共查询到20条相似文献，搜索用时 153 毫秒
1.
We investigated the motion of the perijove and ascending node of the 8th satellite of Jupiter, Pasiphae. The main perturbations by the Sun on the satellite permitted to use an intermediate orbit obtained by approximated solutions of differential equations previously transformed by the Von Zeipel method. The orbit is a non-Keplerian ellipse. The secular motion of the ascending node, argument of perijove, and essential periodic perturbations were taken into account. Using our theory we showed that the inclination and eccentricity of Pasiphae can acquire values by which the orbit becomes a librating one; but, within Pasiphae’s observation period, the motion of its perijove is circulating. Taking into account the results of our previous works on Pasiphae motion, we can conclude that the mean motion of the ascending node is similar for different values of the satellite inclination and eccentricity. But the mean motion of the perijove strongly depends on the orbit inclination and eccentricity, according to the Lidov–Kozai mechanism. 相似文献
2.
A modified periodic orbit of the third kind is introduced that is closely related to periodic orbits of the third kind as defined by Poincaré. It is shown that Pluto librates about the periodic orbit with apparent stability. This further explains the librational motion of the resonant argument of Pluto and the avoidance of a Pluto-Neptune close approach as found by Cohen and Hubbard and the long-term motion of Pluto and the librational motion of the perihelion as found by Williams and Benson. With libration about a periodic orbit, the numerical solution of Williams and Benson can be extrapolated to longer times in the past and future. 相似文献
3.
A detailed derivation of the effect of solar radiation pressure on the orbit of a body about a primary orbiting the Sun is
given. The result is a set of secular equations that can be used for long-term predictions of changes in the orbit. Solar
radiation pressure is modeled as a Fourier series in the body’s rotation state, where the coefficients are based on the shape
and radiation properties of the body as parameters. In this work, the assumption is made that the body is in a synchronous
orbit about the primary and rotates at a constant rate. This model is used to write explicit variational equations of the
energy, eccentricity vector, and angular momentum vector for an orbiting body. Given that the effect of the solar radiation
pressure and the orbit are periodic functions, they are readily averaged over an orbit. Furthermore, the equations can be
averaged again over the orbit of the primary about the Sun to give secular equations for long-term prediction. This methodology
is applied to both circular and elliptical orbits, and the full equations for secular changes to the orbit in both cases are
presented. These results can be applied to natural systems, such as the binary asteroid system 1999 KW4, to predict their
evolution due to the Binary YORP effect, or to artificial Earth orbiting, nadir-pointing satellites to enable more precise
models for their orbital evolution. 相似文献
4.
5.
C. G. Zagouras 《Celestial Mechanics and Dynamical Astronomy》1991,51(4):331-348
In this article the effect of radiation pressure on the periodic motion of small particles in the vicinity of the triangular equilibrium points of the restricted three body problem is examined. Second order parametric expansions are constructed and the families of periodic orbits are determined numerically for two sets of values of the mass and radiation parameters corresponding to the non-resonant and the resonant case. The stability of each orbit is also studied. 相似文献
6.
József Vanyó Bruno Escribano Julyan H. E. Cartwright Diego L. González Oreste Piro Tamás Tél 《Celestial Mechanics and Dynamical Astronomy》2011,109(2):181-200
We study tidal synchronization and orbit circularization in a minimal model that takes into account only the essential ingredients
of tidal deformation and dissipation in the secondary body. In previous work we introduced the model (Escribano et al. in
Phys. Rev. E, 78:036216, 2008); here we investigate in depth the complex dynamics that can arise from this simplest model of tidal synchronization and
orbit circularization. We model an extended secondary body of mass m by two point masses of mass m/2 connected with a damped spring. This composite body moves in the gravitational field of a primary of mass M ≫ m located at the origin. In this simplest case oscillation and rotation of the secondary are assumed to take place in the plane
of the Keplerian orbit. The gravitational interactions of both point masses with the primary are taken into account, but that
between the point masses is neglected. We perform a Taylor expansion on the exact equations of motion to isolate and identify
the different effects of tidal interactions. We compare both sets of equations and study the applicability of the approximations,
in the presence of chaos. We introduce the resonance function as a resource to identify resonant states. The approximate equations
of motion can account for both synchronization into the 1:1 spin-orbit resonance and the circularization of the orbit as the
only true asymptotic attractors, together with the existence of relatively long-lived metastable orbits with the secondary
in p:q (p and q being co-prime integers) synchronous rotation. 相似文献
7.
