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1.
The existence and linear stability of the planar equilibrium points for photogravitational elliptical restricted three body problem is investigated in this paper. Assuming that the primaries, one of which is radiating are rotating in an elliptical orbit around their common center of mass. The effect of the radiation pressure, forces due to stellar wind and Poynting–Robertson drag on the dust particles are considered. The location of the five equilibrium points are found using analytical methods. It is observed that the collinear equilibrium points L1, L2 and L3 do not lie on the line joining the primaries but are shifted along the y-coordinate. The instability of the libration points due to the presence of the drag forces is demonstrated by Lyapunov’s first method of stability. 相似文献
2.
Due to various perturbations, the collinear libration points of the real Earth–Moon system are not equilibrium points anymore.
Under the assumption that the Moon’s motion is quasi-periodic, special quasi-periodic orbits called dynamical substitutes
exist. These dynamical substitutes replace the geometrical collinear libration points as time-varying equilibrium points.
In the paper, the dynamical substitutes of the three collinear libration points in the real Earth–Moon system are computed.
For the points L
1 and L
2, linearized motions around the dynamical substitutes are described, and the variational equations of the dynamical substitutes
are reduced to a form with a near constant coefficient matrix. Then higher order analytical formulae of the central manifolds
are constructed. Using these analytical solutions as initial seeds, Lissajous orbits and halo orbits are computed with numerical
algorithms. 相似文献
3.
The effect of small perturbations in the coriolis and the centrifugal forces on the location of equilibrium points in the restricted problems of three bodies with variable mass has been studied. It is found that the points L4 and L5 form nearly equilateral triangles with the primaries and the points L1, L2, L3 remain collinear and lie on the line joining the primaries. 相似文献
4.
M. K. Ammar 《Astrophysics and Space Science》2008,313(4):393-408
In this paper the effect of solar radiation pressure on the location and stability of the five Lagrangian points is studied,
within the frame of elliptic restricted three-body problem, where the primaries are the Sun and Jupiter acting on a particle
of negligible mass. We found that the radiation pressure plays the rule of slightly reducing the effective mass of the Sun
and changes the location of the Lagrangian points. New formulas for the location of the collinear libration points were derived.
For large values of the force ratio β, we found that at β=0.12, the collinear point L3 is stable and some families of periodic orbits can be drawn around it. 相似文献
5.
T. A. Heppenheimer 《Celestial Mechanics and Dynamical Astronomy》1973,7(2):177-194
Out-of-plane motion about libration points is studied within the framework of the elliptic restricted three-body problem. Nonlinear motion in the circular restricted problem is given to third order in the out-of-plane amplitudeA
z by Jacobi elliptic functions. Linear motion in the elliptic problem is studied using Mathieu's and Hill's equations. Additional terms needed for a complete third-order theory are found using Lindsted's method. This theory is constructed for the case of collinear libration points; for the case of triangular points, a third-order nonlinear solution is given separately in terms of Jacobi elliptic functions. 相似文献
6.
We consider the modified restricted three body problem with power-law density profile of disk, which rotates around the center
of mass of the system with perturbed mean motion. Using analytical and numerical methods, we have found equilibrium points
and examined their linear stability. We have also found the zero velocity surface for the present model. In addition to five
equilibrium points there exists a new equilibrium point on the line joining the two primaries. It is found that L
1 and L
3 are stable for some values of inner and outer radius of the disk while other collinear points are unstable, but L
4 is conditionally stable for mass ratio less than that of Routh’s critical value. Lastly, we have studied the effects of radiation
pressure, oblateness and mass of the disk on the motion and stability of equilibrium points. 相似文献
7.
8.
《New Astronomy》2020
This paper deals with the existence and stability of libration points in linear sense in the central-body square configuration of restricted six-body problem. It is found that there exist twelve libration points, four collinear and eight non-collinear. All libration points lie on the concentric circles C1, C2 and C3 centered at origin. The libration points L1,3,5,7 lie on circle C1, L9,10,11,12 on C2 and L2,4,6,8 on C3. This is also observed that the eight libration points are on the axes and four are off the axes, i.e., L1,2,3,4 are on x-axis, L5,6,7,8 on y-axis and rest are off the axes. The libration points on circles C1 and C3 are unstable for all values of mass parameter µ while the libration points on circle C2 are stable for the critical mass parameter µc = 0.00910065. 相似文献
9.
