Gravitational Parameter Research Articles

Studying the Properties of Spacetime with an Improved Dynamical Model of the Inner Solar System

Physical properties of the Sun (orientation of rotation axis, oblateness coefficient J2⊙, and change rate of the gravitational parameter μ˙⊙) are determined using a dynamical model describing the motion of the Sun, planets, the Moon, asteroids, and Trans-Neptunian objects (TNOs). Among the many kinds of observations used to determine the orbits and physical properties of the bodies, the most important for our study are precise interplanetary ranging data: Earth–Mercury ranges from MESSENGER spacecraft and Earth–Mars ranges from Odyssey and MRO. The findings allow us to improve the model of the Sun in modern planetary ephemerides. First, the dynamically determined direction of the Sun’s pole is ≈2° off the visible axis of rotation of the Sun’s surface, which is corroborated by present knowledge of the Sun’s interior. Second, the change rate of the Sun’s gravitational parameter is found to be smaller (in absolute value) than the nominal value derived from the estimate of mass loss through radiation and solar wind. Possible interpretations are discussed.

The Variation of G and Λ in Cosmology

The idea of varying constants of nature is very old, and has commanded a lot of attention since first mooted. The variation in the gravitational parameter G and cosmological parameter Λ is still an active area of research. Since the idea of a varying G was introduced by Dirac almost a century ago, there are even theories that have variable G such as the Brans–Dicke theory and the scale covariant theory. Both these theories also have a varying Λ in their full generalisations. A varying Λ was also introduced around the same time as that of varying G. It is interesting to note that a possible solution to the cosmological constant problem can be realised from a dynamic Λ. In this work, we focus on a varying Λ and G framework. In almost all studies in the simplest framework of variables Λ and G, it is found that one of them has to increase with time. However, observations and theoretical considerations indicate that both Λ and G should decrease with time. In this paper, we propose a solution to this problem, finding theories in which both Λ and G decrease with time.

Shock wave propagation in a real gas with or without gravitational field in the presence of magnetic field and monochromatic radiation via group invariance method

PurposeThis article aims to find the similarity solutions for the one-dimensional motion of spherical symmetric shock wave in non-ideal gas influenced by the azimuthal magnetic field and monochromatic radiation in the presence or absence of gravitational field. This paper also aims to study the effects of physical parameters on the strength of shock wave, and on the flow variables in the flow-field region behind the shock front.Design/methodology/approachThe Roche model is used to describe the gravitational field effects due to a massive nucleus at the point of symmetry. To derive the similarity solutions, the Lie group symmetry method has been used. Also, the numerical solutions to the present problem are obtained by using Rung–Kutta method of the fourth order with the use of Mathematica software. The effects of variation in the parameter of non-idealness of the gas, the gravitation parameter, the strength of the ambient magnetic field and the adiabatic index of the gas on the shock wave, and on the flow variables is discussed. A comparative study between with and without gravitational field is also, made.FindingsFor different choices of the arbitrary constants that appeared in the solution of infinitesimal generators, we have obtained seven distinct cases of similarity solutions. In the absence of the gravitational field, the similarity solution exists to the power and exponential law shock paths, but in the presence of gravitational field, the similarity solution exists to the power law shock path case only. In the absence of gravitational field, the shock strength is enhanced in the exponential law shock path case in comparison to the power law shock path case. It is found that the shock wave decays with an increase in the value of the adiabatic exponent, the strength of magnetic field, non-idealness of the gas or gravitational parameter.Research limitations/implicationsThe consideration of medium under the influence of gravitational field due to a heavy nucleus at the center and presence of magnetic field decrease the shock strength. This result may be helpful in designing space vehicle and jet engine.Practical implicationsThe result of the present study may be used in the analysis of data from the measurements by space craft in the solar wind and in neighborhood of the Earth’s magnetosphere.Social implicationsThe obtained results may be used for mankind.Originality/valueThe study of spherical shock wave propagation influenced by monochromatic radiation and azimuthal magnetic field in a non-ideal gas with or without gravitational field has yet to be discussed by any authors by using the Lie group symmetry method. In this article, we have discussed all possible cases of similarity solutions using the Lie group symmetry method, which is not studied by anyone as known to us.

