Oblateness Parameter Research Articles

Analysis of radiation pressure and albedo effect in the generalized CR3BP with oblateness

This research investigates the impact of radiation pressure, albedo effect, and oblateness in the generalized Circular Restricted Three-Body Problem (CR3BP). We have considered the bigger primary is a radiating primary and the smaller primary produces the albedo effect. Moreover, the smaller primary is also considered as oblate body with zonal harmonic coefficient Ji;i=2,4. In this study, we have computed the equilibrium points and analyzed their stability, examined zero velocity curves to determine regions of possible motion, and described the periodic orbits around the equilibrium points. We observed that the equilibrium points are more significantly influenced by radiation pressure compared to the albedo effect. Furthermore, larger values of the oblateness parameters J2 and J4 notably impact on the equilibrium points. Moreover, an analysis is performed using the radiation pressure and albedo effect to assess the linear stability of all equilibrium points, and it is found that the collinear points are unstable, whereas, non-collinear equilibrium points are stable. We have obtained periodic orbits around the equilibrium points and observed that the amplitudes in the y− axes of the periodic orbit around L1 and L2 affected due to consideration of these perturbations, whereas the orbit around L3 is not affected by any of these considered perturbations. This research provides a comprehensive analysis of these perturbations, offering new perspectives on their roles in the generalized CR3BP.

Retrograde orbits associated separatrices in perturbed restricted three-body problem

This study develops single and multivariate nonlinear regression models for predicting Jacobi constant related to separatrix associated with simply symmetric retrograde periodic orbits in the framework of CRTBP with and without perturbations effects. These models are constructed using data from real and hypothetical systems considering that the parameter of mass is independent variable, while the Jacobi constant is displayed as a function of mass and oblateness parameters. Third-degree polynomials from single-variable regression and fourth-degree polynomials from multivariate regression accurately predict the Jacobi constant for given mass and oblateness values, facilitating the identification of separatrices in the PSS without intensive construction efforts. Error analysis confirms the model’s high accuracy across all parameters values. Additionally, chaos detection techniques, including the SALI, GALI, and Lyapunov exponent methods, along with bifurcation analysis, are employed to identify the regions of local and global chaos.

Dynamics around small irregularly shaped objects modeled as a mass dipole

In this work, we investigate the dynamics of a spacecraft near two primary bodies. The massive body is considered to have a spherical shape, while the less massive one is elongated and modeled as a dipole. The dipole consists of two connected masses, one is spherical and the other is an oblate spheroid. The gravitational potential of the elongated body is determined by four independent parameters. To study the dynamics, we construct the equations of motion of a spacecraft with negligible mass under the effect of the current force model. The existence and locations of the equilibrium points are analyzed for various values of the system parameters. We found that the existence and locations of the points are affected by the system parameters. Also, we studied the linear stability of the equilibrium points. We found some stable collinear points when the oblateness parameter is negative, otherwise the points are not stable. We used the curves of zero velocity to identify the regions of allowed motion. Furthermore, we discussed the 2001 SN263 asteroid system and found some stable collinear points when the oblateness parameter is negative. In addition, the triangular points of the system are stable in a linear sense.

Orbital and Physical Characterization of Asteroid Dimorphos Following the DART Impact

The Double Asteroid Redirection Test (DART) mission impacted Dimorphos, the satellite of binary near-Earth asteroid (65803) Didymos, on 2022 September 26 UTC. We estimate the changes in the orbital and physical properties of the system due to the impact using ground-based photometric and radar observations, as well as DART camera observations. Under the assumption that Didymos is an oblate spheroid, we estimate that its equatorial and polar radii are 394 ± 11 m and 290 ± 16 m, respectively. We estimate that the DART impact instantaneously changed the along-track velocity of Dimorphos by −2.63 ± 0.06 mm s−1. Initially, after the impact, Dimorphos’s orbital period had changed by −32.7 minutes ± 16 s to 11.377 ± 0.004 hr. We find that over the subsequent several weeks the orbital period changed by an additional 34 ± 15 s, eventually stabilizing at 11.3674 ± 0.0004 hr. The total change in the orbital period was −33.25 minutes ±1.5 s. The postimpact orbit exhibits an apsidal precession rate of 6.7 ± 0.°2 day−1. Under our model, this rate is driven by the oblateness parameter of Didymos, J 2, as well as the spherical harmonics coefficients, C 20 and C 22, of Dimorphos’s gravity. Under the assumption that Dimorphos is a triaxial ellipsoid with a uniform density, its C 20 and C 22 estimates imply axial ratios, a/b and a/c, of about 1.3 and 1.6, respectively. Preimpact images from DART indicate Dimorphos’s shape was close to that of an oblate spheroid, and thus our results indicate that the DART impact significantly altered the shape of Dimorphos.

