scholarly journals Effect on L4,5 in the ER3BP when Both Primaries are Radiating with Oblateness up to Zonal Harmonic J4

2019 ◽  
Vol 83 ◽  
pp. 1-11
Author(s):  
Jagadish Singh ◽  
Blessing Ashagwu
Keyword(s):  
Body Problem ◽  
Critical Mass ◽  
Major Axis ◽  
Mass Ratio ◽  
Three Body Problem ◽  
Semi Major Axis ◽  
Zonal Harmonic ◽  
Triangular Points ◽  
Oblate Spheroids ◽  
Three Body

This study examines the triangular points in the elliptic restricted three-body problem when both primaries are sources of radiation as well as oblate spheroids with oblateness up to zonal harmonic J4. The positions of triangular points and their critical mass ratio are seen to be affected by the eccentricity, semi major axis, radiation and oblateness of both primaries up to zonal harmonic J4. We highlight the effects of the said parameters on the locations of the triangular points of 61 CYGNI and STRUVE 2398. The triangular points of these systems are found to be unstable.

scholarly journals On stability of triangular points of the restricted relativistic elliptic three-body problem with triaxial and oblate primaries

2017 ◽  
pp. 47-52
Author(s):  
K. Zahra ◽  
Z. Awad ◽  
H.R. Dwidar ◽  
M. Radwan
Keyword(s):  
Linear Stability ◽  
Body Problem ◽  
Critical Mass ◽  
Combined Effects ◽  
Mass Ratio ◽  
Three Body Problem ◽  
Triangular Points ◽  
The Stability ◽  
Three Body ◽  
Ratio Range

This paper investigates the location and linear stability of triangular points under combined effects of perturbations: triaxialty of a massive primary, oblateness of a less massive one, and relativistic corrections. The primaries in this system are assumed to move in elliptical orbits around their common barycenter. It is found that the locations of the triangular points are affected by the involved perturbations. The stability of orbits near these points is also examined. We observed that these points are stable for the mass ratio, ?, range 0 < ? < ?c, where ?c is the critical mass ratio, and unstable for the range ?c ? ? ? 0.5.

scholarly journals On the Stability ofL4,5in the Relativistic R3BP with Oblate Secondary and Radiating Primary

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Nakone Bello ◽  
Jagadish Singh
Keyword(s):  
Stability Region ◽  
Body Problem ◽  
Critical Mass ◽  
Mass Ratio ◽  
Three Body Problem ◽  
Triangular Points ◽  
Numerical Exploration ◽  
The Stability ◽  
Oblate Secondary ◽  
Three Body

We consider a version of the relativistic restricted three-body problem (R3BP) which includes the effects of oblateness of the secondary and radiation of the primary. We determine the positions and analyze the stability of the triangular points. We find that these positions are affected by relativistic, oblateness, and radiation factors. It is also seen that both oblateness of the secondary and radiation of the primary reduce the size of stability region. Further, a numerical exploration computing the positions of the triangular points and the critical mass ratio of some binaries systems consisting of the Sun and its planets is given in the tables.

scholarly journals Effects of Perturbations on the Stability of Equilibrium Points in the CR3BP with Luminous and Heterogeneous Spheroid Primaries

2021 ◽  
Author(s):  
Jagadish Singh ◽  
Shitu Muktar Ahmad
Keyword(s):  
Body Problem ◽  
Equilibrium Points ◽  
Critical Mass ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Triangular Points ◽  
Stability Of Equilibrium ◽  
Oblate Spheroids ◽  
The Stability ◽  
Three Body

Abstract This paper studies the position and stability of equilibrium points in the circular restricted three-body problem (CR3BP) under the influence of small perturbations in the Coriolis and centrifugal forces when the primaries are radiating and heterogeneous oblate spheroids. It is seen that there exist five libration points as in the classical restricted three-body problem, three collinear Li(i=1,2,3) and two triangular Li(i= 4,5). It is also seen that the triangular points are no longer to form equilateral triangles with the primaries rather they form simple triangles with line joining the primaries. It is further observed that despite all perturbations the collinear points remain unstable while the triangular points are stable for 0 < µ < µc and unstable for µc ≤ µ ≤ ½, where µc is the critical mass ratio depending upon aforementioned parameters. It is marked that small perturbation in the Coriolis force, radiation and heterogeneous oblateness of the both primaries have destabilizing tendencies. Their numerical examination is also performed.

