Effect Of Oblateness Research Articles

Perturbing and Oblateness's Impact on the Generalized Photogravitational Restricted Three-Body Problem

In this research work, the effects of perturbing and oblateness on the generalised photogravitational restricted three body problem (RTBP) are examined when the primary are regarded as radiation sources and oblate spheroid. The perturbing forces were included in the equations of motion that we developed for the system. The triangular libration points were derived in terms of the perturbing parameters using linear approximations, and their influence was seen. Applying Murray's criteria, we determined that the triangular libration points remained unstable due to the nature of the characteristics equation matching to the variational equations of motion of the system generated.

Stability of Triangular Equilibrium Points in BiER4BP under the Radiation and Oblateness Effect of Primaries Applied for Sun–Earth–Moon System

Stability of Triangular Equilibrium Points in BiER4BP under the Radiation and Oblateness Effect of Primaries Applied for Sun–Earth–Moon System

Combined effect of Poynting-Robertson (P-R) drag, oblateness and radiation on the triangular points in the elliptic restricted three-body problem

This study investigates the motion of a test particle around triangular equilibrium points in the elliptic restricted three-body problem (ER3BP) under the influence of the two oblate and radiating primaries having Poynting-Robertson (P-R) drag. It is observed that the position of triangular points of the problem is affected by oblateness, radiation pressure, eccentricity, semi-major axis and Poynting-Robertson (P-R) drag. The stability of these points is demonstrated analytically by the Routh-Hurwitz criterion. It is seen that they are unstable under the combined effect of involved parameters. The effect of these parameters on the position of triangular points is examined numerically using the binary systems, 61 Cygni and Archird. The results obtained by these binary systems can be used to broaden the scope of interest in astronomy, astrophysics, space science and celestial mechanics in general.

Analysis of albedo and disc effects in the generalized restricted four-body problem

This manuscript explores the Generalized Restricted Four-Body Problem within the context of radiation pressure, the albedo effect, oblateness, and a disc-like structure that orbits around the primary bodies. We have considered that one of the primaries is a bigger primary, and the rest of the two smaller primaries are of equal masses, in which one of the smaller primaries is considered as a black body. Moreover, the perturbing forces by the effect of radiation pressure and oblateness are considered in the bigger primary. The effect of albedo and oblateness due to the second smaller primary is also taken into count. This study yields nine equilibrium points corresponding to various parameter values, including three collinear and six non-collinear equilibria. We conduct an analysis of the equilibrium points, their linear stability, and the motion around them. In the context of the considered parameter set, certain collinear equilibrium points exhibit stability, while others are unstable. Additionally, most of the non-collinear equilibrium points display linear stability. We also investigate variations in Jacobi’s constant and the positions of existing equilibrium points caused by the albedo and disc effects. It is found that the value of Jacobi constant CLj decreases with an increase in the mass parameter μ at the collinear points, which results in an expansion in the prohibited region. The inhibited zone of motion of the infinitesimal body is shown for different sets of parameters.

The Analysis of the Photogravitational R4BP Under the Combined Effect of Stokes Drag and Oblateness with Variable Mass

The Analysis of the Photogravitational R4BP Under the Combined Effect of Stokes Drag and Oblateness with Variable Mass

Trajectory Controllability of Artificial Satellite Under the Effect of Oblateness of Earth

Trajectory Controllability of Artificial Satellite Under the Effect of Oblateness of Earth

Controllability Analysis of Motion of Artificial Satellite Under the Effect of Oblateness of the Earth

In this article we have studied the controllability of artificial satellite under the effect of zonal harmonic J2 in cylindrical polar coordinates systems. Seven different cases of thrusters in various directions have been analyzed and it is found that the system is controllable if we apply thrusters in either r, θ and z or θ and z direction. The equations governing motion of satellite have been linearized and Kalman controllability test is applied to check the controllability of the system. We have also derived controller u for the linearized system. The trajectory of the system has been plotted to show the controllability of the system.

