Position and velocity perturbations for the determination of geopotential from space geodetic measurements

Although space geodetic observing systems have been advanced recently to such a revolutionary level that low Earth Orbiting (LEO) satellites can now be tracked almost continuously and at the unprecedented high accuracy, none of the three basic methods for mapping the Earth’s gravity field, namely, Kaula linear perturbation, the numerical integration method and the orbit energy-based method, could meet the demand of these challenging data. Some theoretical effort has been made in order to establish comparable mathematical modellings for these measurements, notably by Mayer-Gürr et al. (J Geod 78:462–480, 2005). Although the numerical integration method has been routinely used to produce models of the Earth’s gravity field, for example, from recent satellite gravity missions CHAMP and GRACE, the modelling error of the method increases with the increase of the length of an arc. In order to best exploit the almost continuity and unprecedented high accuracy provided by modern space observing technology for the determination of the Earth’s gravity field, we propose using measured orbits as approximate values and derive the corresponding coordinate and velocity perturbations. The perturbations derived are quasi-linear, linear and of second-order approximation. Unlike conventional perturbation techniques which are only valid in the vicinity of reference mean values, our coordinate and velocity perturbations are mathematically valid uniformly through a whole orbital arc of any length. In particular, the derived coordinate and velocity perturbations are free of singularity due to the critical inclination and resonance inherent in the solution of artificial satellite motion by using various types of orbital elements. We then transform the coordinate and velocity perturbations into those of the six Keplerian orbital elements. For completeness, we also briefly outline how to use the derived coordinate and velocity perturbations to establish observation equations of space geodetic measurements for the determination of geopotential.     

Secular influence of change in the heliocentric gravitation constant <Emphasis Type="Italic">GM</Emphasis><Subscript>⊙</Subscript> on evolution of orbits of Meteor Streams

The Secular influence of the change in the heliocentric gravitational constant on the evolution of orbits of Meteor Streams is examined by using the method of celestial mechanics with variable mass and variable gravitational constant. The change in the heliocentric gravitational constant includes the combined changes in the sun’s mass and gravitational constant obtained from the modern observation of planets and spacecraft. The perturbation equations are solved by expanding series with mean anomaly. The solutions of the secular and periodic variation of orbital elements are derived. The theoretical results for the secular variables of the semi-major axes, solar distances at perihelion and orbital periods are given for three Meteor Streams: Dracorids, Quadrantids, and Ursids. The numerical results are shown in Table 2. The discussion and conclusion are drawn.     

Adaptive particle swarm optimization for optimal orbital elements of binary stars

The paper presents an adaptive particle swarm optimization (APSO) as an alternative method to determine the optimal orbital elements of the star η Bootis of MK type G0 IV. The proposed algorithm transforms the problem of finding periodic orbits into the problem of detecting global minimizers as a function, to get a best fit of Keplerian and Phase curves. The experimental results demonstrate that the proposed approach of APSO generally more accurate than the standard particle swarm optimization (PSO) and other published optimization algorithms, in terms of solution accuracy, convergence speed and algorithm reliability.     

Compression of intensity interferometry signals

Correlations between photon currents from separate light-collectors provide information on the shape of the source. When the light-collectors are well separated, for example in space, transmission of these currents to a central correlator is limited by band-width. We study the possibility of compression of the photon fluxes and find that traditional compression methods have a similar chance of achieving this goal compared to compressed sensing.     

Gravitational Instability of Cylindrical Viscoelastic Medium Permeated with Non Uniform Magnetic Field and Rotation

The self-gravitating instability of an infinitely extending axisymmetric cylinder of viscoelastic medium permeated with non uniform magnetic field and rotation is studied for both the strongly coupled plasma (SCP) and weakly coupled plasma (WCP). The non uniform magnetic field and rotation are considered to act along the axial direction of the cylinder. The normal mode method of perturbations is applied to obtain the dispersion relation. The condition for the onset of gravitational instability has been derived from the dispersion relation under both strongly and weakly coupling limits. It is found that the Jeans criterion for gravitational collapse gets modified due to the presence of shear and bulk viscosities for the SCP, however, the magnetic field and rotation whether uniform or non uniform has no effect on the Jeans criterion of an infinitely extending axisymmetric cylinder of a self-gravitating viscoelastic medium.     

Probing Statistical Isotropy of Cosmological Radio Sources using Square Kilometre Array

There currently exist many observations which are not consistent with the cosmological principle. We review these observations with a particular emphasis on those relevant for the Square Kilometre Array (SKA). In particular, several different data sets indicate a preferred direction pointing approximately towards the Virgo cluster. We also observe a hemispherical anisotropy in the Cosmic Microwave Background radiation (CMB) temperature fluctuations. Although these inconsistencies may be attributed to systematic effects, there remains the possibility that they indicate new physics and various theories have been proposed to explain them. One possibility, which we discuss in this review, is the generation of perturbation modes during the early pre-inflationary epoch, when the Universe may not obey the cosmological principle. Better measurements will provide better constraints on these theories. In particular, we propose measurement of the dipole in number counts, sky brightness, polarized flux and polarization orientations of radio sources. We also suggest test of alignment of linear polarizations of sources as a function of their relative separation. Finally we propose measurement of hemispherical anisotropy or equivalently dipole modulation in radio sources.     

Probing Magnetic Fields with Square Kilometre Array and its Precursors

Origin of magnetic fields, its structure and effects on dynamical processes in stars to galaxies are not well understood. Lack of a direct probe has remained a problem for its study. The first phase of Square Kilometre Array (SKA-I), will have almost an order of magnitude higher sensitivity than the best existing radio telescope at GHz frequencies. In this contribution, we discuss specific science cases that are of interest to the Indian community concerned with astrophysical turbulence and magnetic fields. The SKA-I will allow observations of a large number of background sources with detectable polarization and measure their Faraday depths (FDs) through the Milky Way, other galaxies and their circum-galactic mediums. This will probe line-of-sight magnetic fields in these objects well and provide field configurations. Detailed comparison of observational data (e.g., pitch angles in spirals) with models which consider various processes giving rise to field amplification and maintenance (e.g., various types of dynamo models) will then be possible. Such observations will also provide the coherence scale of the fields and its random component through RM structure function. Measuring the random component is important to characterize turbulence in the medium. Observations of FDs with redshift will provide important information on magnetic field evolution as a function of redshift. The background sources could also be used to probe magnetic fields and its coherent scale in galaxy clusters and in bridges formed between interacting galaxies. Other than FDs, sensitive observations of synchrotron emission from galaxies will provide complimentary information on their magnetic field strengths in the sky plane. The core shift measurements of AGNs can provide more precise measurements of magnetic field in the sub parsec region near the black hole and its evolution. The low band of SKA-I will also be useful to study circularly polarized emission from Sun and comparing various models of field configurations with observations.     

Exact Bianchi type-II, VIII and IX perfect fluid cosmological models in Saez-Ballester theory of gravitation

Exact Bianchi type-II, VIII and IX cosmological models are obtained in a scalar tensor theory proposed by Saez and Ballester (Phys. Lett. A 113:467, 1986) with perfect fluid as a source. Some physical and geometrical properties of the models are studied. It is observed that the models are free from initial singularities and they are expanding with time.