共查询到20条相似文献，搜索用时 31 毫秒
1.
Approximate formulae for the evaluation of the effect of direct solar radiation pressure (neglecting the POYNTING -ROBERTSON effect and shadow effect) on the nodal period of artificial Earth satellites with quasi-circular orbits are derived. The cases of osculating elements considered in the ascending node and of circular orbits are studied. 相似文献
2.
Approximate formulae for the evaluation of the influence of direct solar radiation pressure (neglecting the POYNTING -ROBERTSON effect) on the anomalistic period of artificial satellites with quasi-circular and completely illuminated orbits are derived. 相似文献
3.
V. A. Brumberg 《Celestial Mechanics and Dynamical Astronomy》2003,85(3):269-291
The distinctive feature of the relativistic restricted three-body problem within the c
–5 order of accuracy (2
post-Newtonian approximation) is the presence of the gravitational radiation. To simplify the problem the motion of the massive binary components is assumed to be quasi-circular. In terms of time these orbits have linearly changing radii and quadratically changing phase angles. By substituting this motion into the Newtonian-like equations of motion one gets the quasi-Newtonian restricted quasi-circular three-body problem sufficient to take into account the main indirect perturbations caused by the binary radiation terms. Such problem admits the Lagrange-like quasi-libration solutions and rather simple quasi-circular orbits lying at large distance from the binary. 相似文献
4.
Nina A. Solovaya 《Earth, Moon, and Planets》1995,71(3):273-279
Some peculiarities in the motion of retrograde satellites of Jupiter have been investigated. The intermediate orbits were obtained by approximated solution of differential equations before transformation by the Zeipel's method. These orbits are non-keplerian ellipses. For their construction the secular motion of nodes, perijoves, and essential periodic perturbations were taken into account.The eccentricities and inclinations of all the retrograte satellites change in a large range. The motion may happen in a region, which is located very near to the limit cases of our theory. For some satellites the sign of the constant, which characterizes the type of orbit, librating or circular, may change. In some cases the value of this constant may be close to zero. Then the motion of the longitude of perijove will reduce the speed and in some moment the circular orbit may change its direction. 相似文献
5.
The concept of closest approach is analyzed in Hill’s problem, resulting in a partitioning of the position space. The different
behavior between the direct and retrograde motion is explained analytically, resulting in a simple estimate of the variation
of Hill’s periodic and quasi-circular orbits as a function of the Jacobi constant. The local behavior of the orbits on the
zero velocity surfaces and an analytical definition of local escape and capture in Hill’s problem are also given. 相似文献
6.
We investigate the significance of long time stabilty predictions in the light of Nekhoroshev's theory by studying the orbits
of artificial satellites. As a simplified model problem we consider the so-called J2problem for an earth's satellite, neglecting luni-solar perturbations and nonconservative effects. We consider a wide range
of orbits, excluding those which are too close to the critical inclination. Most of the orbits turn out to be stable for times
larger than the estimated age of the solar system, thus proving that, as far as dissipation can be neglected, stability in
Nekhoroshev's sense may be effective for physically realistic systems.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
7.
The Orbital Evolution of Two Sounding Satellites and Analysis of the Accuracy of Orbit Determination
Gong-you Wu Chang-yin Zhao Rong-zhi Zhang Jia-song Wang Hong-bo Wang 《Chinese Astronomy and Astrophysics》2007,31(4):420-429
The satellites TC-1 and TC-2 are the two Chinese satellites with great elliptical orbits which are still in orbit around the earth at present. Since the launch the orbits of the two satellites have continuously evolved, which has a certain effect on the orbit determination and prediction precision. The regularities of the orbital evolution of the two sounding satellites are qualitatively and quantitatively analyzed. Under the current tracking mode the corresponding prediction precision of orbit determination is analyzed based on the different stages of the orbital evolution, thereby providing the basis for the adjustment of planning mode by the satellite application departments and the guarantee of normal satellite payload. Finally, the orbital lifetimes of the two satellites are predicted through the trend of the orbital evolution. 相似文献
8.