An Orbit-flip Mechanism by Eccentric Lidov–Kozai Effect with Stellar Oblateness

Orbit flips have been previously found under the eccentric Lidov–Kozai effect (ELK) in hierarchical three-body systems. Recently, we have found that, in certain conditions, the orbit can flip its orientation in a much different manner, where the stellar oblateness plays an important role. In this paper, orbit-flip behaviors with the ELK effect are investigated as the stellar oblateness varies within a wide range. This is of significance because recent works have shown that the oblateness of young stars has a widespread distribution and may have critical effects on sculpting the final orbital states of close-in planets. Our dynamical model includes the secular potential of the perturber to octupole order and the secular effects of the stellar oblateness. An alignment between the orbit plane of the outer perturber and the stellar bulge is assumed. Our findings mainly consist of two aspects. (i) A new type of orbit-flipping mechanism induced by a combination of the ELK and stellar oblateness effects, referred to as the ELK–J 2 effect, is discovered and confirmed. (ii) We demonstrate that, in the considered aligned configuration, the stellar oblateness suppresses orbit flips due to the ELK effect and produces new flips through the ELK–J 2 effect. Moreover, if the stellar oblateness perturbations are of the same order as the octupole perturbations of the outer perturber, the ELK-induced orbit flips are almost entirely suppressed, while the ELK–J 2 effect reaches its peak for the considered strength of the octupole perturbations. However, from a global view, stellar oblateness always reduces flipping orbits.

Effect of finite straight segment and oblateness in the restricted 2+2 body problem

Effect of finite straight segment and oblateness in the restricted 2+2 body problem

Evolution of Periodic Orbits in the Sun-Jupiter and Sun-Earth Systems

Objective: The periodic orbits around smaller and larger primaries are studied in the Sun-Jupiter and Sun-Earth systems, considering smaller primary as an oblate spheroid. Methods: We used the Poincare surface section method to find the periodic orbits and discussed the differences between these orbits with and without oblateness. Findings: Different trajectories are drawn with the change of Jacobi constant and radiation pressure. Size variations, location, and eccentricity of an orbit around smaller primary are observed due to oblateness effect of the Jupiter and Earth. Oblateness of the smaller primary and radian pressure of the bigger primary have a significant effect on eccentricity, orbit shape, size, and position in phase space. Novelty : Small solar system bodies, such as asteroids and comets in the Sun-Jupiter and Sun-Earth systems, can be explored using periodic orbits. Perturbation caused by oblateness of the smaller primary must be understood and addressed during human exploration missions. Keywords: Circular Restricted Three Body Problem; Poincare Surface Sections; Jacobi Constant; Radiation Factor; Oblateness; Trajectories; Resonance

ON TWINNING-MEDIATED VOID GROWTH IN HEXAGONAL CRYSTALS

Aspects of plastic anisotropy in damage accumulation are considered for a class of hexagonal crystals that deform by combined slip and twinning. Focus is placed on crystallographic aspects that are currently absent from constitutive formulations of ductile damage. To this end, three-dimensional finite-element calculations are carried out using a cubic unit cell containing a single void embedded in a crystal matrix. Plastic flow in the latter is described using crystal plasticity with parameters representative of single crystal pure magnesium. The effect of void oblateness is analyzed in some detail, as voids often form as blunted microcracks in Mg alloys. The analyses reveal two aspects peculiar to twinning-mediated void growth: (1) insensitivity of the effective stress-strain response to void oblateless and (2) a plastic auxetic effect. Both aspects manifest under certain circumstances. Some implications in terms of incorporating the uncovered crystallographic aspects in coupled plasticity-damage formulations of anisotropic materials are discussed.

Effects of Albedo and Oblateness in the Bi-Circular Restricted Four-Body Problem

In this paper, a bicircular model describing motion of a spacecraft around the Sun–Earth–Moon system is studied. The impact of important characterizations such as radiation from the Sun, the Earth’s and Moon’s Albedo and oblateness of the Moon are all included and analysed​ in this work. This quantitative investigation shows how significant the reflective property of the Earth and its Moon affect the existence of the system’s libration points as well as the stability of motion of the spacecraft about the libration points. The Albedo phenomenon is seen to have dominant effect on the location of the libration points of the spacecraft than the perturbation due to oblateness. It is revealed by the Poincare Surface of Section that the system exhibits chaotic behaviour as it is sensitive to change in initial conditions.

