Surface photometry of theHii regions S254–S257

The surface photometry of S254–S257 has been carried out by means of a wide range image processing technique in the reduction system. The photographic plates in the H+[NII] andV-bands are taken with the Schmidt telescope. Especially, we have obtained the calibrated map of theHii region, superposing two or more plates with different exposure times, and removing the star images. Three kinds of calibrated maps of theHii regions are drawn: (1)E-map in the (H+[NII]+continuum) (2)V-map in the continuum atV-band, (3)(E-V)-map in the (H+[NII]) line emission. The intensity profiles across the nebular centers were also obtained. Based on calibrated maps, the morphological structure and mass distribution of S255 and S257 are discussed. The location of observed nebulae on the (m _H–m _v) diagram, wherem _H andm _v denote the surface brightness, expressed in the magnitude per square arcmin, is shown together with that of some other nebulae. Some arguements on the age sequence of observedHii regions are presented.     

A stabilization procedure for the differential equations of the symmetric gyroscope including perturbing torques

This paper shows that for the free symmetric top a formulation of the equations of motion is possible, which is Liapunov stable. The formalism applied is equivalent to the conservative stabilization of the Keplerian problem. The perturbed problem appears in -stable form. This stabilization procedure could be useful in celestial mechanics, if the gyroscopic motion of a satellite is considered and one is interested in the exact position of the angles.     

The clustering of Lα absorption lines in the QSO spectra

For nine published high-resolution QSO spectra a correlation analysis of their L forest lines has been performed. The two-point correlation functions show some quasi-periodic structure of magnitude ||0.3. Their characteristic separation along the line-of-sight amounts to s ₀=3×10^–3 or to s ₀=5×10^–3 for =1 and 0.2, respectively. Especially the distribution of nearest neighbouring line positions in two close QSO pairs allows for the interpretation that the absorption clouds lie in sheet-like structures as predicted by the pancake theory. The correlation data contain some hints on metal absorbers within the forest of unidentified lines.     

A two-dimensional multi-band spectroheliograph

The present paper describes a two-dimensional multi-band spectrograph which is located at Yunnan Observatory (25° N 103° E), Kunming. The instrument consists of a coelostat system with an aperture of 40 cm, and spatial resolution better than 1 under excellent seeing, and a spectrograph equipped with a plane reflecting grating. It can simultaneously obtain spectral data in ten bands, including the Balmer lines, metallic lines [Fei 6173 ,D _{1, 2, 3}, Mg, and Caii (H + K)] and Heii 4686 . We are able to control the observational processes by means of a computer and obtain the following data synchronously or quasi-synchronously: multi-band spectra, H filtergrams, magnetic field, and white light. With the aid of H slit-jaw filtergrams, we can determine where and when the spectral data are obtained and, on the basis of analysing the spectral line profiles, we can understand the physical characteristics of an active region and derive the fields of physical parameters. For the line-of-sight velocities, the values measured are as high as hundreds of kilometers per second and as low as a few kilometers per second.     

On the motion of a satellite in resonance with its rotating planet

The influence of resonance perturbations due to the gravitational field of an oblate planet on its satellite whose motion is commensurable with rotation of the planet has been investigated. It has been shown that in special case of the critical inclination or circular orbit the Lagrange equations can be integrated for all resonance terms simultaneously. The method is applied to the investigation of the motion of the 12-hour communication and navigation satellites of the Molniya and Navstar type. The computations has been performed by the use of four models of the geopotential.     

The stability parameters of three-body periodic orbits

Formulae containing the elements of the variational matrix are obtained which determine the linear iso-energetic stability parameters of periodic orbits of the general three-body problem. This requires the numerical integration of the variational equations but produces the stability parameters with the effective accuracy of the numerical integration. The procedure is applied for the determination of horizontally critical orbits among the members of sets of vertical-critical periodic orbits of the threebody problem. These critical-critical orbits have special importance as they delimit the regions in the space of initial conditions which correspond to possibly stable three-dimensional periodic motion of low inclination.     

A new time element for a general time transformation

The paper introduces a new time element to be used with a general time transformation for satellite equations of motion. The purpose of this time element is to reduce the growth of the numerical errors with respect to the time integration. It is characteristic for the new time element , that the relation between the timet and the element does not depend on the independent variables.     

Liapunov stability of spinning satellites with long flexible appendages

The equations of motion are derived for the case of a spinning satellite which has a central rigid body, and long flexible appendages which are nominally in the spin plane. The major-axis theorem is found to be necessary, but not sufficient for this case, and appropriate sufficiency criteria are derived from a Liapunov function. The results are presented in a form amenable to satellite design.     

A study on Bianchi-IX cosmological model

In this paper the inflationary solutions are studied for the Bianchi-IX space-time in presence of a massless scalar field with a flat potential. Also a class of cosmological solutions of massive strings are obtained following the techniques used by Letelier and Stachel. Some solutions are calculated for pure massive strings following the Takabayashi equation of state =(1+w).     