The theory of velocity dependent inertial induction, based upon extended Mach’s principle, has been able to generate many interesting results related to celestial mechanics and cosmological problems. Because of the extremely minute magnitude of the effect its presence can be detected through the motion of accurately observed bodies like Earth satellites. LAGEOS I and II are medium altitude satellites with nearly circular orbits. The motions of these satellites are accurately recorded and the past data of a few decades help to test many theories including the general theory of relativity. Therefore, it is hoped that the effect of the Earth’s inertial induction can have any detectable effect on the motion of these satellites. It is established that the semi-major axis of LAGEOS I is decreasing at the rate of 1.3 mm/d. As the atmospheric drag is negligible at that altitude, a proper explanation of the secular change has been wanting, and, therefore, this paper examines the effect of the Earth’s inertial induction effect on LAGEOS I. Past researches have established that Yarkovsky thermal drag, charged and neutral particle drag might be the possible mechanisms for this orbital decay. Inertial induction is found to generate a perturbing force that results in 0.33 mm/d decay of the semi major axis. Some other changes are also predicted and the phenomenon also helps to explain the observed changes in the orbits of a few other satellites. The results indicate the feasibility of the theory of inertial induction i.e. the dynamic gravitation phenomenon of the Earth on its satellites as a possible partial cause for orbital decay. 相似文献
9.
K. Uldall Kristiansen P. L. Palmer M. Roberts 《Celestial Mechanics and Dynamical Astronomy》2010,106(4):371-390
This paper builds upon the work of Palmer and Imre exploring the relative motion of satellites on neighbouring Keplerian orbits.
We make use of a general geometrical setting from Hamiltonian systems theory to obtain analytical solutions of the variational
Kepler equations in an Earth centred inertial coordinate frame in terms of the relevant conserved quantities: relative energy,
relative angular momentum and the relative eccentricity vector. The paper extends the work on relative satellite motion by
providing solutions about any elliptic, parabolic or hyperbolic reference trajectory, including the zero angular momentum
case. The geometrical framework assists the design of complex formation flying trajectories. This is demonstrated by the construction
of a tetrahedral formation, described through the relevant conserved quantities, for which the satellites are on highly eccentric
orbits around the Sun to visit the Kuiper belt. 相似文献
10.
11.
The system of Saturn's inner satellites is saturated with many resonances. Its structure should be strongly affected by tidal forces driving the satellites through several orbit–orbit resonances. The evolution of these satellites is investigated using analytic and numerical methods. We show that the pair of satellites Prometheus and Pandora has a particularly short lifetime (<20 Myr) if the orbits of the satellites converge without capture into a resonance. The capture of Pandora into a resonance with Prometheus increases the lifetime of the couple by a few tens of Myr. However, resonances of the system are not well separated, and capture results in a chaotic motion. Secondary resonances also disrupt the resonant configurations. In all cases, the converging orbits of these two satellites result in a close encounter. The implications for the origin of Saturn's rings are discussed. 相似文献
12.
Attitude motion of spinning axisymmetric satellites in presence of gravity-gradient and solar radiation pressure torques is studied analytically. The approximate closed-form solution developed for the nonlinear, nonautonomous, coupled fourth-order system proves to be an excellent tool in locating periodic solutions of the system in both circular and noncircular orbits. The variational stability of the periodic motion is examined using the Floquet theory. The resonance analysis suggests the existence of critical combinations of system parameters leading to large amplitude oscillations.
相似文献13.
We develop an analytical Hamiltonian formalism adapted to the study of the motion of two planets in co-orbital resonance. The Hamiltonian, averaged over one of the planetary mean longitudes, is expanded in power series of eccentricities and inclinations. The model, which is valid in the entire co-orbital region, possesses an integrable approximation modeling the planar and quasi-circular motions. First, focusing on the fixed points of this approximation, we highlight relations linking the eigenvectors of the associated linearized differential system and the existence of certain remarkable orbits like the elliptic Eulerian Lagrangian configurations, the anti-Lagrange (Giuppone et al. in MNRAS 407:390–398, 2010) orbits and some second sort orbits discovered by Poincaré. Then, the variational equation is studied in the vicinity of any quasi-circular periodic solution. The fundamental frequencies of the trajectory are deduced and possible occurrence of low order resonances are discussed. Finally, with the help of the construction of a Birkhoff normal form, we prove that the elliptic Lagrangian equilateral configurations and the anti-Lagrange orbits bifurcate from the same fixed point $L_4$ L 4 . 相似文献
14.