We explore the effect of oblateness of Saturn (more massive primary) on the periodic orbits and the regions of quasi-periodic motion around both the primaries in the Saturn-Titan system in the framework of planar circular restricted three-body problem. First order interior and exterior mean motion resonances are located. The effect of oblateness is studied on the location, nature and size of periodic and quasi-periodic orbits, using the numerical technique of Poincare surface of sections. Some of the periodic orbits change to quasi-periodic orbits due to the effect of oblateness and vice-versa. The stability of the orbits around Saturn, Titan and both varies with the inclusion of oblateness. The centers of the periodic orbits around Titan move towards Saturn, whereas those around Saturn move towards Titan. For the orbit around Titan at C=2.9992, x=0.959494, the apocenter becomes pericenter. By incorporating oblateness effect, the orbit around Titan at C=2.99345, x=0.924938 is captured by Saturn, remains in various trajectories around Saturn, and as time progresses it spirals away around both the primaries. 相似文献
8.
A. P. Markeev 《Astronomy Letters》2005,31(9):627-633
We investigate the stability of the periodic motion of a satellite, a rigid body, relative to the center of mass in a central Newtonian gravitational field in an elliptical orbit. The orbital eccentricity is assumed to be low. In a circular orbit, this periodic motion transforms into the well-known motion called hyperboloidal precession (the symmetry axis of the satellite occupies a fixed position in the plane perpendicular to the radius vector of the center of mass relative to the attractive center and describes a hyperboloidal surface in absolute space, with the satellite rotating around the symmetry axis at a constant angular velocity). We consider the case where the parameters of the problem are close to their values at which a multiple parametric resonance takes place (the frequencies of the small oscillations of the satellite’s symmetry axis are related by several second-order resonance relations). We have found the instability and stability regions in the first (linear) approximation at low eccentricities. 相似文献
9.
P. C. Kammeyer 《Celestial Mechanics and Dynamical Astronomy》1980,22(3):289-296
In this paper three results on the linearized mapping associated with the plane three body problem near a periodic orbit are established. It is first shown that linear stability of such an orbit is independent of initial position on the orbit and of coordinate system. Second, the relation of Hénon connecting the rates of change of rotation angle and period on an isoenergetic family of periodic orbits is proved, together with a similar relation for families of orbits closing exactly in a rotating coordinate system. Finally, a condition for a critical orbit is given which is applicable to any family of periodic orbits. 相似文献
10.
David Parry Rubincam 《Celestial Mechanics and Dynamical Astronomy》1977,15(1):21-33
The motion of a satellite with negligible mass in the Schwarzschild metric is treated as a problem in Newtonian physics. The relativistic equations of motion are formally identical with those of the Newtonian case of a particle moving in the ordinary inverse-square law field acted upon by a disturbing function which varies asr ?3. Accordingly, the relativistic motion is treated with the methods of celestial mechanics. The disturbing function is expressed in terms of the Keplerian elements of the orbit and substituted into Lagrange's planetary equations. Integration of the equations shows that a typical Earth satellite with small orbital eccentricity is displaced by about 17 cm from its unperturbed position after a single orbit, while the periodic displacement over the orbit reaches a maximum of about 3 cm. Application of the equations to the planet Mercury gives the advance of the perihelion and a total displacement of about 85 km after one orbit, with a maximum periodic displacement of about 13 km. 相似文献
11.