Estimating the Oblateness of Dark Matter Halos Using Neutral Hydrogen Velocity Dispersion

We derive the oblateness parameter q of the dark matter halo of a sample of gas-rich, face-on disk galaxies. We have assumed that the halos are triaxial in shape but their axes in the disk plane (a and b) are equal, so that q = c/a measures the halo flattening. We have used the H i velocity dispersion, derived from the stacked H i emission lines and the disk surface density, determined from the H i flux distribution, to determine the disk potential and the halo shape at the R 25 and 1.5R 25 radii. We have applied our model to 20 nearby galaxies, of which six are large disk galaxies with M(stellar) > 1010, eight have moderate stellar masses, and six are low-surface-brightness dwarf galaxies. Our most important result is that gas-rich galaxies that have M(gas)/M(baryons) > 0.5 have oblate halos (q < 0.55), whereas stellar-dominated galaxies have a range of q values from 0.21 ± 0.07 in NGC4190 to 1.27 ± 0.61 in NGC5194. Our results also suggest a positive correlation between the stellar mass and the halo oblateness q, which indicates that galaxies with massive stellar disks have a higher probability of having halos that are spherical or slightly prolate, whereas low-mass galaxies have oblate halos (q < 0.55).

New total transmission modes of the Kerr geometry with Schwarzschild limit frequencies at complex infinity

In addition to the well-known quasinormal modes, the gravitational modes of the Kerr geometry also include sets of total-transmission modes. Each mode can be considered as an element of a sequence of modes parameterized by the angular momentum of the black hole. One family of gravitational total-transmission modes of Kerr have been known for some time. Modes in this family connect to a Schwarzschild limit where the mode frequency is finite and purely imaginary. Recently, what was thought to be an additional branch of this original family of modes was discovered. However, this new branch is actually a part of one of two entirely new families of total-transmission modes. Modes in these new families, surprisingly, connect to a Schwarzschild limit where the mode frequencies exist at complex infinity. We have numerically constructed full sets of sequences of gravitational total-transmission modes for harmonic indices $\ell=[2,8]$. Using these numerical sequences, we have been able to construct analytic asymptotic expansions for the mode frequencies and their associated separation constants. The asymptotic expansion for the separation constant used in constructing the total-transmission modes seems to be valid for general complex values of the oblateness parameter.

Supergravity p -branes with scalar charge

Standard dilatonic supergravity $p$-branes have scalar charges that are not independent parameters, but are determined by the brane tension and Page charges. This feature can be traced to the no-hair theorem in the four-dimensional Einstein-scalar gravity, implying that more general solutions with independent scalar charges can have naked singularities. Since singular branes are also of interest as tentative classical counterparts of unstable tachyonic branes and/or brane-antibrane systems, it is worth investigating branes with independent scalar charges in more detail. Here we study singular branes associated with the Fisher-Janis-Newman-Winicour solution of four-dimensional gravity. In the case of codimension three, we also construct singular branes endowed with a Zipoy-Voorhees-type oblateness parameter. It is expected that such branes will not be supersymmetric in the string theory. We demonstrate this in the special case of NS5-branes of type II theory. We analyze geodesics and test scalar perturbations of new solutions focusing on possible quantum healing of classical singularities.

