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 (’).

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 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 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 New relativistic effects in the motion of the Moon

1986 ◽  
Vol 114 ◽  
pp. 407-410
Author(s):  
Bahram Mashhoon
Keyword(s):  
Body Problem ◽  
Gravitational Constant ◽  
Relativistic Effects ◽  
Restricted Three Body Problem ◽  
The Sun ◽  
The Moon ◽  
Three Body Problem ◽  
Novel Approach ◽  
Lunar Motion ◽  
Three Body

A summary of the main relativistic effects in the motion of the Moon is presented. The results are based on the application of a novel approach to the restricted three-body problem in general relativity to the lunar motion. It is shown that the rotation of the Sun causes a secular acceleration in the relative Earth-Moon motion. This might appear to be due to a temporal “variation” of the gravitational constant.

scholarly journals Three Dimensional Stability of A Rectilinear Periodic Solution of the Three-Body Problem, for all Values of the Masses

1977 ◽  
Vol 33 ◽  
pp. 161-161
Author(s):  
M. Hénon
Keyword(s):  
Periodic Solution ◽  
Dimensional Stability ◽  
Body Problem ◽  
Central Body ◽  
Three Dimensional ◽  
Three Body Problem ◽  
Stability And Instability ◽  
The Masses ◽  
Three Body ◽  
Triple Stars

AbstractWe consider a rectilinear periodic solution in which the central body collides alternately with each of the two other bodies. This solution is found to exist for all values of the three masses. Its stability with respect to three-dimensional perturbations is computed. Domains of stability and instability are delimited in a triangular mass diagram. Large domains of stability are found. This reinforces the conclusion that triple stars may have an “interplay” type of motion.

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