Equivalence of magnetic flux and energy

Magnetic flux and energy equivalence is the principle that everything that has magnetic flux has an equivalent amount of energy, and vice versa. The main methods used: transformation of natural units, algebra, analogy. The equivalence of magnetic flux and energy, despite its widespread use in describing the principles of physics, has not yet been formulated. This paper presents the formula for this equivalence. This is done based on known measurement systems, parameters and principles of physics. Five examples (Stoney units, Planck units, standard gravitational parameter, Lorentz force, and Ampere force) of the algebraic representation of this principle show its universality. Five examples should justify the universality of the new principle and its use in physics and astrophysics. Using the equivalence of magnetic flux and energy, new physical units of mass and magnetic flux are proposed, each of which is suitable for measuring both mass and magnetic flux. Natural values of electric current and voltage, linear density of electric capacitance and inductance, linear density of magnetic flux, linear density of electric charge, as well as natural units of electric voltage and current, electrical resistance, magnetic flux, electrical capacitance and inductance are also described. The article presents the Einstein field equation (additional magnetic stress–energy–momentum tensor) and a standard astrophysical parameter for refining the orbits of celestial bodies.

Similarity solution for the magnetogasdynamic shock wave in a self-gravitating and rotating ideal gas under the influence of radiation heat flux

The Lie invariance method is used to analyze the one-dimensional, unsteady flow of a cylindrical shock wave in a rotating, self-gravitating, radiating ideal gas under the influence of an axial or azimuthal magnetic field, with an emphasis on adiabatic conditions. The analysis assumes a stationary environment just ahead of the shock wave and considers variations in fluid velocity, magnetic field, and density within the perturbed medium just behind the shock front. In the governing equations, the impact of thermal radiation under an optically thin limit is integrated into the energy equation. Utilizing the Lie invariance method, the set of partial differential equations governing the flow in this medium is transformed into a system of nonlinear ordinary differential equations (ODEs) using similarity variables. Two distinct cases of similarity solutions are obtained by selecting different values for the arbitrary constants associated with the generators. Among these cases, one yields similarity solutions assuming a power-law shock path and the other an exponential-law shock path. For both cases, the resulting set of nonlinear ODEs are numerically solved using the 4th-order Runge–Kutta method in MATLAB software. The article thoroughly explores the influence of various parameters, including γ (adiabatic index of the gas), Ma−2 (Alfvén–Mach number), σ (ambient density exponent), l1 (rotational parameter), and G0 (gravitational parameter) on the flow properties. The findings are visually presented to offer a comprehensive insight into the effects of these parameters.

Uncertainties associated with integral-based solutions to geodetic boundary-value problems

Physical geodesy applies potential theory to study the Earth’s gravitational field in space outside and up to a few km inside the Earth’s mass. Among various tools offered by this theory, boundary-value problems are particularly popular for the transformation or continuation of gravitational field parameters across space. Traditional problems, formulated and solved as early as in the nineteenth century, have been gradually supplemented with new problems, as new observational methods and data are available. In most cases, the emphasis is on formulating a functional relationship involving two functions in 3-D space; the values of one function are searched but unobservable; the values of the other function are observable but with errors. Such mathematical models (observation equations) are referred to as deterministic. Since observed data burdened with observational errors are used for their solutions, the relevant stochastic models must be formulated to provide uncertainties of the estimated parameters against which their quality can be evaluated. This article discusses the boundary-value problems of potential theory formulated for gravitational data currently or in the foreseeable future used by physical geodesy. Their solutions in the form of integral formulas and integral equations are reviewed, practical estimators applicable to numerical solutions of the deterministic models are formulated, and their related stochastic models are introduced. Deterministic and stochastic models represent a complete solution to problems in physical geodesy providing estimates of unknown parameters and their error variances (mean squared errors). On the other hand, analyses of error covariances can reveal problems related to the observed data and/or the design of the mathematical models. Numerical experiments demonstrate the applicability of stochastic models in practice.