On the topology of basins of convergence linked to libration points in the modified R3BP with oblateness

We numerically investigate the effect of oblateness parameter on the topology of basins of convergence connected with the equilibrium points in the restricted three-body problem when the test particle is an oblate spheroid, and the influence of the gravitational potential from the belt is taken into consideration. Additionally, the primaries are also not spherical in shape, on the contrary, it is oblate or prolate spheroid. The parametric variation of the equilibrium points, their stability, and the regions of possible motion are illustrated as the function of the parameters involved. The domain of convergence, on the several two dimensional planes, are unveiled by applying the bi-variate version of the Newton–Raphson iterative method. In addition, we perform a systematic investigation in an order to show how the used parameters affect the topology as well as the degree of fractality of basins of convergence. Moreover, it is also unveiled that how the region of the convergence is related with the number of the required iterations to achieve the desired accuracy with the corresponding probability distribution.

Slowly rotating black holes in quasitopological gravity

While cubic Quasi-topological gravity is unique, there is a family of quartic Quasi-topological gravities in five dimensions. These theories are defined by leading to a first order equation on spherically symmetric spacetimes, resembling the structure of the equations of Lovelock theories in higher-dimensions, and are also ghost free around AdS. Here we construct slowly rotating black holes in these theories, and show that the equations for the off-diagonal components of the metric in the cubic theory are automatically of second order, while imposing this as a restriction on the quartic theories allows to partially remove the degeneracy of these theories, leading to a three-parameter family of Lagrangians of order four in the Riemann tensor. This shows that the parallel with Lovelock theory observed on spherical symmetry, extends to the realm of slowly rotating solutions. In the quartic case, the equations for the slowly rotating black hole are obtained from a consistent, reduced action principle. These functions admit a simple integration in terms of quadratures. Finally, in order to go beyond the slowly rotating regime, we explore the consistency of the Kerr-Schild ansatz in cubic Quasi-topological gravity. Requiring the spacetime to asymptotically match with the rotating black hole in GR, for equal oblateness parameters, the Kerr-Schild deformation of an AdS vacuum, does not lead to a solution for generic values of the coupling. This result suggests that in order to have solutions with finite rotation in Quasi-topological gravity, one must go beyond the Kerr-Schild ansatz.

First-order resonant in periodic orbits

In the frame work of Saturn–Titan system, the resonant orbits of first-order are analyzed for three different families of periodic orbits, namely, interior resonant orbits, exterior resonant orbits and [Formula: see text]-Family orbits. This analysis is developed by considering Saturn as a spherical and oblate body. The initial position, semi-major axis, eccentricity, orbital period and order of resonant orbits of these families are investigated for different values of Jacobi constant and oblateness parameter.

On the spatial collinear restricted four-body problem with non-spherical primaries

In the present work a systematic study has been presented in the context of the existence of libration points, their linear stability, the regions of motion where the third particle can orbit and the domain of basins of convergence linked to libration points in the spatial configuration of the collinear restricted four-body problem with non-spherical primaries (i.e., the primaries are oblate or prolate spheroid). The parametric evolution of the positions of the libration points as function of the oblateness and prolateness parameters of the primaries and the stability of these points in linear sense are illustrated numerically. Moreover, the numerical investigation shows that the only libration points which lie on either of the axes are linearly stable for several combinations of the oblateness parameter and mass parameter whereas the non-collinear libration points are found linearly unstable, consequently unstable in nonlinear sense also, for studied value of mass parameter and oblateness parameter. Moreover, the regions of possible motion are also depicted, where the infinitesimal mass is free to orbit, as function of Jacobian constant. In addition, the basins of convergence (BoC) linked to the libration points are illustrated by using the multivariate version of the Newton-Raphson (NR) iterative scheme.

Computation of the perturbed locations of L1 for all Sun-Planet RTBP systems with oblate primaries

The location of the equilibrium point ΔL1 in the restricted three body problem with oblate primaries is investigated. The zonal harmonic coefficients are retained up to the fourth harmonic coefficient of both primaries. The perturbed mean motion is determined. The perturbed location of L1 is computed for eight restricted three body systems within the solar system as well as two restricted three body lunar systems. The nondimensionalized and dimensionalized locations for different combinations of perturbing oblateness parameters of the primaries are obtained. The linear stability is investigated. The study shows that the equilibrium point is unstable for the whole considered systems.