S. M. Elshaboury 《Astrophysics and Space Science》1989,155(2):209-214
In this paper we consider the circular planar restricted problem of three rigid bodiesS
i(i=1, 2, 3), two of them are axisymmetric ellipsoids and a third bodyS
3 is a spherical satellite with decreasing mass, under the gravitational forces. The effect of small perturbations in the Coriolis force and the centrifugal forces on the location of equilibrium points has been studied. It is found only in the case when the primaries have equal differences between their respective principal moments of inertial the pointsL
4 andL
5 form nearly equilateral tringles with the primaries. The equilibrium pointsL
1,L
2,L
3 remain collinear an ies on the line joining the primaries. 相似文献
10.
The stability of collinear and triangular libration points is investigated in the photogravitational elliptic restricted three-body problem, in which two primary bodies emit light energy simultaneously. The conditions of stability of the collinear and triangular libration points are obtained based on a linearized set of equations of perturbed motion for various values of the eccentricity of the Keplerian orbits and the mass ratio of the primary bodies. The maximal numerical value is defined for the eccentricity at which a stable libration point can still exist. It is demonstrated how the parametric resonance causes an instability of collinear and triangular libration points; the evolution of the origination of the instability zones is traced. The minimal eccentricity value is found at which zones of instability of triangular libration points arise. 相似文献
11.
This paper deals with the existence and the stability of the libration points in the restricted three-body problem when the smaller primary is an ellipsoid. We have determined the equations of motion of the infinitesimal mass which involves elliptic integrals and then we have investigated the collinear and non collinear libration points and their stability. This is observed that there exist five collinear libration points and the non collinear libration points are lying on the arc of the unit circle whose centre is the bigger primary. Further observed that the libration points either collinear or non-collinear all are unstable. 相似文献
12.
R. K. Choudhry 《Celestial Mechanics and Dynamical Astronomy》1977,16(4):411-419
In this paper the existence of collinear as well as equilateral libration points for the generalised elliptic restricted three body problem has been studied distinct from Kondurar and Shinkarik (1972) where a study has been made for the generalised circular restricted three body problem. Here the coordinates of the libration points have been found to be functions of timet. 相似文献
13.
In this paper we have proved the existence of libration points for the generalised photogravitational restricted problem of three bodies. We have assumed the infinitesimal mass of the shape of an oblate spheroid and both of the finite masses to be radiating bodies and the effect of their radiation pressure on the motion of the infinitesimal mass has also been taken into account. It is seen that there is a possibility of nine libration points for small values of oblateness, three collinear, four coplanar and two triangular. 相似文献
14.
Peter J. Brown Alice A. Breeveld Stephen Holland Paul Kuin Tyler Pritchard 《Astrophysics and Space Science》2014,353(1):89-96
This paper studies the motion of an infinitesimal mass in the framework of Robe’s circular restricted three-body problem in two cases; the first case is when the hydrostatic equilibrium figure of the first primary is an oblate spheroid, the shape of the second primary is considered as an oblate spheroid with oblateness coefficients up to the second zonal harmonic, while the first primary is a Roche ellipsoid in the second case and the full buoyancy of the fluid is taken into account. In case one; it is observed that there are two axial libration points on the line joining the centres of the primaries, points on the circle within the first primary are also libration points under certain conditions. It is further found that the first axial point is stable, while the second one is conditionally stable, and the circular points are unstable. It is found in case two that there is exist only one libration point (0,0,0) this point is stable. 相似文献
15.
This paper investigates the triangular libration points in the photogravitational restricted three-body problem of variable
mass, in which both the attracting bodies are radiating as well and the infinitesimal body vary its mass with time according
to Jeans’ law. Firstly, applying the space-time transformation of Meshcherskii in the special case when q=1/2, k=0, n=1, the differential equations of motion of the problem are given. Secondly, in analogy to corresponding problem with constant
mass, the positions of analogous triangular libration points are obtained, and the fact that these triangular libration points
cease to be classical ones when α≠0, but turn to classical L
4 and L
5 naturally when α=0 is pointed out. Lastly, introducing the space-time inverse transformation of Meshcherskii, the linear stability of triangular
libration points is tested when α>0. It is seen that the motion around the triangular libration points become unstable in general when the problem with constant
mass evolves into the problem with decreasing mass. 相似文献
16.
