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1.
J. P. S. Carvalho R. Vilhena de Moraes A. F. B. A. Prado 《Celestial Mechanics and Dynamical Astronomy》2010,108(4):371-388
In this paper we present an analytical theory with numerical simulations to study the orbital motion of lunar artificial satellites.
We consider the problem of an artificial satellite perturbed by the non-uniform distribution of mass of the Moon and by a
third-body in elliptical orbit (Earth is considered). Legendre polynomials are expanded in powers of the eccentricity up to
the degree four and are used for the disturbing potential due to the third-body. We show a new approximated equation to compute
the critical semi-major axis for the orbit of the satellite. Lie-Hori perturbation method up to the second-order is applied
to eliminate the terms of short-period of the disturbing potential. Coupling terms are analyzed. Emphasis is given to the
case of frozen orbits and critical inclination. Numerical simulations for hypothetical lunar artificial satellites are performed,
considering that the perturbations are acting together or one at a time. 相似文献
2.
It is well known that in artifical satellite theory special techniques must be employed to construct a formal solution whenever the orbital inclination is sufficiently close to the critical value cos–1 (1/5). In this article the authors investigate the consequences of introducing certain relativistic effects into the motion of a satellite about an oblate primary. Particular attention is paid to the critical inclination(s), and for such critical motions an appropriate method of solution is formulated. 相似文献
3.
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
4.
The critical inclination in artificial satellite theory 总被引：1，自引：0，他引：1
Shannon L. Coffey André Deprit Bruce R. Miller 《Celestial Mechanics and Dynamical Astronomy》1986,39(4):365-406
Certain it is that the critical inclination in the main problem of artificial satellite theory is an intrinsic singularity. Its significance stems from two geometric events in the reduced phase space on the manifolds of constant polar angular momentum and constant Delaunay action. In the neighborhood of the critical inclination, along the family of circular orbits, there appear two Hopf bifurcations, to each of which there converge two families of orbits with stationary perigees. On the stretch between the bifurcations, the circular orbits in the planes at critical inclinmation are unstable. A global analysis of the double forking is made possible by the realization that the reduced phase space consists of bundles of two-dimensional spheres. Extensive numerical integrations illustrate the transitions in the phase flow on the spheres as the system passes through the bifurcations.A delicacy so very susceptible of offence...—Hester Lynch PIOZZI,Observations and Reflections made in the Course of a Journey through France, Italy and Germany (1789)NAS/NRC Postgraduate Research Associate in 1984–1985. 相似文献
5.
Fabienne Delhaise Alessandro Morbidelli 《Celestial Mechanics and Dynamical Astronomy》1993,57(1-2):155-173
The luni-solar effects of a geosynchronous artificial satellite orbiting near the critical inclination is investigated. To tackle this four-degrees-of-freedom problem, a preliminary exploration separately analyzing each harmonic formed by a combination of the satellite longitude of the node and the Moon longitude of the node is opportune. This study demonstrates that the dynamics induced by these harmonics does not show resonance phenomena. In a second approach, the number of degrees of freedom is halved by averaging the total Hamiltonian over the two non-resonant angular variables. A semi-numerical method can now be applied as was done when considering solely the inhomogeneity of the geopotential (see Delhaise et Henrard, 1992). Approximate surfaces of section are constructed in the plane of the inclination and argument of perigee. The main effects of the Sun and Moon attractions compared to the terrestrial attraction alone are a strong increase in the amplitude of libration in inclination (from 0.6° to 3.2°) and a decrease of the corresponding libration period (from the order of 200 years to the order of 20 years).Research Assistant for the Belgian National Fund for Scientific Research 相似文献
6.
Sebastián Ferrer Juan Félix San-Juan Alberto Abad 《Celestial Mechanics and Dynamical Astronomy》2007,99(1):69-83
In the analytical approach to the main problem in satellite theory, the consideration of the physical parameters imposes a
lower bound for normalized Hamiltonian. We show that there is no elliptic frozen orbits, at critical inclination, when we
consider small values of H, the third component of the angular momentum. The argument used suggests that it might be applied also to more realistic
zonal and tesseral models. Moreover, for almost polar orbits, when H may be taken as another small parameter, a different approach that will simplify the ephemerides generators is proposed. 相似文献
7.