Effects of Viscosity and Oblateness on the Perturbed Robe’s Problem with Non-Spherical Primaries

Effects of Viscosity and Oblateness on the Perturbed Robe’s Problem with Non-Spherical Primaries

Effects of viscosity and oblateness on the perturbed Robe’s problem with non-spherical primaries

Effects of viscosity and oblateness on the perturbed Robe’s problem with non-spherical primaries

Motion about equilibrium points in the Jupiter-Europa system with oblateness

Abstract The study of motion of a test mass in the vicinity of an equilibrium point under the frame of restricted three body problem (RTBP) plays an important role in the trajectory design for different space missions. In this paper, motion of an infinitesimal mass has been described under the frame of Jupiter-Europa system with oblateness. At first, we have determined equilibrium points and then performed linear stability tests under the influence of oblateness of both the primaries. We found that due to oblateness, a considerable deviation in the existing results has occurred. Next, we have computed tadpole and horseshoe orbits in the neighbourhood of triangular equilibrium points and then the oblateness effect is recorded on these orbits. Finally, the evolution of orbits of infinitesimal mass about triangular equilibrium points have been estimated by using Poincaré surface of section technique and it is noticed that in presence of oblateness, quasi-periodic orbit dominates over the chaotic zones. These results will help in further study of more generalised models with perturbations.

The atmosphere and architecture of WASP-189 b probed by its CHEOPS phase curve

Context. Gas giants orbiting close to hot and massive early-type stars can reach dayside temperatures that are comparable to those of the coldest stars. These ‘ultra-hot Jupiters’ have atmospheres made of ions and atomic species from molecular dissociation and feature strong day-to-night temperature gradients. Photometric observations at different orbital phases provide insights on the planet’s atmospheric properties. Aims. We aim to analyse the photometric observations of WASP-189 acquired with the Characterising Exoplanet Satellite (CHEOPS) to derive constraints on the system architecture and the planetary atmosphere. Methods. We implemented a light-curve model suited for an asymmetric transit shape caused by the gravity-darkened photosphere of the fast-rotating host star. We also modelled the reflective and thermal components of the planetary flux, the effect of stellar oblateness and light-travel time on transit-eclipse timings, the stellar activity, and CHEOPS systematics. Results. From the asymmetric transit, we measure the size of the ultra-hot Jupiter WASP-189 b, Rp = 1.600−0.016+0.017 RJ, with a precision of 1%, and the true orbital obliquity of the planetary system, Ψp = 89.6 ± 1.2deg (polar orbit). We detect no significant hotspot offset from the phase curve and obtain an eclipse depth of δecl = 96.5−5.0+4.5 ppm, from which we derive an upper limit on the geometric albedo: Ag < 0.48. We also find that the eclipse depth can only be explained by thermal emission alone in the case of extremely inefficient energy redistribution. Finally, we attribute the photometric variability to the stellar rotation, either through superficial inhomogeneities or resonance couplings between the convective core and the radiative envelope. Conclusions. Based on the derived system architecture, we predict the eclipse depth in the upcoming Transiting Exoplanet Survey Satellite (TESS) observations to be up to ~165 ppm. High-precision detection of the eclipse in both CHEOPS and TESS passbands might help disentangle reflective and thermal contributions. We also expect the right ascension of the ascending node of the orbit to precess due to the perturbations induced by the stellar quadrupole moment J2 (oblateness).

Periodic orbit in the photo-gravitational restricted three body problem around the collinear Lagrangian points when more massive primary is an oblate spheroid and source of radiation

The circular Restricted Three Body Problem is considered with the more massive primary as an oblate spheroid and source of radiation. A new mean motion expression given by n2=1+6A is used in the present study, when the secular effect of the oblateness on the mean motion, argument of perigee and right ascension of the ascending node is considered. The locations of the collinear Lagrangian points are found. It is found to have some variation from the previous study conducted on the same because of the new mean motion that is considered in this study. The variations of the location of the Lagrangian points due to the unperturbed as well as the perturbed problem due to oblateness and radiation pressure are studied. A study on the eccentricity e and angular frequency s at L1, L2 and L3 is carried out. It is observed how the change in effect of oblateness and radiation pressure has affected the location, angular frequency and eccentricity at L3, though there are only small changes noticed in the case of L1 and L2. Â

Dynamics of Satellite Formation Utilizing the Perturbed Restricted Three-Body Problem

The dynamics of satellites formation is of great interest for the space mission. This work discusses a more efficient model of the relative motion dynamics of satellites formation. The model is based on employing the concepts restricted three-body problem (R3BP) and for more accuracy, it considers the effects of both oblateness and radiation pressure on deputy relative motion w.r.t the chief satellite. A model of deputy relative motion w.r.t the chief satellite is derived in the local-vertical local-horizontal system and simplified assuming the concept of the circular restricted three-body problem (CR3BP). The deputy equations of motion were rewritten in the form of recurrence relations and solved numerically using the Lie series approach. Assuming that the formation is revolving around the Moon in the Earth-Moon system, the effects of both oblateness and radiation pressure on the deputy satellite orbit were assessed through a particular example of satellites formation. A comparison between the perturbed and unperturbed R3BP shows a significant difference in the deputy relative position that has to be considered for the formation dynamics.