Application of the Jacobi integral for the investigation of satellite librations around the centre of mass in a gravitational field

This paper deals with a three-dimensional rotationally and dynamically symmetrical satellite. The centre of mass of the satellite moves in a circular orbit. The existence of two first integrals of motion enables one to transform the system of differential equations to a special form facilitating the choice of the zero-approximation solution. The angles of precession and nutation as well as the amplitude functionk ²(t) are taken as variables of the motion. The first approximation solution is constructed for the case of spatial libration of the satellite axis of dynamical symmetry about the position of stable equilibrium. The series representing the functionk ²(t) is fast convergent due to the fast convergence of the expansions for elliptic functions.     

Expansions of elliptic motion based on elliptic function theory

New expansions of elliptic motion based on considering the eccentricitye as the modulusk of elliptic functions and introducing the new anomalyw (a sort of elliptic anomaly) defined byw=u/2K–/2,g=amu–/2 (g being the eccentric anomaly) are compared with the classic (e, M), (e, v) and (e, g) expansions in multiples of mean, true and eccentric anomalies, respectively. These (q,w) expansions turn out to be in general more compact than the classical ones. The coefficients of the (e,v) and (e,g) expansions are expressed as the hypergeometric series, which may be reduced to the hypergeometric polynomials. The coefficients of the (q,w) expansions may be presented in closed (rational function) form with respect toq, k, k=(1–k ²)^1/2,K andE, q being the Jacobi nome relatedk whileK andE are the complete elliptic integrals of the first and second kind respectively. Recurrence relations to compute these coefficients have been derived.on leave from Institute of Applied Astronomy, St.-Petersburg 197042, Russia     

The motion of a satellite in an axi-symmetric gravitational field

The equations for the variation of the osculating elements of a satellite moving in an axi-symmetric gravitational field are integrated to yield the complete first-order perturbations for the elements of the orbit. The expressions obtained include the effects produced by the second to eighth spherical harmonics. The orbital elements are presented in the most general form of summations by means of Hansen coefficients. Due to their general forms it is a simple matter to estimate the perturbations of any higher harmonic by simply increasing the index of summation. Finally, this paper gives the respective general expressions for the secular perturbations of the orbital elements. The formulae presented should be useful for the reductions of Earth-satellite observations and geopotential studies based on them.List of Symbols semi-major axis - C _jk ⁿ (, ) cosine functions of and - e eccentricity of the orbit - f acceleration vector of perturbing force - f sin²t - i inclination of the orbit - J _n coefficients in the potential expansion - M mean anomaly - n mean motion - p semi-latus rectum of the orbit - R, S, andW components of the perturbing acceleration - r radius-vector of satellite - r magnitude ofr - S _jk ⁿ (, ) sine functions of and - T time of perigee passage - u argument of latitude - U gravitational potential - true anomaly - V perturbing potential - G(M₊+m) (gravitational constant times the sum of the masses of Earth and satellite) - _n,k coefficients ofR component of disturbing acceleration (funtions off) - _n,k coefficients ofS andW components of disturbing acceleration (functions off) - mean anomaly at timet=0 - X ₀ ^n,m zero-order Hansen coefficients - argument of perigee - right ascension of the ascending node     

Multistep methods of numerical integration using back-corrections

A new class of linear multistep methods is proposed for the solution of the equations of motion of certain dynamical systems encountered in celestial mechanics and astrodynamics. These methods are distinguished from the classical predictor-corrector methods in that they permit back-corrections of the solution to be made. As the integration advances in time, the numerical solution is corrected or improved at certain points in the past. The enhanced numerical stability of these methods allows the meaningful application of high-order algorithms. Consequently, stepsizes larger than those attainable with the classical methods may be adopted and thus greater over-all efficiency may be realized. The application of these methods to the problem of determining the orbit of an artificial satellite is accomplished and the results are compared with those obtained using classical methods.     

A satellite relative motion model including $$J_2$$ and $$J_3$$J3 via Vinti’s intermediary

Vinti’s potential is revisited for analytical propagation of the main satellite problem, this time in the context of relative motion. A particular version of Vinti’s spheroidal method is chosen that is valid for arbitrary elliptical orbits, encapsulating \(J_2\), \(J_3\), and generally a partial \(J_4\) in an orbit propagation theory without recourse to perturbation methods. As a child of Vinti’s solution, the proposed relative motion model inherits these properties. Furthermore, the problem is solved in oblate spheroidal elements, leading to large regions of validity for the linearization approximation. After offering several enhancements to Vinti’s solution, including boosts in accuracy and removal of some singularities, the proposed model is derived and subsequently reformulated so that Vinti’s solution is piecewise differentiable. While the model is valid for the critical inclination and nonsingular in the element space, singularities remain in the linear transformation from Earth-centered inertial coordinates to spheroidal elements when the eccentricity is zero or for nearly equatorial orbits. The new state transition matrix is evaluated against numerical solutions including the \(J_2\) through \(J_5\) terms for a wide range of chief orbits and separation distances. The solution is also compared with side-by-side simulations of the original Gim–Alfriend state transition matrix, which considers the \(J_2\) perturbation. Code for computing the resulting state transition matrix and associated reference frame and coordinate transformations is provided online as supplementary material.     

