A survey of Poisson series processors

The sheer magnitude of the work involved in the construction of perturbation theories (the astronomical computations) made it inevitable that astronomers would very early become interested in the possibility of constructing them with the aid of computers. Since then general systems for symbolic manipulations have been developed and used widely. Nevertheless there still remain problems for which these general systems are not well adapted and many specialized systems of algebraic manipulation (mostly Poisson series processors) are in use. An attempt is made to review this field by sketching some of the ideas on which these Poisson series processors are built.     

A more general system for Poisson Series manipulation

We describe the design of a working Poisson Series Processor that is more general than others in use today. We try to show that the price of generality is worth paying in active research areas in celestial mechanics.This work was supported in part by grant NGR 09-015-002 from the National Aeronautics and Space Administration.     

A note on velocity-related series expansions in the two-body problem

The present note describes a few important series expansions in the two-body problem. They are related to the magnitudeV of the velocity vector and they are important for the treatment of atmospheric drag with the method of general perturbations. These series have been obtained with computerized Poisson series Manipulations. The results are given to order seven in the eccentricity, for both the Mean Anomaly and the True Anomaly.     

A FORTRAN-based Poisson series processor and its applications in celestial mechanics

The present article describes the design and applications of our Poisson series subroutine package developed and maintained since 1968. The programs are written in standard FORTRAN-77 and are almost independent of the wordlength of the particular computer. The system has no restriction on the number of polynomial and angular variables and the storage allocations are completely automatic, invisible to the user.The nucleus of the system consists of about 20 basic traffic subroutines that handle the terms of the different series. Besides these subroutines, we have a number of I/O routines as well as arithmetic subroutines and a large number of Celestial Mechanics applications such as the classical expansions of the Kepler Problem and several expansions of Disturbing Functions. A preprocessor has also been built, allowing the user to write code in a high-level language, such as Jefferys' Trigman, and then translate it in our call-statements.The system was developed on several different computers: first on the Univac 1108 at the Jet Propulsion Laboratory in 1968, then the IBM 360-91 at UCLA, Los Angeles, California and finally the CDC 6600 and CYBER 170/750 at the University of Texas, Austin, Texas. The latest version is entirely geared towards the IBM-PC and compatibles.     

A note on chromospheric fine structure at active region polarity boundaries

High resolution H filtergrams from Big Bear Solar Observatory reveal that some filamentary features in active regions have fine structure and hence magnetic field transverse to the gross structure and the zero longitudinal field line. These features are distinct from the usual active region filament, in which fine structure, magnetic field and filament are all parallel to the zero longitudinal field line. The latter occur on boundaries between regions of weaker fields while the former occur at boundaries between regions of stronger field.     

A note on antimatter meteors

It is argued here that unless antimatter meteors can be shown to possess some unambiguously unique characteristic not displayed by ordinary koinomatter meteors, it will be difficult to infer their existence given the standard interpretation of meteoroid structure. It is also argued, however, that the existence of antimatter meteors is extremely unlikely.     

A note on variable-G cosmologies

An example of a cosmological model with variable gravitational couplingG and a time-dependent cosmological term , has recently been presented. It has been shown that there is no creation of matter and that the rest mass of particles stays constant in this model. In this paper we will generalize the field equations to the case where bothG and depend both on time and position. It is shown that even in this case there may be no creation.     

A note on Kowalevski exponents and the non-existence of an additional analytic integral

In Hamiltonian systems with a homogeneous rational potential and two degrees of freedom, the presence of imaginary Kowalevski exponents implies the non-existence of an additional analytic integral, i.e., non-integrability of the system.     

A note on the very small grains (VSGs) observed at Halley's comet

The most striking feature in the spatial distribution of the smallest dust grains observed at Halley's comet by the VEGA-1 spacecraft is the sharp glitch at a cometocentric distance of about 180 000 km, which approximately corresponds to the so-called cometopause inside which the contaminated solar wind plasma was rapidly cooled. We propose that this glitch was caused by the electrostatic disruption of larger composite grains which rapidly charged up as they traversed the cometopause. The clear asymmetry in the distribution between the inbound and outbound portion of the spacecraft trajectory is also consistent with the dynamical effects of grain charging although other causes are not excluded.     

A note on critically rotating polytropes

The structure of critically rotating polytropes is calculated using two (reated) Roche-type approximation schemes, one of which has been developed for stellar models. Comparisons with other results are made as a validation of these methods in stellar structure calculations.     

A note on the averaging method

When time-averaged equations are used to discuss the secular behavior of dynamical systems, the action-angle variables conjugate to the action variables of the unperturbed motion of the system should be chosen as dependent variables; otherwise, the results are not correct.Presented at the Division of Dynamical Astronomy Meeting of the American Astronoming Society, Chapel Hill, N.C., U.S.A., December 4, 1976.     

A note on weak stability boundaries

This paper is devoted to clarify the algorithmic definition of the weak stability boundary in the framework of the planar Restricted Three Body Problem. The role of the invariant hyperbolic manifolds associated to the central manifolds of the libration points L ₁ and L ₂, as boundary of the weak stability region, is shown.     

A note on the Hori-Lie perturbation technique

In this paper we describe how to avoid the introduction of Hori's pseudo time in general planetary theory in the case of two planets.     

A note on the linear stellar model

For a purely gaseous self-gravitating stellar configuration with linear matter density distribution the total power generated by nuclear reactions is considered. The analytic connection between physical parameters of the macroscopic and microscopic levels of the stellar equilibrium configuration is revealed.     

A note on computer-aided planetary remote sensing

An example is presented to assist remote sensing scientists in their orientation towards the digital analysis of planetary image data.     

A note on the BBSAG visual observations

This Letter contains some comments on the communication by Diethelm and Locher (1988) concerning the period variations in the eclipsing binary systems EE Aqr, BZ Eri, IZ Per, and VZ Hya. Significance of the BBSAG visual observations has been discussed.     

A note on some static scalar-gravitational fields

In this note extending the technique developed for static fields by De (1964) to the static plane-symmetric solution of Taub (1951) and the conformastat gravitational universe of Das (1971) solutions for coupled gravitational and zero-rest-mass scalar fields have been obtained. Furthermore, it is found that the singularities of these empty spaces cannot be removed by the introduction of zero-rest-mass scalar fields.     

A second note on Hori-Lie perturbation technique

In this second note we show how to avoid the introduction of Hori's pseudo-time in analytical planetary theory in the case of the eight principal planets of our solar system excluding Pluto.     

A note on vacuum self-creation cosmological models

The vacuum field equations of the self-creation theory of gravitation are solved for the Robertson-Walker space-time, by using a correspondence to known solutions of general relativity.