On the Convergence Dynamics of the Sitnikov Problem with Non-spherical Primaries

We investigate, using numerical methods, the convergence dynamics of the Sitnikov problem with non-spherical primaries, by applying the Newton-Raphson (NR) iterative scheme. In particular, we examine how the oblateness parameter $A$ influences several aspects of the method, such as its speed and efficiency. Color-coded diagrams are used for revealing the convergence basins on the plane of complex numbers. Moreover, we compute the degree of fractality of the convergence basins on the complex space, as a relation of the oblateness, by using different computational tools, such the fractal dimension as well as the (boundary) basin entropy.

Instability analysis of a filament-wound composite tube subjected to compression/bending

The aim of this study is to investigate the global buckling of a relatively long composite cord–rubber tube subjected to axial compression and its cross-sectional instability due to bending by a macromechanical nonlinear finite element (FE) model (nonlinear buckling analysis). Composite reinforcement layers are modelled as transversely isotropic ones, while elastomer liners are described by a hyperelastic material model that assumes incompressibility. Force–displacement, equivalent strain, equivalent stress results along with oblateness and curvature results for the complete process have been presented. It is justified that bending leads to ovalization of the cross section and results in a loss of the load-carrying capacity of the tube. Strain states in reinforcement layers have been presented, which imply that the probable failure modes of the reinforcement layers are both delamination and yarn-matrix debonding. There is a significant increase in strains due to cross-sectional instability, which proves that the effect of cross-sectional instability on material behaviour of the tube is crucial. A parametric analysis has been performed to investigate the effect of the member slenderness ratio on cross-sectional instability of the composite tube. It shows that Brazier force is inversely proportional to the slenderness ratio. It further shows that higher oblateness parameters occur in case of a lower slenderness ratio and that cross-sectional instability takes place at a lower dimensionless displacement in case of a lower slenderness ratio. FE results have been validated by a compression/bending test experiment conducted on a tensile test machine.

A Nonparametric Approach for Assessing Precision in Georeferenced Point Clouds Best Fit Planes: Toward More Reliable Thresholds

AbstractThe fitting of a plane to data points is essential to the geosciences. However, it is recognized that the reliability of these best fit planes depends upon the point set distribution and geometry, evaluated in terms of the eigen‐based parameters derived from the moment of inertia analysis. Despite its significance, few studies have addressed the uncertainties of the analysis, which can adversely affect the reproduction of results one of the cornerstones of scientific endeavor. Aiming to contribute toward the neglected issue of the moment of inertia precision, we have developed a bootstrap resampling scheme to empirically discover the distribution of uncertainties in the orientation of best fit planes. Dispersion of the bootstrapped normal vectors to the best fit plane is regarded as a measure of precision, evaluated with the maximum angular distance from the optimal solution. This rationale was tested using Monte Carlo‐generated samples covering a comprehensive range of shape parameters to assess the dependence between eigen parameters and their inherent bias. Our results show that the oblateness of the point cloud is a robust parameter to assess the reliability of the best fit plane. Given this, the method was then applied to a publicly available lidar data set. We argue that georeferenced point clouds with an oblateness parameter greater than 3 and 1.5 may be placed at 95% confidence levels of 5° and 10°, respectively. We propose using these values as thresholds to obtain robust best fit planes, guaranteeing reproducible results for scientific research.

Exploring the fractal basins of convergence in the restricted four-body problem with oblateness

The present manuscript deals with the restricted four-body problem when all the primaries are oblate spheroids. This paper unveils the effect of oblateness on the existence, locations and stability of the libration points. It is assumed that three oblate primaries having equal masses are set in Lagrangian equilateral triangle configuration. It is observed that there exist ten libration points in configuration (x,y)-plane out of which four are collinear and six are non-collinear for oblateness parameter A∈[0,0.681949). Further, for the oblateness parameter A∈(0.681949,1), there exist only four libration points out of which two are collinear and two are non-collinear. Out-of-plane libration points are also investigated and it is found that in-plane and out-of-plane libration points are unstable. It is further observed that oblateness parameter has substantial effect on the regions of possible motion. Further, we have numerically investigated the Newton–Raphson basins of convergence associated with the libration points to unveil that how the oblateness parameter influences the domain of convergence.