Wall temperature oscillation on convection flow in a rotating fluid with hall and ion-slip currents

An analysis of Hall and ion-slip current effects on the MHD free-convection flow of a partiallyionised gas past an infinite vertical porous plate in a rotating frame of reference is carried out. A strong magnetic field is applied perpendicular to the plate and the plate temperature oscillates in time about a constant non-zero mean. The problem has been solved for the velocity and temperature fields and the effects of _e (the Hall parameter), _i (the ion-slip parameter),E _r (rotation parameter), and have been discussed and shown graphically.     

A model of interplanetary and coronal magnetic fields

A model of the large-scale magnetic field structure above the photosphere uses a Green's function solution to Maxwell's equations. Sources for the magnetic field are related to the observed photospheric field and to the field computed at a source surface about 0.6 R above the photosphere. The large-scale interplanetary magnetic field sector pattern is related to the field pattern at this source surface. The model generates magnetic field patterns on the source surface that compare well with interplanetary observations. Comparisons are shown with observations of the interplanetary magnetic field obtained by the IMP-3 satellite.     

The French-Russian 3 satellite γ-burst experiment

A -burst monitoring network, involving an eccentric satellite and two interplanetary spacecraft, is planned for completion in 1977. the satellite in earth orbit will have 2 sets of scintillation counters with moderate spatial resolution, covering an energy range of 20 keV-1 MeV, and viewing about 2 steradians. Each of the interplanetary probes will have one set of scintillation counters. The intersatellite timing accuracy will be about 10 ms, which will permit the determination of the arrival direction withon about 5 are min. Special attention is given to fine time resolution and the detection of bursts with relatively long onset times.Paper presented at the COSPAR Symposium on Fast Transients in X-and Gamma-Rays, held at Varna, Bulgaria, 29–31 May, 1975.     

Some investigations into the atmospheric drag problem

This paper calls into question the validity of the well-known formulae for the perturbations in the Keplerian elements, over one revolution of an orbit, for the motion of a drag-perturbed artificial satellite. These formulae are derived from Gauss's form of the planetary equations, by averaging over a single revolution of the orbit, and using the eccentric anomaly as the independent variable.It is shown that for light balloon-type satellites in near-circular orbits neither the eccentric anomaly nor the true longitude is a suitable choice of independent variable for the averaging procedure. Under these circumstances, it would seem that simple formulae for the variations in the elements cannot be derived from Gauss's equations.     

Effects of gravity-gradient torque on the rotational motion of A triaxial satellite in a precessing elliptic orbit

A method of general perturbations, based on the use of Lie series to generate approximate canonical transformations, is applied to study the effects of gravity-gradient torque on the rotational motion of a triaxial, rigid satellite. The center of mass of the satellite is constrained to move in an elliptic orbit about an attracting point mass. The orbit, which has a constant inclination, is free to precess and spin. The method of general perturbations is used to obtain the Hamiltonian for the nonresonant secular and long-period rotational motion of the satellite to second order inn/0, wheren is the orbital mean motion of the center of mass and0 is a reference value of the magnitude of the satellite's rotational angular velocity. The differential equations derivable from the transformed Hamiltonian are integrable and the solution for the long-term motion may be expressed in terms of Jacobian elliptic functions and elliptic integrals. Geometrical aspects of the long-term rotational motion are discussed and a comparison of theoretical results with observations is made.     

Tidal effects and the motion of a satellite

The effect of resonant planetary perturbations on the evolution of the orbit of a satellite driven by tidal forces is studied in this paper. The basic equations that govern it are similar to the equations found in orbit-orbit and in spin-orbit couplings. The general form of these equations is: A general treatment of such equations, proposed earlier (J. Kovalevsky, in Dynamical Trapping and Evolution of the Solar system, IAU Colloquium n^o74, V. V. Markellos and Y. Kozai, eds., 1983) is sketched.In particular, the effects of the large long periodic variations of the excentricity e' of the planet are analysed on an example taken from the lunar theory and the Earth's general theory due to Bretagnon.The argument of the well known planetary term =18 V-16T due to the tidal friction and quasi-periodic variations due to the presence of e' in the expression of the mean motion of the Moon. Their joint effect, has been to produce in the past resonant situations for this argument that repeated more than 100 times. Every such situation can be treated by equation (1).Numerical integration, using conditions that might have occurred while or similar other arguments were quasi resonant, have produced the following results: (a) In some cases, the argument becomes temporarily resonant. Between the capture to and the escape from the resonance, the semi-major axis undergoes oscillations, but the tidal secular evolution is stopped. (b) In other cases, the argument is not trapped into a resonant conditions, but the semi-major axis undergoes a quick change while d/dt is close to zero.A number of arguments that have been quasi resonant in the past history of the Earth-Moon system has been identified from the Chapront and Chapront-Touzé Lunar Theory. It appears that the phenomena described are frequent features in the evolution of the Lunar orbit.