scholarly journals Effects of radiation and triaxiality of triangular equilibrium points in elliptical restricted three body problem

2015 ◽  
Vol 3 (2) ◽  
pp. 97 ◽  
Author(s):  
Ashutosh Narayan ◽  
Krishna Kumar Pandey ◽  
Sandip Kumar Shrivastava
Keyword(s):  
Radiation Pressure ◽  
Body Problem ◽  
Equilibrium Points ◽  
Critical Mass ◽  
Major Axis ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Semi Major Axis ◽  
The Stability ◽  
Three Body

<p>This paper studies effects of the triaxiality and radiation pressure of both the primaries on the stability of the infinitesimal motion about triangular equilibrium points in the elliptical restricted three body problem(ER3BP), assuming that the bigger and the smaller primaries are triaxial and the source of radiation as well. It is observed that the motion around these points is stable under certain condition with respect to the radiation pressure and oblate triaxiality. The critical mass ratio depends on the radiation pressure, triaxiality, semi -major axis and eccentricity of the orbits. It is further analyzed that an increase in any of these parameters has destabilizing effects on the orbits of the infinitesimal.</p>

scholarly journals Progression of bifurcated family f type periodic orbits in the circular restricted three-body problem

2017 ◽  
Vol 5 (2) ◽  
pp. 69
Author(s):  
Nishanth Pushparaj ◽  
Ram Krishan Sharma
Keyword(s):  
Solar Radiation ◽  
Periodic Orbits ◽  
Radiation Pressure ◽  
Body Problem ◽  
Solar Radiation Pressure ◽  
Restricted Three Body Problem ◽  
Mass Ratio ◽  
Three Body Problem ◽  
Semi Major Axis ◽  
Three Body

Progression of f-type family of periodic orbits, their nature, stability and location nearer the smaller primary for different mass ratios in the framework of circular restricted three-body problem is studied using Poincaré surfaces of section. The orbits around the smaller primary are found to decrease in size with increase in Jacobian Constant C, and move very close towards the smaller primary. The orbit bifurcates into two orbits with the increase in C to 4.2. The two orbits that appear for this value of C belong to two adjacent separate families: one as direct orbit belonging to family g of periodic orbits and other one as retrograde orbit belonging to family f of periodic orbits. This bifurcation is interesting. These orbits increase in size with increase in mass ratio. The elliptic orbits found within the mass ratio 0 < µ ≤ 0.1 have eccentricity less than 0.2 and the orbits found above the mass ratio µ > 0.1 are elliptical orbits with eccentricity above 0.2. Deviations in the parameters: eccentricity, semi-major axis and time period of these orbits with solar radiation pressure q are computed in the frame work of photogravitational restricted Three-body problem in addition to the restricted three-body problem. These parameters are found to decrease with increase in the solar radiation pressure.

scholarly journals Investigation of the Stability of a Test Particle in the Vicinity of Collinear Points with the Additional Influence of an Oblate Primary and a Triaxial-Stellar Companion in the Frame of ER3BP

2018 ◽  
Vol 13 ◽  
pp. 12-27 ◽  
Author(s):  
Aminu Abubakar Hussain ◽  
Aishetu Umar ◽  
Jagadish Singh
Keyword(s):  
Numerical Analysis ◽  
Body Problem ◽  
Major Axis ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Semi Major Axis ◽  
Primary Body ◽  
Additional Influence ◽  
The Stability ◽  
Three Body