Simultaneous geometric calibration and orbit-attitude determination of Hayabusa2’s deployable camera (DCAM3)

Hayabusa2’s deployable camera (DCAM3) was deployed from the spacecraft near the asteroid Ryugu to successfully monitor the artificial cratering experiment. Scientific analyses of the observed impact ejecta require accurate determination of the camera’s position and orientation. However, in contrast to conventional spacecraft operations, DCAM3 lacked the capability to acquire orbit tracking data and attitude sensor data due to its limited onboard resources. Even though the optical images obtained by DCAM3 itself are the only source of geometric information, they were subject to significant distortion caused by the rolling shutter effect and lens distortion. This research is, therefore, designed to simultaneously estimate the image distortion and the orbital and attitude motions of DCAM3, relying solely on its image data. The relative geometry between the camera and the asteroid is reconstructed from the geographic information of the observed feature points by incorporating distortion effects. The proposed method involves segmenting the geometry reconstruction, with more than ten thousand feature measurements, into smaller-scale least-squares problems. The image-based estimation yields consistent distortion, orbit, and attitude solutions with pixel-scale accuracy. The analysis results indicate that DCAM3 experienced significant nutation of its optical axis during ballistic flight in a semi-elliptical orbit. In addition, these motions were sensitive enough to simultaneously determine system parameters, such as the gravitational parameter of Ryugu and the inertia moment of DCAM3. This paper illustrates the potential of deployable camera systems as a promising option for enhancing the scientific and engineering aspects of asteroid exploration.

Space time energy equivalence

Space–time–energy equivalence is the principle that everything that has space and time (in the presence of a constant force with an impact point) has an equivalent amount of energy, and vice versa. This equivalence is widespread in physics and astrophysics. Five examples (Stoney units, Planck units, Newton's law and Interaction of light rays, standard gravitational parameter and Coulomb's law) of the algebraic notation of this principle show its universality. Five examples (repetitions) of the same principle should justify the universality of the new principle and its use in physics and astrophysics. The proposed equivalence reveals the functional relationship between physical constants: Planck's constant, electric charge of an electron, vacuum permittivity and vacuum permeability. The realization of this equivalence will allow, through deepening the understanding of the nature of space–time, to take a fresh look at physics, when describing natural laws and principles.

Physical characterization of cumin (Cuminum cyminum L.) schizocarps of different origins cultivated in Morocco

An initial investigation on the physical traits of the cumin (Cuminum cyminum L.) schizocarps was examined in order to select the best genotypes of cumin grown in three regions of Morocco (Drâa-Tafilalet, Marrackech-Safi, and Oriental). This operation was conducted on 34 cumin accessions from six origins (local, India, Syria, Egypt, Turkey, and Saudi Arabia). To evaluate differences between the physical properties among accessions, length, width, thickness, and both the volumetric mass and the thousand-schizocarp mass were measured. Geometric properties (geometric mean diameter, sphericity index, specific mass and surface area) and gravitational parameters (bulk density, true density, and porosity) were calculated for each accession. Heritability (broad sense), phenotypic and genetic variabilities are also assessed. The average values of the evaluated parameters were found to be significantly different (p < 0.01) between accessions. The physical characteristics of schizocarps were significantly influenced by their origin, cultivated provinces and irrigation methods. Length, width, thickness and length of style range on average from 5.7 to 6.8 mm, 1.5 to 2.5 mm, 1.2 to 1.8 mm and 0.6 to 0.9 mm, respectively. Local and Egyptian accessions were the best-sized accessions. Regarding the weight, the Indian accession C11 registered the best volumetric mass 52.9 g, while the thousand-mass was found to be higher in the local accession from Zagora C19 with 7.3 g. The results showed that the phenotypic coefficient of variation (PCV) was higher than the genotypic coefficient of variation (GCV). The highest PCV and GCV were length of style (30.0%) and true density (24.4%), respectively. Volumetric mass had the highest value of heritability (99%). PCA analysis of seed origin showed clearly the ordination of cumin schizocarps into three groups. The big-sized schizocarps group is composed of local and Egyptian accessions, while the Saudi Arabia accession was individualized in a single group. Regarding the cultivated zone in Morocco, the ordination of schizocarps according to the province revealed four distinct groups. Finally, this study showed that irrigation mode may also affect the physical properties of cumin schizocarps.

