共查询到20条相似文献，搜索用时 15 毫秒
1.
J. F. Palacián 《Celestial Mechanics and Dynamical Astronomy》2007,98(4):219-249
We study the dynamics of a satellite (artificial or natural) orbiting an Earth-like planet at low altitude from an analytical
point of view. The perturbation considered takes into account the gravity attraction of the planet and in particular it is
caused by its inhomogeneous potential. We begin by truncating the equations of motion at second order, that is, incorporating
the zonal and the tesseral harmonics up to order two. The system is formulated as an autonomous Hamiltonian and has three
degrees of freedom. After three successive Lie transformations, the system is normalised with respect to two angular co-ordinates
up to order five in a suitable small parameter given by the quotient between the angular velocity of the planet and the mean
motion of the satellite. Our treatment is free of power expansions of the eccentricity and of truncated Fourier series in
the anomalies. Once these transformations are performed, the truncated Hamiltonian defines a system of one degree of freedom
which is rewritten as a function of two variables which generate a phase space which takes into account all of the symmetries
of the problem. Next an analysis of the system is achieved obtaining up to six relative equilibria and three types of bifurcations.
The connection with the original system is established concluding the existence of various families of invariant 3-tori of
it, as well as quasiperiodic and periodic trajectories. This is achieved by using KAM theory techniques. 相似文献
2.
Gwenaël Boué Nicolas Rambaux Andy Richard 《Celestial Mechanics and Dynamical Astronomy》2017,129(4):449-485
We revisit the rotation dynamics of a rigid satellite with either a liquid core or a global subsurface ocean. In both problems, the flow of the fluid component is assumed inviscid. The study of a hollow satellite with a liquid core is based on the Poincaré–Hough model which provides exact equations of motion. We introduce an approximation when the ellipticity of the cavity is low. This simplification allows to model both types of satellite in the same manner. The analysis of their rotation is done in a non-canonical Hamiltonian formalism closely related to Poincaré’s “forme nouvelle des équations de la mécanique”. In the case of a satellite with a global ocean, we obtain a seven-degree-of-freedom system. Six of them account for the motion of the two rigid components, and the last one is associated with the fluid layer. We apply our model to Titan for which the origin of the obliquity is still a debated question. We show that the observed value is compatible with Titan slightly departing from the hydrostatic equilibrium and being in a Cassini equilibrium state. 相似文献
3.
R. Vilhena De Moraes P. A. F. Da Silva 《Celestial Mechanics and Dynamical Astronomy》1989,47(3):225-243
Using Hamiltonian formalism the translational-rotational motion of a satellite is studied near a resonance considering the orbital and rotational motions. A first order perturbation theory is derived by Hori's transformation in order to eliminate short and long periodic terms, preserving in the new Hamiltonian secular and resonant terms. This theory is again applied to study the resonant system whose analysis lead us to a system of equations equivalent to the equations of a simple pendulum which is integrable in terms of elliptical integrals. 相似文献
4.
The paper deals with the study of a satellite attracted by n primary bodies, which form a relative equilibrium. We use orthogonal
degree to prove global bifurcation of planar and spatial periodic solutions from the equilibria of the satellite. In particular,
we analyze the restricted three body problem and the problem of a satellite attracted by the Maxwell’s ring relative equilibrium. 相似文献
5.
We address the occurrence of narrow planetary rings and some of their structural properties, in particular when the rings
are shepherded. We consider the problem as Hamiltonian scattering of a large number of non-interacting massless point particles in an effective potential. Using the existence of stable motion
in scattering regions in this set up, we describe a mechanism in phase space for the occurrence of narrow rings and some consequences
in their structure. We illustrate our approach with three examples. We find eccentric narrow rings displaying sharp edges,
variable width and the appearance of distinct ring components (strands) which are spatially organized and entangled (braids).
We discuss the relevance of our approach for narrow planetary rings. 相似文献
6.
John E. Cochran 《Celestial Mechanics and Dynamical Astronomy》1972,6(2):127-150
A method of general perturbations, based on the use of Lie series to generate approximate canonical transformations, is applied to study the effects of gravity-gradient torque on the rotational motion of a triaxial, rigid satellite. The center of mass of the satellite is constrained to move in an elliptic orbit about an attracting point mass. The orbit, which has a constant inclination, is free to precess and spin. The method of general perturbations is used to obtain the Hamiltonian for the nonresonant secular and long-period rotational motion of the satellite to second order inn/0, wheren is the orbital mean motion of the center of mass and0 is a reference value of the magnitude of the satellite's rotational angular velocity. The differential equations derivable from the transformed Hamiltonian are integrable and the solution for the long-term motion may be expressed in terms of Jacobian elliptic functions and elliptic integrals. Geometrical aspects of the long-term rotational motion are discussed and a comparison of theoretical results with observations is made. 相似文献
7.
8.