Artificial Equilibrium Points in the Low-Thrust Restricted Three-Body Problem When Both the Primaries Are Oblate Spheroids

This paper studies the existence and stability of the artificial equilibrium points (AEPs) in the low-thrust restricted three-body problem when both the primaries are oblate spheroids. The artificial equilibrium points (AEPs) are generated by canceling the gravitational and centrifugal forces with continuous low-thrust at a non-equilibrium point. Some graphical investigations are shown for the effects of the relative parameters which characterized the locations of the AEPs. Also, the numerical values of AEPs have been calculated. The positions of these AEPs will depend not only also on magnitude and directions of low-thrust acceleration. The linear stability of the AEPs has been investigated. We have determined the stability regions in the xy, xz and yz-planes and studied the effect of oblateness parameters A1(0<A1<1) and A2(0<A2<1) on the motion of the spacecraft. We have found that the stability regions reduce around both the primaries for the increasing values of oblateness of the primaries. Finally, we have plotted the zero velocity curves to determine the possible regions of motion of the spacecraft.

Analysis on nonlinear stability of the triangular libration points for radiating and oblate primaries in ER3BP

In this paper we study the non linear stability of the triangular librations points in ER3BP considering both the primaries as radiating and oblate. The study is carried out near the resonance frequency satisfying the conditions  in resonance as well as non resonance case. The study is conducted for various values of radiation pressure and oblateness parameters. It is observed that the case corresponds to the boundary region of the stability for the system Further, it is examined that the system experiences resonance at for different values of radiation pressures and oblateness parameter. In non resonance case, it is observed that the equilibrium points are stable. In resonance case, for and the triangular equilibrium points are unstable. In case, when for some values of radiation pressure and oblateness parameter, it is stable and for some it is unstable. The model is best suited to the binary systems (Achird, Luyten, α Cen AB, Kruger- 60, Xi- Bootis).

Combined Effects of Radiation and Oblateness on the Existence and Stability of Equilibrium Points in the Perturbed Restricted Four-Body Problem

We study numerically the perturbed problem of four bodies, where an infinitesimal body is moving under the Newtonian gravitational attraction of three much bigger bodies (called the primaries). The three bodies are moving in circles around their centre of mass fixed at the origin of the coordinate system, according to the solution of Lagrange where they are always at the apices of an equilateral triangle. The fourth body does not affect the motion of the primaries. The problem is perturbed in the sense that the dominant primary body m1 is a radiation source while the second smaller primary m2 is an oblate spheroid, with masses of the two small primaries m2 and m3 taken to be equal. The aim of this study is to investigate the effects of radiation and oblateness parameters on the existence and location of equilibrium points and their linear stability. It is observed that under the perturbative effect of oblateness, collinear equilibrium points do not exist (numerically and of course analytically) whereas the positions of the noncollinear equilibrium points are affected by the radiation and oblateness parameters. The stability of each equilibrium points ( Li,i = 1,...,6) is examined and we found that points Li,i = 1,...,6 are unstable while L7 and L8 are stable.

Combined effects of radiation and oblateness on the existence and stability of equilibrium points in the perturbed restricted four-body problem

We study numerically the perturbed problem of four bodies, where an infinitesimal body is moving under the gravitational attraction of three primary bodies which move on circular orbits around their common centre of gravity, such that their configuration is always an equilateral triangle. The problem is perturbed in the sense that the dominant primary body m1 is a radiation source while the second primary m2 is an oblate spheroid, with masses of the two small primaries m2 and m3 taken to be equal. We investigate the effects of radiation and oblateness parameters on the existence and location of equilibrium points and their linear stability. The zero-velocity surfaces are also given. It is observed that under the perturbative effect of oblateness, collinear equilibrium points do not exist whereas the positions of the non-collinear equilibrium points are affected by the parameters. The stability of each points (Li, i = 1,, 8) is also studied.