Gravitational slip parameter and gravitational waves in Einstein–Cartan theory

We study the evolution of scalar and tensor cosmological perturbations in the framework of the Einstein–Cartan theory of gravity. The value of the gravitational slip parameter which is defined as the ratio of the two scalar potentials in the Newtonian gauge, can be used to determine whether or not the gravity is modified. We calculate the value of slip parameter in the Einstein–Cartan cosmology and show that it falls within the observed range. We also discuss the evolution of the cosmic gravitational waves as another measure of the modification of gravity.

Wave-optics limit of the stochastic gravitational wave background

The stochastic gravitational wave background (SGWB) is a rich resource of cosmological information, encoded both in its source statistics and anisotropies induced by propagation effects. We provide a theoretical description of it, without employing tools which rely on the geometric optics assumption. Our formalism is based on the so-called classical matter approximation and it is able to capture wave-optics effects, such as interference and diffraction. We show that the interaction between the gravitational waves and the cosmic structures along the line-of-sight produce observable scalar and vector polarization modes, on top of modulating the tensorial ones. We build the two point correlation function describing the statistics of the SGWB, and introduce the intensity and gravitational Stokes parameters for all its components. In the case of an unpolarized, Gaussian and statistically homogeneous SGWB, we show that the interaction with matter modulates its intensity and does not generate a net difference between left- and right-helicity tensor and vector modes, as expected. We demonstrate that, in order to produce QT- and UT-tensor polarization modes the background must possess a hexadecapole anisotropy, while a quadrupole anisotropy can source the vector QV- and UV-Stokes parameters.

Orbital dynamics in the vicinity of asteroid 4660 Nereus

Spacecrafts operating in close proximity to small celestial bodies within our Solar System, such as asteroids, face dynamic environments that differ significantly from those encountered in the near-Earth space. Understanding the characteristics of orbital dynamics in the vicinity of asteroids is essential for the successful execution of asteroid exploration missions. Focusing on the asteroid 4660 Nereus, this paper studies the equilibrium points of it and the potentially natural, long-lifetime orbits subject to perturbations from both the asteroid's non-spherical gravitational field and the solar radiation pressure (SRP). Using the semi-analytical method based on averaged Lagrange planetary equations (LPEs), heliotropic and terminator orbits are found more likely to have long lifetimes. It is noteworthy that the conventional near-equatorial heliotropic orbits around Nereus struggle to maintain a long lifetime. In contrast, orbits characterized by a specific inclination and geometry where the apocenter approximately points toward the Sun tend to offer prolonged lifetimes. Moreover, the impact of variations in SRP, gravitational parameter, and pole direction on feasibility of long-term orbit solutions has been explored, resulting in an enhanced comprehension of the intricate orbital dynamics. This study contributes valuable insights for the design of exploration orbits in the vicinity of the Nereus asteroid.

Propagation of magnetogasdynamics spherical shock wave in a gravitating gas with radiation heat flux

This article presents a mathematical model for characterizing the dynamic behavior of spherical shock waves in a self-gravitating, radiating ideal gas with the presence of an azimuthal magnetic field, emphasizing adiabatic conditions. The analysis assumes that the environment just ahead of the shock wave is stationary, and it accounts for variations in density, magnetic field, and fluid velocity within the disturbed medium just behind the shock front. Furthermore, the impact of thermal radiation within the context of an optically thin limit is incorporated into the energy equation of the governing system. Employing the Lie invariance method, the set of partial differential equations governing the flow within this medium is transformed into a system of nonlinear ordinary differential equations through the use of similarity variables. Four distinct cases of similarity solutions are derived by selecting different values for the arbitrary constants associated with the generators. Among these four cases, only two yield similarity solutions, one assuming a power-law shock path and the other an exponential-law shock path. In the case of a power-law shock path, the resulting set of nonlinear ordinary differential equations is numerically solved using the 4th-order Runge-Kutta method in MATLAB software. The article thoroughly discusses the influence of various parameters, including γ (adiabatic index of the gas), Ma−2 (Alfvén–Mach number), ϕ (ambient density exponent), and G0 (gravitational parameter), on the flow properties. The findings are presented graphically to provide a comprehensive understanding of the effects of these parameters.