On the Dominant Lunisolar Perturbations for Long-Term Eccentricity Variation: The Case of Molniya Satellite Orbits

The aim of this work is to investigate the main dominant terms of lunisolar perturbations that affect the orbital eccentricity of a Molniya satellite in the long term. From a practical point of view, these variations are important in the context of space situational awareness—for instance, to model the long-term evolution of artificial debris in a highly elliptical orbit or to design a reentry end-of-life strategy for a satellite in a highly elliptical orbit. The study assumes a doubly averaged model including the Earth’s oblateness effect and the lunisolar perturbations up to the third-order expansion. The work presents three important novelties with respect to the literature. First, the perturbing terms are ranked according to their amplitudes and periods. Second, the perturbing bodies are not assumed to move on circular orbits. Third, the lunisolar effect on the precession of the argument of pericenter is analyzed and discussed. As an example of theoretical a application, we depict the phase space description associated with each dominant term, taken as isolated, and we show which terms can apply to the relevant dynamics in the same region.

Effects of oblateness of the primaries on natural periodic orbit-attitude behaviour of satellites in three body problem

• Equations of Motion for the Perturbed Circular Restricted Three Body Problem (P-CR3BP) with considering A 2 - A 6 primaries oblate coefficients have derived for the first time. • It was shown that considering primaries zonal harmonic coefficients j 2 - j 6 has a significant effect on satellite orbit-attitude behavior. It is observed that considering A 2 - A 6 primaries oblate coefficients amplify the effect of oblate perturbations and the zonal harmonic coefficients after j 6 have negligible effect. • Proper initial guess of periodic solution of perturbed model identified by Poincaré maps. • As an innovation, finding the appropriate value of inertia ratio K to find periodic response of orbit-attitude was performed using Poincaré mapping for the first time. • It was shown for the first time, by more accurately simulating the study environment by considering oblate perturbations, the density of points on the islands created on Poincaré map appeared to increase, and in fact, it became easier to identify the initial guess of attitude states. • Increasing the inertia ratio and increasing the orbital period reduces the chances of finding periodic responses. This study was done to investigate the effect of perturbations of both oblate massive primaries on the periodic orbit-attitude behavior of satellites at the three-body problem. Governing equations of the perturbed coupled orbit-attitude were derived using principles of the Lagrangian mechanics. As initial conditions of the coupled model play a key role in finding periodic responses of both orbit and attitude, so the perturbed circular restricted three-body problem (P-CR3BP) coupled orbit-attitude correction algorithm was proposed to correct the initial guess of the coupled model. The correction algorithm requires an appropriate initial guess vector as the number of periodic solutions is limited. This initial guess vector consists of two parts: orbital and attitude dynamic state parameters. A suitable initial guess was suggested for orbital parameters considering a small error at the initial conditions of the unperturbed periodic orbits. These initial conditions were extracted by another orbital correction algorithm to correct orbital states of periodic orbits in the unperturbed circular restricted three-body problem (U-CR3BP). Furthermore, the initial guess of attitude dynamic parameters was identified by the Poincaré mapping method. Considering oblate perturbations would change the initial conditions of periodic orbits at P-CR3BP relative to U-CR3BP. Also, because the proposed model of the coupled orbit-attitude governing equations is such that only orbital state parameters influence attitude dynamic parameters, so the behavior of attitude dynamics will also change by altering orbital motion. Comparison of patterns in Poincaré maps, satellites angular velocity, and initial conditions of periodic coupled orbit-attitude response in U-CR3BP and P-CR3BP indicated the effect of both oblate primaries perturbations. Consideration of these perturbations resulted in a more accurate simulation of the study environment that helps to understand the natural motion of the satellite.