R. A. Broucke 《Celestial Mechanics and Dynamical Astronomy》1994,58(2):99-123
We describe a collection of results obtained by numerical integration of orbits in the main problem of artificial satellite theory (theJ
2 problem). The periodic orbits have been classified according to their stability and the Poincaré surfaces of section computed for different values ofJ
2 andH (whereH is thez-component of angular momentum). The problem was scaled down to a fixed value (–1/2) of the energy constant. It is found that the pseudo-circular periodic solution plays a fundamental role. They are the equivalent of the Poincaré first-kind solutions in the three-body problem. The integration of the variational equations shows that these pseudo-circular solutions are stable, except in a very narrow band near the critical inclincation. This results in a sequence of bifurcations near the critical inclination, refining therefore some known results on the critical inclination, for instance by Izsak (1963), Jupp (1975, 1980) and Cushman (1983). We also verify that the double pitchfork bifurcation around the critical inclination exists for large values ofJ
2, as large as |J
2|=0.2. Other secondary (higher-order) bifurcations are also described. The equations of motion were integrated in rotating meridian coordinates. 相似文献
8.
The critical inclination is of special interest in artificial satellite theory. The critical inclination can maintain minimal
deviations of eccentricity and argument of pericentre from the initial values, and orbits at this inclination have been applied
to some space missions. Most previous researches about the critical inclination were made under the assumption that the oblateness
term J
2 is dominant among the harmonic coefficients. This paper investigates the extension of the critical inclination where the
concept of the critical inclination is different from that of the traditional sense. First, the study takes the case of Venus
for instance, and provides some preliminary results. Then for general cases, given the values of argument of pericentre and
eccentricity, the relationship between the multiplicity of the solutions for the critical inclination and the values of J
2 and J
4 is analyzed. Besides, when given certain values of J
2 and J
4, the relationship between the multiplicity of the solutions for the critical inclination and the values of semimajor axis
and eccentricity is studied. The results show that for some cases, the value of the critical inclination is far away from
that of the traditional sense or even has multiple solutions. The analysis in this paper could be used as starters of correction
methods in the full gravity field of celestial bodies. 相似文献
9.
F. Namouni 《Monthly notices of the Royal Astronomical Society》1998,300(3):915-930
We study the interaction of a satellite and a nearby ringlet on eccentric and inclined orbits. Secular torques originate from mean motion resonances and the secular interaction potential which represents the m = 1 global modes of the ring. The torques act on the relative eccentricity and inclination. The resonances damp the relative eccentricity. The inclination instability owing to the resonances is turned off by a finite differential eccentricity of the order of 0.27 for nearly coplanar systems. The secular potential torque damps the eccentricity and inclination and does not affect the relative semi-major axis; also, it suppresses the inclination instability that persists at small differential eccentricities. The damping of the relative eccentricity and inclination forces an initially circular and planar small mass ringlet to reach the eccentricity and inclination of the satellite. When the planet is oblate, the interaction of the satellite damps the proper precession of a small mass ringlet so that it precesses at the satellite's rate independently of their relative distance. The oblateness of the primary modifies the long-term eccentricity and inclination magnitudes and introduces a constant shift in the apsidal and nodal lines of the ringlet with respect to those of the satellite. These results are applied to Saturn's F-ring, which orbits between the moons Prometheus and Pandora. 相似文献
10.
Martín Lara André Deprit Antonio Elipe 《Celestial Mechanics and Dynamical Astronomy》1995,62(2):167-181
In the zonal problem of a satellite around the Earth, we continue numerically natural families of periodic orbits with the polar component of the angular momentum as the parameter. We found three families; two of them are made of orbits with linear stability while the third one is made of unstable orbits. Except in a neighborhood of the critical inclination, the stable periodic (or frozen) orbits have very small eccentricities even for large inclinations. 相似文献
11.
Perturbation theory based on Lie transforms is used to obtain a second-order long period solution for inclination and right ascension of ascending node, of near-equatorial circular satellite orbits. The solution includes the average effects of the Earth's oblateness and the luni-solar perturbations. Three algorithms, useful in mission analysis, are then given. The first algorithm finds the initial node location that results in a decrease of inclination to zero and it also finds the corresponding time to arrive at this zero inclination. The second algorithm determines the initial nodal band that maintains the orbital inclination below a specified value for a given time interval. The third algorithm obtains the initial node location that maximizes the time in which the satellite can be maintained within a given inclination tolerance without the use of any active control and it also obtains the corresponding maximum time. The results of the first and the third algorithms are given for 24-h near-equatorial circular satellite orbits and are cast in simple closed forms. 相似文献
12.
Alan H. Jupp 《Celestial Mechanics and Dynamical Astronomy》1980,21(4):361-393
A qualitative solution is presented of the critical inclination problem in artificial satellite theory for motions in which the orbits are nearly circular. The effects of all the zonal harmonics are taken into account, and bothshallow anddeep resonance regimes are considered. An investigation of the (e sing,e cosg)-plane reveals that six fundamentally different types of phase-plane portraits exist. These portraits illustrate the long-term behaviour of the eccentricity and line of apsides. 相似文献
13.