We study the short-term effects of “shepherding” satellites on narrow rings, in the general case where all bodies move along eccentric orbits. We do this by following numerically a ring of test particles as their orbits evolve under the gravitational perturbations of the shepherds. Planar motion is assumed. Our numerical scheme vastly improves (by a factor of ～104) the computation speed over conventional orbital integration methods by constructing a table of the perturbation integrals and then utilizing it over and over. The approach is applicable to any narrow ring with a nearby satellite, such as a ring confined by the shepherding mechanism of P. Goldreich and S. Tremaine [Nature277, 97–99 (1979)]. We arrive at results for a variety of orbital configurations, and then apply these to the F-ring of Saturn. Several features of the numerical integration are reminiscent of the kinks and clumps observed by Voyager. If the ring-to-satellite distance changes significantly due to eccentricities, then the ring can break up into periodic clumps in an azimuthal domain which trails the satellite. This region may lag somewhat in longitude. The perturbations may also cause the ring to vary significantly in width, being narrowest near the point of closest approach of the shepherd and widest at the opposite side. It is as yet unclear whether this effect is, or could be, observed in the Voyager images. And finally, the perturbations of the shepherds can impact a significant, but probably time variable, eccentricity to the ring. The short-term tendency is not toward alignment of ring and satellite apsides; longer time effects have not been explored. 相似文献
9.
10.
José F. Cariñena Luis A. Ibort Ernesto A. Lacomba 《Celestial Mechanics and Dynamical Astronomy》1987,42(1-4):201-213
We show that time scaling transformations for Hamiltonian systems are infinitesimal canonical transformations in a suitable extended phase space constructed from geometrical considerations. We compute its infinitesimal generating function in some examples: regularization and blow up in celestial mechanics, classical mechanical systems with homogeneous potentials and Scheifele theory of satellite motion.Research partially supported by CONACYT (México), Grant PCCBBNA 022553 and CICYT (Spain). 相似文献
11.
This paper analyzes a process that has been observed in simulations of numerous systems where ring material is strongly perturbed by a nearby moon. If the ring particles can be imparted with a forced eccentricity on the order of 10−5 in a single pass by the moon, particle orbits are observed to move towards regions of higher density as a result of the organized collisions that occur in the dense peaks of the satellite wake. The width of the ring can decrease by as much as 90% if the forced eccentricity is greater than 3 × 10−5 and the unperturbed geometric optical depth is greater than 0.03. The fractional change in ring width is relatively insensitive to the particle size so long as the particle radius is much less than the product of the semimajor axis and the forced eccentricity. Including a power law particle size distribution with slope of −2.8 spanning a decade in particle radius reduces the fractional width change by about 10% compared to the uniform particle-size case. Adding gravitational interactions between ring particles only has a significant effect on ring confinement if the unperturbed geometric optical depth exceeds .03, but a 40% reduction in ring width is still achieved in a self-gravitating ring of geometric optical depth 0.3 if the forced eccentricity exceeds 3 × 10−5. This process does not require the material to be in resonance with the moon, nor does it have any minimum mass constraints because particle self-gravity is not required. The collisional damping of satellite wakes therefore provides a simple mechanism by which a single moon can reduce the radial extent of any ringlet that is close to it and has sufficient optical depth for collisions to be significant. 相似文献
12.
We present a scenario for building the equatorial ridge and de-spinning Iapetus through an impact-generated disk and satellite. This impact puts debris into orbit, forming a ring inside the Roche limit and a satellite outside. This satellite rapidly pushes the ring material down to the surface of Iapetus, and then itself tidally evolves outward, thereby helping to de-spin Iapetus. This scenario can de-spin Iapetus an order of magnitude faster than when tides due to Saturn act alone, almost independently of its interior geophysical evolution. Eventually, the satellite is stripped from its orbit by Saturn. The range of satellite and impactor masses required is compatible with the estimated impact history of Iapetus. 相似文献
13.
Osman M. Kamel 《Earth, Moon, and Planets》1992,59(2):111-140
We eliminate the 1:2 critical terms — after a previous elimination of the short period terms — in the Hamiltonian of a first order U-N theory. We take into account terms of degree 0, 1, 2, 3, 4 in the eccentricity-inclination. We apply for this elimination the Hori-Lie technique through the Poincaré canonical variables and the Jacobi coordinates. The purely principal first order secular U-N Hamiltonian admits a complete solution. We obtained the U-N equations of motion generated by the principal first order long period U-N Hamiltonian which will be solved later. This part III is closely related to the two previous papers (Kamel, 1982, 1983). 相似文献
14.
《Icarus》1987,71(1):69-77
The gravitational influence of moonlets or satellites on the radial structure of the rings of Saturn has been calculated numerically. A drastic change in the surface mass density is obtained even after a single scattering process of the ring particles on a moonlet (satellite). The final surface density shows a significant radial structure, which has been used to estimate the radius and the mass of moonlets or satellites embedded in rings of low optical depth (E ring, Cassini division, C ring). 相似文献
15.
