A Comparative study on generalized Manev potential and Newtonian potential in perturbed restricted four-body problem

The motion of a test particle within the context of the restricted four-body problem(R4BP)driven by a new kind of potential,called the generalized Manev potential,with perturbations in the Coriolis and centrifugal forces is considered in this study.The system possesses eight libration points which were distributed on its plane of motion in different manner from those of the usual Newtonian potential.Unlike the case of the perturbed R4BP under Newtonian potential,where two of these librations are stable,all of them are unstable in linear sense under Manev potential.We found that a gradual perturbation in the centrifugal force causes the trajectories of motion to drift inward but the Coriolis force was proven to have no effect on the location of the libration points of the system.Using first order Lyapunov characteristic exponents,the dynamical behavior of the system is found irregular.We experimented with a high velocity stellar system(82 G.Eridani)to establish the applicability of the model in astrophysics.

Isolation and in vivo hep-atoprotective activity of Melothria heterophylla(Lour.) Cogn.against chemically induced liver injuries in rats

Objective:To investigate hepatoprotective activity of ethanol extract of Melothria heterophyila Lour Cogn.（EEMH） against CCl4-induced hepatic damage in rats.Methods:β-sitosterol was isolated by column chromatography and characterized spectroscopically.Two different doses（200 and 400 mg/kg bw） of EEMH were administered orally in alternate days.The hepatoprotective activity was studied in liver by measuring biochemical parameters such as serum aspartate amino transferase（AST）,alanine amino transferase（ALT）,alkaline phosphatase（ALP）,total protein and total bilirubin.Lipid peroxidation product and different antioxidant enzyme activities were assessed in liver homogenate.Results:EEMH reduced all biochemical parameters and lipid peroxidation,as well as it increased the antioxidant enzyme activities in comparison with silymarin.The protective effect of the extract on CCl4 induced damage was confirmed by histopathological examination of the liver.Conclusions:This result strongly supports the protective effect of EEMH against acute liver injury,and may be attributed to its antioxidative activity.

Periods, Eccentricities and Axes around <i>L</i>4,5 in the ER3BP under Radiating and Oblate Primaries

In the framework of the elliptic restricted three-body problem, using a semi-analytic approach, we investigate the effects of oblateness, radiation and eccentricity of both primaries on the periodic orbits around the triangular Lagrangian points of oblate and luminous binary systems. The frequencies of the long and short orbits of the periodic motion are affected by the oblateness and radiation of both primaries, so are their eccentricities, semi-major and semi-minor axes.

Collinear Libration Points in the Photogravitational CR3BP with Zonal Harmonics and Potential from a Belt

We have studied a reformed type of the classic restricted three-body problem where the bigger primary is radiating and the smaller primary is oblate;and they are encompassed by a homogeneous circular cluster of material points centered at the mass center of the system (belt). In this dynamical model, we have derived the equations that govern the motion of the infinitesimal mass under the effects of oblateness up to the zonal harmonics J4 of the smaller primary, radiation of the bigger primary and the gravitational potential generated by the belt. Numerically, we have found that, in addition to the three collinear libration points Li (i = 1, 2, 3) in the classic restricted three-body problem, there appear four more collinear points Lni (i = 1, 2, 3, 4). Ln1 and Ln2 result due to the potential from the belt, while Ln3 and Ln4 are consequences of the oblateness up to the zonal harmonics J4 of the smaller primary. Owing to the mutual effect of all the perturbations, L1 and L3 come nearer to the primaries while Ln3 advances away from the primaries;and L2 and Ln1 tend towards the smaller primary whereas Ln2 and Ln4 draw closer to the bigger primary. The collinear libration points Li (i = 1, 2, 3) and Ln2 are linearly unstable whereas the Ln1, Ln3 and Ln4 are linearly stable. A practical application of this model could be the study of motion of a dust particle near a radiating star and an oblate body surrounded by a belt.

The Collinear Libration Points in the Elliptic R3BP with a Triaxial Primary and an Oblate Secondary

This paper examines the motion of a dust grain around a triaxial primary and an oblate companion orbiting each other in elliptic orbits about their common barycenter in the neighborhood of collinear libration points. The positions and stability of these points are found to be affected by the triaxiality and oblateness of the primaries, and by the semi-major axis and eccentricity of their orbits. The stability behavior of the collinear points however remains unchanged;they are unstable in the Lyapunov sense.

Existence and Stability of Equilibrium Points in the Robe’s Restricted Three-Body Problem with Variable Masses

The positions and linear stability of the equilibrium points of the Robe’s circular restricted three-body problem, are generalized to include the effect of mass variations of the primaries in accordance with the unified Meshcherskii law, when the motion of the primaries is determined by the Gylden-Meshcherskii problem. The autonomized dynamical system with constant coefficients here is possible, only when the shell is empty or when the densities of the medium and the infinitesimal body are equal. We found that the center of the shell is an equilibrium point. Further, when k﹥1;k?being the constant of a particular integral of the Gylden-Meshcherskii problem;a pair of equilibrium point, lying in the -plane?with each forming triangles with the center of the shell and the second primary exist. Several of the points exist depending on k;hence every point inside the shell is an equilibrium point. The linear stability of the equilibrium points is examined and it is seen that the point at the center of the shell of the autonomized system is conditionally stable;while that of the non-autonomized system is unstable. The triangular equilibrium points on the -plane of both systems are unstable.

Impact of radiation pressure and circumstellar dust on motion of a test particle in Manev’s field

In this paper,we present a study on the impact of radiation pressure and circumstellar dust on the motion of a test particle in the framework of the restricted four-body problem under the Manev’s field.We show that the distribution of equilibrium points on the plane of motion is slightly different from that of the classical Newtonian problem.With the aid of the Lyapunov characteristic exponents,we show that the system is sensitive to changes in initial conditions;hence,the orbit of the system is found to be chaotic in the phase space for the given initial conditions.Furthermore,a numerical application of this model to a stellar system(Gliese 667C)is considered,which validates the dependence of the equilibrium points on the mass parameter.We show that the non-collinear equilibrium points of this stellar system are distributed symmetrically about the x-axis,and five of them are linearly stable.The basins of attraction of the system show that the equilibrium points have irregular boundaries,and we use the energy integral and the Manev parameter to illustrate the zero-velocity curves showing the permissible region of motion of the test particle with respect to the Jacobi constant.