A. H. Jupp 《Celestial Mechanics and Dynamical Astronomy》1987,43(1-4):127-138
The critical inclination problem in artificial satellite theory, first discovered 30 years ago, has aroused great interest and provoked much discussion and controversy in the intervening years. It was this problem which essentially provided the seed corn for the development of the theory of the Ideal Resonance Problem (IRP). The latter theory provides good first-approximation solutions to a number of important resonance problems in celestial mechanics. It is not applicable, however, to certain other interesting resonant systems within the solar system. For these resonances a new fundamental mathematical model of resonance, in the spirit of the IRP, has recently been formulated and successfully applied.This paper reviews the history of the critical inclination problem and highlights the controversies it has generated over the years. The Problem's strong connection with the IRP is outlined with both thenormal andabnormal forms featuring. Finally, with reference to the critical inclination problem, the essential properties of the newer fundamental model are described and compared with the IRP. A strong correspondence is established between recent independent investigations of a variety of resonance problems and earlier work of Andoyer. 相似文献
14.
《大气一号》气球卫星轨道倾角变化分析 总被引：1，自引：0，他引：1
引起《大气一号》两颗气球卫星（ＤＱ－１Ａ和ＤＱ－１Ｂ）轨道倾角变化的摄动因素主要是太阳光压摄动、大气旋转和日月引力摄动。太阳光压摄动引起气球卫星轨道倾角增大，平均每天变化约０．００１７，大气旋转引起轨道倾角减小，平均每天变化不到０．０００１，但随着高度下降，变化量亦增大，陨落前达０．００２。本文根据卫星轨道摄动理论，给出气球卫星轨道倾角变化的一种定量分析方法，得到的分析结果为：（１）由太阳光压摄动 相似文献
15.
In this paper the two-degree of freedom problem of a geosynchronous artificial satellite orbiting near the critical inclination is studied. First a local approach of this problem is considered. A semi-numerical method, well suited to describe the perturbations of a non-trivial separable system, is then applied such that surfaces of section illustrating the global secular dynamics are obtained. The results are confirmed by numerical integrations of the full Hamiltonian.Research Assistant for the Belgian National Fund for Scientific Research 相似文献
16.
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
17.
It has been claimed that the representation of satellite motion in the vicinity of the critical inclination is a matter of practical, as well as theoretical interest, since the perturbations in the coordinates are of the order of 25 times greater near the critical inclination than away from it (Messageet al., 1962). In this paper we show, using Encke's method of numerical integration for satellites which are at, near, and away from the critical inclination, that there are no discernible features in the coordinate perturbations which distinguish the critical inclination from any other. 相似文献
18.
L. Sehnal 《Planetary and Space Science》1981,29(10):1089-1090
The changes of the orbital inclination of the satellite 1974-70 A show some peculiarities which cannot be explained by the usual disturbing effects (odd zonal harmonics, lunisolar perturbations, rotation of the atmosphere). The effect of a lift force normal to the orbital plane explains the residual inclination variations if a changing value of the thermal accommodation coefficient is introduced. The theory agrees well with the observations if the coefficient rises from a low value (～0.1) corresponding to a quasi-specular reflection of the molecules incident to the satellite surface to higher values (>0.9) characterizing a diffuse reflection. 相似文献
19.
We deal with the stability problem of planar periodic motions of a satellite about its center of mass. The satellite is regarded a dynamically symmetric rigid body whose center of mass moves in a circular orbit.By using the method of normal forms and KAM theory we study the orbital stability of planar oscillations and rotations of the satellite in detail. In two special cases we investigate the orbital stability analytically by introducing a small parameter. In the general case, numerical calculations of Hamiltonian normal form are necessary. 相似文献
20.
Alan H. Jupp 《Celestial Mechanics and Dynamical Astronomy》1975,11(3):361-378
The behaviour of the argument of the pericentre is investigated for the orbit of an artificial satellite which is moving under the potential when the inclination of the orbit is close to thecritical value tan?1 2. The theory is developed to first order and it is applicable to all values of the eccentricity, with the exception of those in the neighbourhood of zero and unity. Four principal types of behaviour are noted and these are illustrated in appropriate phase-plane diagrams. It is shown that the two types which exhibit double libration in the argument of the pericentre are restricted to a relatively small domain in the (a, e)-plane of possible motions. Moreover, it is demonstrated that for double libration to occur it is necessary, but not sufficient, that \(e > \sqrt 6/13\) . The ranges of values of the inclination for which libration of the pericentre is a possibility are given for the more important cases. The general results are applied to the specific case of artificial Earth satellites whose orbits are inclined to the equator at angles close to the value of the critical inclination. 相似文献