M. A. Vashkov’yak 《Astronomy Letters》2005,31(1):64-72
We describe an approximate numerical-analytical method for calculating the perturbations of the elements of distant satellite orbits. The model for the motion of a distant satellite includes the solar attraction and the eccentricity and ecliptic inclination of the orbit of the central planet. In addition, we take into account the variations in planetary orbital elements with time due to secular perturbations. Our work is based on Zeipel’s method for constructing the canonical transformations that relate osculating satellite orbital elements to the mean ones. The corresponding transformation of the Hamiltonian is used to construct an evolution system of equations for mean elements. The numerical solution of this system free from rapidly oscillating functions and the inverse transformation from the mean to osculating elements allows the evolution of distant satellite orbits to be studied on long time scales on the order of several hundred or thousand satellite orbital periods. 相似文献
16.
Alice C. Quillen Yuan-Yuan Chen Benoît Noyelles Santiago Loane 《Celestial Mechanics and Dynamical Astronomy》2018,130(2):11
A Hamiltonian model is constructed for the spin axis of a planet perturbed by a nearby planet with both planets in orbit about a star. We expand the planet–planet gravitational potential perturbation to first order in orbital inclinations and eccentricities, finding terms describing spin resonances involving the spin precession rate and the two planetary mean motions. Convergent planetary migration allows the spinning planet to be captured into spin resonance. With initial obliquity near zero, the spin resonance can lift the planet’s obliquity to near 90\(^\circ \) or 180\(^\circ \) depending upon whether the spin resonance is first or zeroth order in inclination. Past capture of Uranus into such a spin resonance could give an alternative non-collisional scenario accounting for Uranus’s high obliquity. However, we find that the time spent in spin resonance must be so long that this scenario cannot be responsible for Uranus’s high obliquity. Our model can be used to study spin resonance in satellite systems. Our Hamiltonian model explains how Styx and Nix can be tilted to high obliquity via outward migration of Charon, a phenomenon previously seen in numerical simulations. 相似文献
17.
An explicit symplectic integrator is constructed for the problem of a rotating planetary satellite on a Keplerian orbit. The
spin vector is fixed perpendicularly to the orbital plane. The integrator is constructed according to the Wisdom-Holman approach:
the Hamiltonian is separated in two parts so that one of them is multiplied by a small parameter. The parameter depends on
the satellite’s shape or the eccentricity of its orbit. The leading part of the Hamiltonian for small eccentricity orbits
is similar to the simple pendulum and hence integrable; the perturbation does not depend on angular momentum which implies
a trivial ‘kick’ solution. In spite of the necessity to evaluate elliptic function at each step, the explicit symplectic integrator
proves to be quite efficient.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
18.
Most existing satellite relative motion theories utilize mean elements, and therefore cannot be used for calculating long-term bounded perturbed relative orbits. The goal of the current paper is to find an integrable approximation for the relative motion problem under the J 2 perturbation, which is adequate for long-term prediction of bounded relative orbits with arbitrary inclinations. To that end, a radial intermediary Hamiltonian is utilized. The intermediary Hamiltonian retains the original structure of the full J 2 Hamiltonian, excluding the latitude dependence. This formalism provides integrability via separation, a fact that is utilized for finding periodic relative orbits in a local-vertical local-horizontal frame and determine an initialization scheme that yields long-term boundedness of the relative distance. Numerical experiments show that the intermediary-based computation of orbits provides long-term bounded orbits in the full J 2 problem for various inclinations. In addition, a test case is shown in which the radial intermediary-based initial conditions of the chief and deputy satellites yield bounded relative distance in a high-precision orbit propagator. 相似文献
19.
When the coordinate system used in perturbation theory presents a geometrical singularity and when the perturbation technique fails to take account of this, the solution developed may present singularities which are no longer easily explained by purely geometrical means. These singularities have been calledvirtual singularities by Deprit and Rom (1970). We propose to demonstrate that virtual singularities can in general be avoided by the use of Lie transforms. In general, it is sufficient to recognize that the original Hamiltonian function presents the d'Alembert characteristic with respect to pairs of action-angle variables and that the averaging operations preserve this characteristic. We then apply this criterion to the artificial satellite theory (for small to moderate eccentricity) showing that all of three possible virtual singularities can be avoided at the same time. A new set of elliptic elements, well suited to the problem at hand, is introduced. 相似文献
20.
The faint E ring of Saturn appears as a narrow ring 246,000 ± 4,000 km from the center of Saturn on photographs taken when the ring-plane inclination was 5°.4. The apparent brightness of the ring was uniform at all observed orbital longitudes and permits an estimate of the normal optical thickness. A faint satellite (1981S1) was observed near the L4 triangular libration point of Tethys and is probably the same object as 1980S13. 相似文献