Astrophysical applications of a boundary integral method for fluid dynamics

A boundary integral formulation for the dynamics of incompressible, inviscid, self-gravitating bodies is described. The method is applied to several problems of astrophysical interest: spheroidal equilibria (Maclaurin and Jeans), oscillations, and a simple version of tidal encounter and breakup.     

Initial value problem of space dynamics in universal Stumpff anomaly

In this paper, the initial value problem of space dynamics in universal Stumpff anomaly \(\psi\) is set up and developed in analytical and computational approach.For the analytical expansions, the linear independence of the functions \(\mathrm{U}_{{ j}} { (\psi;\varsigma)}\); \({j=0,1,2,3}\) are proved. The differential and recurrence equations satisfied by them and their relations with the elementary functions are given. The universal Kepler equation and its validations for different conic orbits are established together with the Lagrangian coefficients. Efficient representations of these functions are developed in terms of the continued fractions.

For the computational developments we consider the following items:

1. 1.
   Top-down algorithm for continued fraction evaluation.
    
2. 2.
   One-point iteration formulae.
    
3. 3.
   Determination of the coefficients of Kepler’s equation.
    
4. 4.
   Derivatives of Kepler’s equation of any integer order.
    
5. 5.
   Determination of the initial guess for the solution of the universal Kepler equation.
    

Finally we give summary on the computational design for the initial value problem of space dynamics in universal Stumpff anomaly. This design based on the solution of the universal Kepler’s equation by an iterative schemes of quadratic up to any desired order \(\ell\).     

On the two-dimensional inverse problem of dynamics

The authors extend the deduction of the equations satisfied by the force fields from inertial to rotating frames, when the curves of a certain family are known to be solutions for the equations of motion. Then Drǎmbâ's equation is obtained as a consequence of this result. The works of Hadamard and Moiseev are proved to be closely related to the inverse problem of dynamics.     

On some applications of the problem of many fixed centres to geophysics

In the present paper, using as examples the problems of four, five and six fixed centres, some applications of the problem of many fixed centres to geophysics are given.The paper was presented at the workshop on the theme The Use of Observations of the Artificial Earth Satellites in Geodesy, held in Slavsk (U.S.S.R.) from 14 to 19 April, 1980.     

The role of magnetohydrodynamics in heliospheric space plasma physics research

Magnetohydrodynamics (MHD) is a fairly recent extension of the field of fluid mechanics. While much remains to be done, it has successfully been applied to the contemporary field of heliospheric space plasma research to evaluate the macroscopic picture of some vital topics via the use of conducting fluid equations and numerical modeling and simulations. Some representative examples from solar and interplanetary physics are described to demonstrate that the continuum approach to global problems (while keeping in mind the assumptions and limitations therein) can be very successful in providing insight and large scale interpretations of otherwise intractable problems in space physics.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.     

Use of cyanobacteria for in-situ resource use in space applications

The regolith of other planetary bodies, such as the Moon and Mars, is rich in inorganic elements that could potentially be exploited for space applications. Lithotrophic microorganisms that are capable of utilising rocks as a growth substrate, and facilitate the extraction of elements, are ideal candidates for in-situ resource use. Of particular interest are the cyanobacteria, which have been suggested for applications, such as oxygen, fuel and biomass production, nutrient acquisition, and feedstock provisions. In this study, Gloeocapsa strain OU_20, isolated from a rock-dwelling community exposed to low Earth orbit; Leptolyngbya strain OU_13 and Phormidium strain OU_10, both isolated from a rock-dwelling community exposed to Mars simulated conditions; Chroococcidiopsis 029; Arthrospira platensis; Synechococcus elongatus; and Anabaena cylindrica, were examined as potential organisms for space in-situ resource use. Volcanic rocks, including basalt (low in SiO₂) analogous to martian and lunar basalt, rhyolite (high in SiO₂), and anorthosite analogous to lunar regolith were used as growth substrates. The growth rate and rock dissolution were significantly lower with rhyolite demonstrating the importance of silica content in defining the potential for in-situ resource use. Biological weathering resulted in the release of bio-essential elements from the rock matrix, highlighting the potential of cyanobacteria for applications such as bio-mining and nutrient acquisition, on other planets. A. cylindrica produced the maximum biomass with the three rock-types and the optimal value was obtained with the basalt. Exposure experiments demonstrated that A. cylindrica, Chroococcidiopsis 029, Gloeocapsa strain OU_20, Phormidium strain OU_10, and Leptolyngbya strain OU_13 were able to survive 28 days of exposure to desiccation and Mars simulated conditions, which is beneficial in case of system malfunction and for storage. The results from this study indicate that cyanobacteria can potentially be used for in-situ planetary resource acquisition.     