The motion of a massless particle in the gravity of a binary asteroid system, referred as the restricted full three-body problem (RF3BP), is fundamental, not only for the evolution of the binary system, but also for the design of relevant space missions. In this paper, equilibrium points and associated periodic orbit families in the gravity of a binary system are investigated, with the binary (66391) 1999 KW4 as an example. The polyhedron shape model is used to describe irregular shapes and corresponding gravity fields of the primary and secondary of (66391) 1999 KW4, which is more accurate than the ellipsoid shape model in previous studies and provides a high-fidelity representation of the gravitational environment. Both of the synchronous and non-synchronous states of the binary system are considered. For the synchronous binary system, the equilibrium points and their stability are determined, and periodic orbit families emanating from each equilibrium point are generated by using the shooting (multiple shooting) method and the homotopy method, where the homotopy function connects the circular restricted three-body problem and RF3BP. In the non-synchronous binary system, trajectories of equivalent equilibrium points are calculated, and the associated periodic orbits are obtained by using the homotopy method, where the homotopy function connects the synchronous and non-synchronous systems. Although only the binary (66391) 1999 KW4 is considered, our methods will also be well applicable to other binary systems with polyhedron shape data. Our results on equilibrium points and associated periodic orbits provide general insights into the dynamical environment and orbital behaviors in proximity of small binary asteroids and enable the trajectory design and mission operations in future binary system explorations. 相似文献
12.
John D. Hadjidemetriou Th. Christides 《Celestial Mechanics and Dynamical Astronomy》1975,12(2):175-187
A periodic orbit of the restricted circular three-body problem, selected arbitrarily, is used to generate a family of periodic motions in the general three-body problem in a rotating frame of reference, by varying the massm 3 of the third body. This family is continued numerically up to a maximum value of the mass of the originally small body, which corresponds to a mass ratiom 1:m 2:m 3?5:5:3. From that point on the family continues for decreasing massesm 3 until this mass becomes again equal to zero. It turns out that this final orbit of the family is a periodic orbit of the elliptic restricted three body problem. These results indicate clearly that families of periodic motions of the three-body problem exist for fixed values of the three masses, since this continuation can be applied to all members of a family of periodic orbits of the restricted three-body problem. It is also indicated that the periodic orbits of the circular restricted problem can be linked with the periodic orbits of the elliptic three-body problem through periodic orbits of the general three-body problem. 相似文献
13.
George Voyatzis John D. Hadjidemetriou 《Celestial Mechanics and Dynamical Astronomy》2006,95(1-4):259-271
We study the dynamics of 3:1 resonant motion for planetary systems with two planets, based on the model of the general planar three body problem. The exact mean motion resonance corresponds to periodic motion (in a rotating frame) and the basic families of symmetric and asymmetric periodic orbits are computed. Four symmetric families bifurcate from the family of circular orbits of the two planets. Asymmetric families bifurcate from the symmetric families, at the critical points, where the stability character changes. There exist also asymmetric families that are independent of the above mentioned families. Bounded librations exist close to the stable periodic orbits. Therefore, such periodic orbits (symmetric or asymmetric) determine the possible stable configurations of a 3:1 resonant planetary system, even if the orbits of the two planets intersect. For the masses of the system 55Cnc most of the periodic orbits are unstable and they are associated with chaotic motion. There exist however stable symmetric and asymmetric orbits, corresponding to regular trajectories along which the critical angles librate. The 55Cnc extra-solar system is located in a stable domain of the phase space, centered at an asymmetric periodic orbit. 相似文献
14.