We investigate in the elliptic framework of the restricted three-body problem, the motion around the collinear points of an infinitesimal particle in the vicinity of an oblate primary and a triaxial stellar companion. The locations of the collinear points are affected by the eccentricity of the orbits, oblateness of the primary body and the triaxiality and luminosity of the secondary. A numerical analysis of the effects of the parameters on the positions of collinear points of CEN X-4 and PSR J1903+0327 reveals a general shift away from the smaller primary with increase in eccentricity and triaxiality factors and a shift towards the smaller primary with increase in the semi-major axis and oblateness of the primary on L1. The collinear points remain unstable in spite of the introduction of these parameters.

scholarly journals The Motion of Out-of-Plane Equilibrium Points in the Elliptic Restricted Three-Body Problem at J4

2021 ◽  
Vol 17 ◽  
pp. 1-11
Author(s):  
Jagadish Singh ◽  
Tyokyaa K. Richard
Keyword(s):  
Binary Systems ◽  
Body Problem ◽  
Equilibrium Points ◽  
Major Axis ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Semi Major Axis ◽  
Out Of Plane ◽  
Three Body ◽  
Plane Equilibrium

We have investigated the motion of the out-of-plane equilibrium points within the framework of the Elliptic Restricted Three-Body Problem (ER3BP) at J4 of the smaller primary in the field of stellar binary systems: Xi- Bootis and Sirius around their common center of mass in elliptic orbits. The positions and stability of the out-of-plane equilibrium points are greatly affected on the premise of the oblateness at J4 of the smaller primary, semi-major axis and the eccentricity of their orbits. The positions L6, 7 of the infinitesimal body lie in the xz-plane almost directly above and below the center of each oblate primary. Numerically, we have computed the positions and stability of L6, 7 for the aforementioned binary systems and found that their positions are affected by the oblateness of the primaries, the semi-major axis and eccentricity of their orbits. It is observed that, for each set of values, there exist at least one complex root with positive real part and hence in Lyapunov sense, the stability of the out-of-plane equilibrium points are unstable.

scholarly journals Locations of Lagrangian points and periodic orbits around triangular points in the photo gravitational elliptic restricted three-body problem with oblateness

2019 ◽  
Vol 7 (2) ◽  
pp. 25
Author(s):  
Ancy Johnson ◽  
Ram Krishan Sharma
Keyword(s):  
Periodic Orbits ◽  
Radiation Pressure ◽  
Body Problem ◽  
Critical Mass ◽  
Stable Region ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Lagrangian Points ◽  
Triangular Points ◽  
Three Body

Locations of the Lagrangian points are computed and periodic orbits are studied around the triangular points in the photogravitational elliptic restricted three-body problem (ER3BP) by considering the more massive primary as the source of radiation and smaller primary as an oblate spheroid. A new mean motion taken from Sharma et al. [13] is used to study the effect of radiation pressure and oblateness of the primaries. The critical mass parameter  that bifurcates periodic orbits from non-periodic orbits tends to reduce with radiation pressure and oblateness. The transition curves defining stable region of orbits are drawn for different values of radiation pressure and oblateness using the analytical method of Bennet [14]. Tadpole orbits with long- and short- periodic oscillations are obtained for Sun-Jupiter and Sun-Saturn systems.  

scholarly journals The Qualitative Explanation of Observed Peculiarities of Hecuba and Hilda Asteroids Distribution by a Common Investigation

1992 ◽  
Vol 152 ◽  
pp. 139-144
Author(s):  
Elena V. Alfimova ◽  
Igor A. Gerasimov
Keyword(s):  
Body Problem ◽  
Gravitational Constant ◽  
Central Body ◽  
Major Axis ◽  
Mass Point ◽  
Three Body Problem ◽  
Qualitative Explanation ◽  
Semi Major Axis ◽  
Planar Case ◽  
Three Body

Let us consider the planar case of the circular restricted three-body problem. The mass of central body is unit, the radius of the circular orbit of perturbing point P′ (of mass μ = 1/1047.39 according to Jupiter's mass) is also unit and the other unit is such that the gravitational constant is equal to 1. The Keplerian elements of the perturbed mass point P (asteroid), with semi-major axis α < 1, are given by usual notations; the elements of P‘ are indicated with a prime (’).

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