Understanding the Predication Mechanism of Deep Learning through Error Propagation among Parameters in Strong Lensing Case

The error propagation among estimated parameters reflects the correlation among the parameters. We study the capability of machine learning of “learning” the correlation of estimated parameters. We show that machine learning can recover the relation between the uncertainties of different parameters, especially, as predicted by the error propagation formula. Gravitational lensing can be used to probe both astrophysics and cosmology. As a practical application, we show that the machine learning is able to intelligently find the error propagation among the gravitational lens parameters (effective lens mass M L and Einstein radius θ E ) in accordance with the theoretical formula for the singular isothermal ellipse (SIE) lens model. The relation of errors of lens mass and Einstein radius, (e.g., the ratio of standard deviations ) predicted by the deep convolution neural network are consistent with the error propagation formula of the SIE lens model. As a proof-of-principle test, a toy model of linear relation with Gaussian noise is presented. We found that the predictions obtained by machine learning indeed indicate the information about the law of error propagation and the distribution of noise. Error propagation plays a crucial role in identifying the physical relation among parameters, rather than a coincidence relation, therefore we anticipate our case study on the error propagation of machine learning predictions could extend to other physical systems on searching the correlation among parameters.

Mixed convection of transient MHD stagnation point flow over a stretching sheet with quadratic convection and thermal radiation

AbstractThis study investigates the influence of quadratic (nonlinear) convection in transient magnetohydrodynamic (MHD) combined convection over a two‐dimensional stretching sheet. It explores the effects of thermal radiation, suction, and heat sources or sinks. The Crank–Nicholson implicit finite difference method is employed for numerical computations. The significance lies in considering secondary convection, which is crucial in understanding nonlinear convective effects affecting flow and heat transfer properties. The study aims to advance our comprehension of how secondary convection impacts the overall system behavior. Through numerical calculations validated against existing literature, strong agreement is demonstrated. The study evaluates secondary convection effects, magnetic, buoyancy, gravitational parameters, Prandtl number, and radiation parameters. Notably, strong quadratic convection alters flow patterns, affecting velocity and temperature profiles. Moreover, it is observed that when increasing the nonlinear (quadratic) convective factors, the temperature profile increases for and decreases for . The prevalence of nonlinear or second‐order convection highlights magnetic dominance. In essence, this research enhances our understanding of complex convection interactions in MHD flow, shedding light on the role of secondary convection in shaping system behavior.

Constraining a one-dimensional wave-type gravitational wave parameter through the shadow of M87* via Event Horizon Telescope

During the glorious success of the EHT in providing the first image of a black hole, numerous papers have been published about the effect of different astrophysical environments on black hole geometry. Motivated by the work on how gravitational wave affects the shadow of a Schwarzschild black hole [Eur. Phys. J. C 10.1140/epjc/s10052-021-09287-2], we extend it by considering a quantum correction on the black hole through the extended uncertainty principle (EUP). Along with this correction, we probe the gravitational wave’s effect on the null geodesics and photonsphere and find constraints to the gravitational wave parameter ϵ using the black hole shadow of M87* for some given test value for the gravitational wave frequency σ. Not only were some nodes found in the light trajectory, but the general behavior of paths changes periodically as the time t progresses. These patterns then confirm the chaotic formation of the shadow seen by some remote observer. Finally, the constraint that we find for ϵ is 10−10 orders of magnitude for the effect of the gravitational wave to be seen at a distance of D=16.8 Mpc. As a consequence of such a value for ϵ, another result reveals that while there is are gravitational wave effect on the shadow perceived at D, the deviations on the photonsphere are nearly non-existent. Apart from Earth-based detectors for gravitational waves, the study implies the possibility of an alternative detection method, especially if a gravitational wave source is near a lone black hole.