Marco Giancotti Mauro Pontani Paolo Teofilatto 《Celestial Mechanics and Dynamical Astronomy》2012,114(1-2):55-76
Analysis and design of low-energy transfers to the Moon has been a subject of great interest for many decades. This paper is concerned with a topological study of such transfers, with emphasis to trajectories that allow performing lunar capture and those that exhibit homoclinic connections, in the context of the circular restricted three-body problem. A fundamental theorem stated by Conley locates capture trajectories in the phase space and can be condensed in a sentence: “if a crossing asymptotic orbit exists then near any such there is a capture orbit”. In this work this fundamental theoretical assertion is used together with an original cylindrical isomorphic mapping of the phase space associated with the third body dynamics. For a given energy level, the stable and unstable invariant manifolds of the periodic Lyapunov orbit around the collinear interior Lagrange point are computed and represented in cylindrical coordinates as tubes that emanate from the transformed periodic orbit. These tubes exhibit complex geometrical features. Their intersections correspond to homoclinic orbits and determine the topological separation of long-term lunar capture orbits from short-duration capture trajectories. The isomorphic mapping is proven to allow a deep insight on the chaotic motion that characterizes the dynamics of the circular restricted three-body, and suggests an interesting interpretation, and together corroboration, of Conley’s assertion on the topological location of lunar capture orbits. Moreover, an alternative three-dimensional representation of the phase space is profitably employed to identify convenient lunar periodic orbits that can be entered with modest propellant consumption, starting from the Lyapunov orbit. 相似文献
15.
The purpose of this paper is the semi-analytical computation of the bounded orbits of Hill’s equations, describing the relative
motion of two particles in their Keplerian motion around a central body. We have considered the case in which one of the particles
moves along a circular reference orbit. The solutions obtained are the generalisation of the usual periodic orbits obtained
for the linearised equations and also of the third-order solution computed by D.L. Richardson and J.W. Mitchell (2003). With
the algorithm presented, those orbits can be computed in a fast and efficient way up to a high-order in the in-plane and out-of-plane
amplitudes. 相似文献
16.
V. A. Shefer 《Solar System Research》2003,37(4):326-332
A new method is suggested for finding the preliminary orbit from three complete measurements of the angular coordinates of a celestial body developed by analogy with the classic Lagrange–Gauss method. The proposed method uses the intermediate orbit that we had constructed in an earlier paper based on two position vectors and the corresponding time interval. This intermediate orbit allows for most of the perturbations in the motion of the body. Using the orbital motion of asteroid 1566 Icarus as an example, we compare the results obtained by applying the classic and the new method. The comparison shows the new method to be highly efficient for studying perturbed motion. It is especially efficient if applied to high-precision observational data covering short orbital arcs. 相似文献
17.
This paper contains an analysis of the attitude stability of a spinning axisymmetric satellite whose mass center moves in any known planar periodic orbit of the restricted three-body problem while the spin axis remains normal to the orbit plane. A procedure based on Floquet theory is developed for constructing attitude instability charts, and examples of these are presented for two stable periodic orbits of the Earth-Moon system—one direct and one retrograde. The physical significance of these instability predictions is then explored by means of numerical integration of the full nonlinear equations of motion. Finally, an analysis based on averaging is performed, leading to approximate instability charts and indicating a possible connection between certain orbital-attitude resonance conditions and unstable attitude motions. 相似文献
18.
19.
M. A. Vashkov’yak 《Astronomy Letters》2006,32(10):707-715
Based on the ideas of Lyapunov’s method, we construct a family of symmetric periodic solutions of the Hill problem averaged over the motion of a zero-mass point (a satellite). The low eccentricity of the satellite orbit and the sine of its inclination to the plane of motion of the perturbing body are parameters of the family. We compare the analytical solution with numerical solutions of the averaged evolutionary system and the rigorous (nonaveraged) equations of the restricted circular three-body problem. 相似文献
20.
A systematic approach to generate periodic orbits in the elliptic restricted problem of three bodies in introduced. The approach is based on (numerical) continuation from periodic orbits of the first and second kind in the circular restricted problem to periodic orbits in the elliptic restricted problem. Two families of periodic orbits of the elliptic restricted problem are found by this approach. The mass ratio of the primaries of these orbits is equal to that of the Sun-Jupiter system. The sidereal mean motions between the infinitesimal body and the smaller primary are in a 2:5 resonance, so as to approximate the Sun-Jupiter-Saturn system. The linear stability of these periodic orbits are studied as functions of the eccentricities of the primaries and of the infinitesimal body. The results show that both stable and unstable periodic orbits exist in the elliptic restricted problem that are close to the actual Sun-Jupiter-Saturn system. However, the periodic orbit closest to the actual Sun-Jupiter-Saturn system is (linearly) stable. 相似文献