D. V. Nikonchuk 《Astronomy Letters》2012,38(12):813-828
Anonlinear analytical theory of secular perturbations in the problem of the motion of a systemof small bodies around a major attractive center has been developed. Themutual perturbations of the satellites and the influence of the oblateness of the central body are taken into account in the model. In contrast to the classical Laplace-Lagrange theory based on linear equations for Lagrange elements, the third-degree terms in orbital eccentricities and inclinations are taken into account in the equations. The corresponding improvement of the solution turns out to be essential in studying the evolution of orbits over long time intervals. A program inC has been written to calculate the corrections to the fundamental frequencies of the solution and the third-degree secular perturbations in orbital eccentricities and inclinations. The proposed method has been applied to investigate the motion of the major Uranian satellites. Over time intervals longer than 100 years, allowance for the nonlinear terms in the equations is shown to give corrections to the coordinates of Miranda on the order of the orbital eccentricity, which is several thousand kilometers in linear measure. For other satellites, the effect of allowance for the nonlinear terms turns out to be smaller. Obviously, when a general analytical theory of motion for the major Uranian satellites is constructed, the nonlinear terms in the equations for the secular perturbations should be taken into account. 相似文献
15.
M. A. Vashkov’yak 《Astronomy Letters》2001,27(7):464-469
We consider the structural peculiarities of Uranus’s satellite system associated with its separation into two groups: inner equatorial satellites moving in nearly circular orbits and distant irregular satellites with retrograde motion in highly elliptical orbits. The intermediate region is free from satellites in a wide range of semimajor axes. By analyzing the evolution of satellite orbits under the combined effect of solar attraction and Uranus’s oblateness, we offer a celestial-mechanical explanation for the absence of equatorial satellites in this region. M.L. Lidov’s studies during 1961–1963 have served as a basis for our analysis. 相似文献
16.
One of the possible early states of the Earth-Moon system was a system of several large satellites around the Earth. The dynamical
evolution of coplanar three-body systems is studied; a planet (Earth) and two massive satellites (proto-moons) with geocentric
orbits of slightly different radii. Such configurations may arise in multiple satellite systems receding from a planet due
to tidal friction. The numerical integration of the equations of motion shows that initially circular Keplerian orbits are
soon transformed into disturbed elliptic orbits which are intersecting. The life-time of such a coplanar system between two
probable physical collisions of satellites is roughly from one day to one year for satellite systems with radii less than
20R⊕, and may reach 100 yr for three-dimensional systems. This time-scale is short in comparison with the duration of the removal
of satellites due to tides raised on the planet, which is estimated as 106–108 yr for the same orbital dimensions. Therefore, the life-time of a system of several proto-moons is mainly determined by their
tidal interactions with the Earth. For conditions which we have considered, the most probable result of the evolution was
coalescence of satellites as the consequence of the collisions. 相似文献
17.
James E. Howard 《Celestial Mechanics and Dynamical Astronomy》1990,48(3):267-288
The spectral stability of synchronous circular orbits in a rotating conservative force field is treated using a recently developed
Hamiltonian method. A complete set of necessary and sufficient conditions for spectral stability is derived in spherical geometry.
The resulting theory provides a general unified framework that encompasses a wide class of relative equilibria, including
the circular restricted three-body problem and synchronous satellite motion about an aspherical planet. In the latter case
we find an interesting class of stable nonequatorial circular orbits. A new and simplified treatment of the stability of the
Lagrange points is given for the restricted three-body problem. 相似文献
18.
Joachim Heimberger Michael Soffel Hanns Ruder 《Celestial Mechanics and Dynamical Astronomy》1989,47(2):205-217
The motion of artificial satellites in the gravitational field of an oblate body is discussed in the post — Newtonian framework using the technique of canonical Lie transformations. Two Lie transformations are used to derive explicit results for the longperiodic and secular perturbations for satellite orbits in the Einstein case. 相似文献
19.
20.
Ryan E. Sherrill Andrew J. Sinclair S. C. Sinha T. Alan Lovell 《Celestial Mechanics and Dynamical Astronomy》2014,119(1):55-73
The relative motion of chief and deputy satellites in close proximity with orbits of arbitrary eccentricity can be approximated by linearized time-periodic equations of motion. The linear time-invariant Hill–Clohessy–Wiltshire equations are typically derived from these equations by assuming the chief satellite is in a circular orbit. Two Lyapunov–Floquet transformations and an integral-preserving transformation are here presented which relate the linearized time-varying equations of relative motion to the Hill–Clohessy–Wiltshire equations in a one-to-one manner through time-varying coordinate transformations. These transformations allow the Hill–Clohessy–Wiltshire equations to describe the linearized relative motion for elliptic chief satellites. 相似文献