Similarity solutions for cylindrical shock wave in a self-gravitating and rotating gas under the influence of monochromatic radiation and azimuthal or axial magnetic field by using Lie invariance method

Abstract The group invariance technique is used to investigate the similarity solution of one-dimensional, unsteady motion of cylindrically symmetric shock waves propagating in a rotating, axisymmetric perfect gas permeated with an azimuthal or axial magnetic field, under the effect of monochromatic radiation, with or without self-gravitational effects. The density is considered to be varying with radiation flux moving through the gas. Considering the absorption coefficient to be variable and choosing different values for the arbitrary constants appearing in infinitesimal generators, all possible cases of similarity solutions with shock paths following the power law and exponential law are discussed in detail, and numerical solutions for both the power law and exponential law path is obtained. The effect of changes in the Alfven–Mach number, density exponent, adiabatic index, gravitational, and rotational parameters on shock formation and shock strength has been obtained for both the power law and the exponential law. Further, the effect of all these parameters on the behaviour of flow variables behind the shock is investigated in detail and the results are depicted graphically via figures. It has been found during the study that, the strength of the shock reduces considerably with an increase in the Alfven–Mach number, rotational parameter and adiabatic index, and it increases with increase in density index and gravitational parameter. Various computations involved in this article are carried out by using the MATLAB software.

Mglens: Modified gravity weak lensing simulations for emulation-based cosmological inference

ABSTRACT We present mglens, a large series of modified gravity lensing simulations tailored for cosmic shear data analyses and forecasts in which cosmological and modified gravity parameters are varied simultaneously. Based on the forge and bridgeN-body simulation suites presented in companion papers, we construct 100 × 5000 deg2 of mock Stage-IV lensing data from two 4D Latin hypercubes that sample cosmological and gravitational parameters in f(R) and nDGP gravity, respectively. These are then used to validate our inference analysis pipeline based on the lensing power spectrum, exploiting our implementation of these modified gravity models within the cosmosis cosmological inference package. Sampling this new likelihood, we find that cosmic shear can achieve 95 per cent CL constraints on the modified gravity parameters of log$_{10}[f_{R_0}] \lt $ −4.77 and log10[H0rc] &amp;gt; 0.09, after marginalizing over intrinsic alignments of galaxies and including scales up to ℓ = 5000. We also investigate the impact of photometric uncertainty, scale cuts, and covariance matrices. We finally explore the consequences of analysing mglens data with the wrong gravity model, and report catastrophic biases for a number of possible scenarios. The Stage-IV mglens simulations, the forge and bridge emulators and the cosmosis interface modules will be made publicly available upon journal acceptance.

Stability of longitudinal sediment waves formed by turbidity currents: linear and weakly nonlinear perspectives

We perform the linear and weakly nonlinear stability analyses of longitudinal sediment waves triggered by the interaction of turbidity currents with an erodible bed. The mathematical framework is based on the two-dimensional flow equations, advection–diffusion equation for sediment concentration and Exner equation for bed evolution. Using the standard linearization, the linear analysis offers the resonant wavenumber that maximizes the growth rate of sediment waves. We study the influence of the key parameters, such as the gravitational parameter, longitudinal bed slope, Rouse number, shear Reynolds number, relative roughness number and erosion coefficient, on the growth rate, resonant wavenumber and phase velocity. The results reveal that the longitudinal sediment waves migrate both upstream and downstream. By plotting the gravitational parameter against the dimensionless wavenumber, we obtain a stability diagram that accurately captures the experimental data plots within the unstable zone. Additionally, we explore the perturbation fields of velocity components, pressure and sediment concentration. Employing the centre manifold projection, the weakly nonlinear analysis provides the equilibrium amplitude of sediment waves and its sensitivity to the key parameters. The predicted wavelength and amplitude of sediment waves are comparable with field observations in the Atlantic Ocean, the Sea of Japan and the Pacific Ocean.

Flow of Third Grade Fluid and Vogel’s Model Viscosity in Cylindrical Pipe

Abstract: The flow of non-Newtonian fluid and Vogel’s model viscosity in cylindrical pipe is treated. The coupled nonlinear equations of motion solved and the effects of sundry parameters of the non-Newtonian fluid and the Vogel model viscosity examined. Results show that the gravitational parameter has a great influence on the flow field. It is observed that as the viscosity index increases, the velocity of the fluid flow reduces. This indicates that the shear strain which reduces the flow velocity, increases the viscosity. Results further show that increase in  increases the temperature of the cylinder indicates a low viscosity. This is because high temperature means that particles have more thermal energy and are easily able to overcome the attractive forces holding them together.