Selection criteria for continuous channel electron multipliers in space applications

Criteria for selecting continuous channel electron multipliers were applied to fifteen Mullard units without significantly affecting their overall lifetime. The gain fatigue vs accumulated counts, the change of the pulse height distribution during lifetime, the gain degradation vs count rates as well as the gain vs operating voltage and the resolution vs operating voltage have been investigated using a tritium source. The results provide several criteria to determine good, marginal and poor multipliers. From all tested devices 25% had a very low gain and did not operate satisfactory at the end of their lifetime investigations (4×10⁹ accumulated counts). 40% of all devices could be classified as good multipliers. Their main characteristic was a gain recovery phenomenon after 3×10⁹ accumulated counts with a progressive gain stabilizing. Multipliers classified as marginal exhibited some unexpected behaviour during the lifetime but a gain recovery phase and gain plateau region could be identified. Furthermore, the relative efficiency of the multipliers vs electron energy as a function of the operating voltage has been measured by using a near monoenergetic electron beam.Originally submitted to the journalSpace Science Instrumentation.     

On the physics of resonant disk-satellite interaction

Within the framework of a single derivation, we study the transfer of angular momentum in a disk subjected to a linear perturbation at Lindblad resonance, whenever the physics include friction, nonstationarity, or self-gravitation, pressure, and viscosity. Each of the above physical processes can be described by one parameter which indicates the main physics at work and the resonance width. We show that dissipation or waves are not formally necessary for a torque to appear, but only for the problem to remain stationary and/or linear. In this framework, the torque exerted at an isolated resonance is independent of the particular physics at work. We consider applications to numerical simulations, the impulse approximation, planetesimal accretion, and edges and gaps in planetary rings.     

On the physics of relativistic double layers

A model of a strong, time-independent, and relativistic double layer is studied. Besides double layers having the electric field parallel to the current the model also describes a certain type of oblique double layers. The Langmuir condition (ratio of ion current density to electron current density) as well as an expression for the potential drop of the double layer are derived. Furthermore, the distributions of charged particles, electric field, and potential within the double layer are clarified and discussed. It is found that the properties of relativistic double layers differ substantially from the properties of corresponding non-relativistic double layers.     

Equations of radiation gas dynamics in tetrad form for astrophysical applications

This paper deals with the representation of relativistic equations of gas dynamics with due regard to the general relativity theory effects in the form accepted and widely applied in the special relativity theory. With this purpose, a strict formal definition of a non-inertial co-moving reference frame without rotation is carried out on the basis of a tetrad formalism by use of the Fermi—Walker rules of transport of 4-frame. The equations of physical kinetics, relativistic collapse, Einstein's equations, equations of relatiivistic radiation gas dynamics for ideal and dissipative gases, Taub's equations for a shock wave, which allow for radiation and electron-positron pairs, are obtained in this reference frame. On the basis of the local Lorentz transformation and the Ricci rotation coefficients, these equations are written in the laboratory reference frame, in order to illustrate the fact that the general relativity effects can be simply taken into account in the equations having a form accepted in the special relativity theory.     

The ELP solution for the main problem of the moon and some applications

First derivatives of the ELP 2000 solution of the main problem have been obtained. They are used for computation of the lunar motion perturbations due to the Earth's oblateness and to secular terms in the solar eccentricity and perigee.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.     

The extended phase space formulation of the Vinti problem

The Vinti problem, motion about an oblate spheroid, is formulated using the extended phase space method. The new independent variable, similar to the true anomaly, decouples the radius and latitude equations into two perturbed harmonic oscillators whose solutions toO(J ₂ ⁴ ) are obtained using Lindstedt's method. From these solutions and the solution to the Hamilton-Jacobi equation suitable angle variables, their canonical conjugates and the new Hamiltonian are obtained. The new Hamiltonian, accurate toO(J ₂ ⁴ ) is function of only the momenta.     

Suprathermal particle distributions in space physics: Kappa distributions and entropy

The energization of a charged test-particle of mass m in contact with a large ensemble of charged particles of mass M at equilibrium is studied with the Fokker-Planck equation for Coulomb collisions and a quasi-linear diffusion operator for wave-particle interactions. The features of the nonequilibrium steady state velocity distribution of the test-particle system is studied as a function of the mass ratio m/M, and the relative strengths of the wave-particle interactions and Coulomb collisions. It is shown that the steady distribution function is not necessarily a Kappa distribution. The temperature of heavy minor ions given by the model is shown to vary linearly with the mass ratio as observed in the solar wind. The time evolution of the distribution function with and without the energization by wave-particle interactions is calculated and it is demonstrated that the Kullback relative entropy rather than the Tsallis nonextensive entropy rationalizes the results obtained.     

On helioseismic tests of basic physics

An important goal of helioseismology is to provide information about the basic physics and parameters that determine the structure of the solar interior. Here we discuss the procedures applied in such analyses, using as an example attempts to obtain significant constraints on the value of Newton's gravitational constant G from helioseismology. The analysis is based on complete direct and inverse helioseismic analysis of a set of accurate observed acoustic frequencies. We confirm, as found by previous investigations based on different approaches, that the actual level of precision of the helioseismic inferences does not allow us to constrain G with a precision better than that which can be reached with direct experimental measurements. The conclusion emphasizes the importance in helioseismic inferences of considering not only the accuracy with which solar oscillations are measured, but also the effect of uncertainties in other aspects of the model computation and helioseismic analysis.     

Notes on applications of General Relativity in free space

Varying the step, at which Lorentz signature is introduced in the scheme of applications of general relativity outside the material distribution, new solutions can be obtained. The interpretations of these solutions can be achieved if the field equations R_μv = 0 are written in a wider space than the Riemannian one. A counter example is given in favour of this claim.