fourier expansion. For the planetary type three body problem a sequence of canonical transformations is given based on Landen transformations coupled with a rescaling of the time. The expansion is carried out to the order 2 in the Hamiltonian.     

The formation of the atmospheres of the terrestrial planets by impact

It is generally supposed that the atmospheres of the terrestrial planets were formed by secondary degassing processes. We propose, instead, that they are of primary origin, forming as an immediate and necessary consequence of the final stages of planetary accretion. Once the planetary embryo reached a critical size, the impacting material began to vaporize. The atmosphere, so created, then decelerated other impacting material, thus limiting the rate of atmospheric growth. We show that, given reasonable assumptions concerning the chemical composition of the impacting material, an acceptable model for the early atmosphere of the Earth, and the present atmospheres of Venus and Mars results.A discussion of the noble gas data for the terrestrial atmosphere indicates that these can be readily reconciled with an impact origin.     

The interactions of the solar wind with planetary magnetic fields: Basic principles and observations

A planetary magnetic field obstructs the supersonic expansion of the solar coronol ions and electrons and creates a cigar shaped bubble in the solar wind. The pressure of the solar wind on the bubble compresses and seriously distorts the planetary magnetic field. A review is given here of the theoretical calculation and experimental observation of the shape of the bubble and the configuration of the compressed magnetic field inside the surface. Other effects, namely the shock structure on the surface, the radiation belts, and the current in the antisolar side of the bubble are described as well as a simplified account of electric fields and the connection of the planetary field lines with interplanetary field lines.     

Periodic orbits of the planetary type and their stability

A review is presented of periodic orbits of the planetary type in the general three-body problem and fourbody problem and the restricted circular and elliptic tnreebody problem. These correspond to planetary systems with one Sun and two or three planets (or a planet and its satellites), the motion of asteoids and also planetary systems with two Suns. The factors which affect the stability of the above configurations are studied in connection with resonance or additional perturbations. Finally, the correspondence of the periodic orbits in the restricted three-body problem with the fixed points obtained by the method of averaging or the method of surface of section is indicated.     

Planetary reflectance measurements in the region of planetary thermal emission

As planetary reflectance measurements are extended into the infrared, the emitted thermal radiation becomes larger than the reflected solar component. This paper describes a method for removal of the thermal component from planetary reflectance measurements and discusses the limitations involved. Examples are shown for the case of lunar observations where the temperature and emissivity are known and for Mercury where it is assumed the temperature and emissivity are unknown.     

Scanner observations of P/Halley (1982i)

We present an outline to calculate the principal and indirect portions of the planetary disturbing function, based on the method of W. M. Smart. We truncate the Taylor expansion at the third power of eccentricity-inclination. The outline of a new method to obtain the negative powers of the mutual distance between two planets is also given, neglecting powers higher than the fourth in the eccentricity-inclination.     

Extrasolar planetary systems

The article deals with the occurrence of planetary systems in the Universe. In Section I, the terms “planet” and “planet-like objects” are defined. Two definitions proposed for the term “planetary system” are examined from the point of view (1) of the relation between planetary systems and binary and multiple star systems and (2) of planetary systems as abodes of intelligent beings. In Section II, the observational search for extrasolar planetary systems is described, as performable by earthbound optical telescopes, by space probes, by long baseline radio interferometry, and finally by inference from the reception of signals sent by intelligent beings in other worlds.In Section III we show that any planetary system must be preceded by a rotating disk of gas and dust around a central mass. Both observational evidence and theoretical reasons indicate the ease of formation of such disk structures in the cosmos. The time scale of collapse of a gaseous medium into a disk and that of the latter's dissipation are examined. This provides us with a new empirical approach and leads us to consider the problem of the frequency of occurrence of planetary systems to be ripe for scientific study. In Section IV, a brief review of theories of the formation of the solar system is given along with a proposed scheme for classification of these theories. In Section V, the evidence for magnetic activity in the early stages of stellar evolution is presented, as developed from six independent clues: the nuclear abundance of light elements, the behavior of flare stars, the intensities of H and K emission in stars, the nonthermal radiation of premain sequence stars, the properties of meteorites, and finally the existence of contact binaries. The magnetic braking theories of solar and stellar rotation are discussed in Section VI, thereby introducing the idea of formation of a rotating disk of gas and dust around stars in Section VII. From this disk a planetary system emerges.Section VIII gives an estimate for the frequency of occurrence of planetary systems in the Universe. It is based on the rotational behavior of main-sequence stars, and concludes that planetary systems have a far greater chance to appear around single main-sequence stars of spectral types later than F5 than around any other kind of star. The combined probability distribution of sizes and masses could be obtained. From physical considerations, it appears that sizes of planetary systems around stars of any given spectral type may not vary greatly from one to another.     

Planetary perturbations of the Moon in ELP 2000

A new solution for the planetary perturbations of the Moon is being built in the frame of ELP 2000, using Bretagnon's planetary theories, and achieved at the first order. It contains the two actions commonly distinguished: direct and indirect. The internal precision of computation is 2×10^–6 arcsec. First-order planetary perturbations, in the direct case (Venus & Mars), have been compared to Standaert's solution. The major discrepancy reaches 70 cm in the longitude of Venus. Perturbations of the second order with respect to planetary masses, have been undertaken and illustrations are given. Finally, new values for the perigee and node motions are proposed.Proceedings of the Conference on Analytical Methods and Ephemerides: Theory and Observations of the Moon and Planets. Facultés universitaires Notre Dame de la Paix, Namur, Belgium, 28–31 July, 1980.