N. Sekiguchi 《Earth, Moon, and Planets》1970,2(2):129-135
In the present paper, the problem of whether the interplanetary matter has a tendency to accumulate around the Lagrangian libration pointsL
4 andL
5, is examined statistically. It is concluded that: (1) If the particles are initially assumed to be distributed uniformly, they keep the uniformity ever after around the libration points. (2) If the particles receive random stochastic perturbations, their distribution tends to become uniform even if initially they have non-uniform distributions. (3) If the particles mutually collide inelastically, they have a tendency to avoid the regions near the libration points. Therefore, the interplanetary matter will not tend to accumulate near the libration points. Even if the observations of the libration cloud so far reported are confirmed, the clouds are likely to be but temporary objects. 相似文献
17.
This paper investigates the orbit radial stabilization of a two-craft virtual Coulomb structure about circular orbits and
at Earth–Moon libration points. A generic Lyapunov feedback controller is designed for asymptotically stabilizing an orbit
radial configuration about circular orbits and collinear libration points. The new feedback controller at the libration points
is provided as a generic control law in which circular Earth orbit control form a special case. This control law can withstand
differential solar perturbation effects on the two-craft formation. Electrostatic Coulomb forces acting in the longitudinal
direction control the relative distance between the two satellites and inertial electric propulsion thrusting acting in the
transverse directions control the in-plane and out-of-plane attitude motions. The electrostatic virtual tether between the
two craft is capable of both tensile and compressive forces. Using the Lyapunov’s second method the feedback control law guarantees
closed loop stability. Numerical simulations using the non-linear control law are presented for circular orbits and at an
Earth–Moon collinear libration point. 相似文献
18.
This paper studies the existence and stability of equilibrium points under the influence of small perturbations in the Coriolis
and the centrifugal forces, together with the non-sphericity of the primaries. The problem is generalized in the sense that
the bigger and smaller primaries are respectively triaxial and oblate spheroidal bodies. It is found that the locations of
equilibrium points are affected by the non-sphericity of the bodies and the change in the centrifugal force. It is also seen
that the triangular points are stable for 0<μ<μ
c
and unstable for
mc ￡ m < \frac12\mu_{c}\le\mu <\frac{1}{2}, where μ
c
is the critical mass parameter depending on the above perturbations, triaxiality and oblateness. It is further observed that
collinear points remain unstable. 相似文献
19.
This paper investigates the combined effect of small perturbations ε,ε′ in the Coriolis and centrifugal forces, radiation pressure q i , and changing oblateness of the primaries A i (t) (i=1,2) on the stability of equilibrium points in the restricted three body problem in which the primaries is a supergiant eclipsing binary system which consists of a pair of bright oblate stars having the appearance of a giant peanut in space and their masses assumed to vary with time in the absence of reactive forces. The equations of motion are derived and the equilibrium points are obtained. For the autonomized system, it is seen that there are more than a pair of the triangular points as κ→∞; κ being the arbitrary sum of the masses of the primaries. In the case of the collinear points, two additional equilibrium points exist on the line joining the primaries when simultaneously κ+ε′<0 and both primaries are oblate, i.e., 0<α i ?1. So there are five collinear equilibrium points in this case. Two non-planar equilibrium points exist for κ>1. Hence, there are at least nine equilibrium points of the system. The stability of these points is explored analytically and numerically. It is seen that the collinear and triangular points are stable with respect to certain conditions controlled by κ while the non-planar equilibrium points are unstable. 相似文献
20.
This paper deals with the existence and stability of the non-collinear libration points in the restricted three-body problem when both the primaries are ellipsoid with equal mass and identical in shape. We have determined the equations of motion of the infinitesimal mass which involves elliptic integrals and then we have investigated the existence and stability of the non-collinear libration points. This is observed that the non-collinear libration points exist only in the interval 52°<φ<90° and form an isosceles triangle with the primaries. Further we observed that the non collinear libration points are unstable in 52°<φ<90°. 相似文献