共查询到20条相似文献，搜索用时 15 毫秒
1.
Michael E. Hough 《Celestial Mechanics and Dynamical Astronomy》1981,25(2):137-157
The long period dynamics of Sun-synchronous orbits near the critical inclination 116.6° are investigated. It is known that, at the critical inclination, the average perigee location is unchanged by Earth oblateness. For certain values of semimajor axis and eccentricity, orbit plane precession caused by Earth oblateness is synchronous with the mean orbital motion of the apparent Sun (a Sun-synchronism). Sun-synchronous orbits have been used extensively in meteorological and remote sensing satellite missions. Gravitational perturbations arising from an aspherical Earth, the Moon, and the Sun cause long period fluctuations in the mean argument of perigee, eccentricity, inclination, and ascending node. Double resonance occurs because slow oscillations in the perigee and Sun-referenced ascending node are coupled through the solar gravity gradient. It is shown that the total number and infinitesimal stability of equilibrium solutions can change abruptly over the Sun-synchronous range of semimajor axis values (1.54 to 1.70 Earth radii). The effect of direct solar radiation pressure upon certain stable equilibria is investigated. 相似文献
2.
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
3.
C. Marchal 《Celestial Mechanics and Dynamical Astronomy》2009,104(1-2):53-67
Trojan asteroids undergo very large perturbations because of their resonance with Jupiter. Fortunately the secular evolution of quasi circular orbits remains simple—if we neglect the small short period perturbations. That study is done in the approximation of the three dimensional circular restricted three-body problem, with a small mass ratio μ—that is about 0.001 in the Sun Jupiter case. The Trojan asteroids can be defined as celestial bodies that have a “mean longitude”, M + ω + Ω, always different from that of Jupiter. In the vicinity of any circular Trojan orbit exists a set of “quasi-circular orbits” with the following properties: (A) Orbits of that set remain in that set with an eccentricity that remains of the order of the mass ratio μ. (B) The relative variations of the semi-major axis and the inclination remain of the order of ${\sqrt{\mu}}$ . (C) There exist corresponding “quasi integrals” the main terms of which have long-term relative variations of the order of μ only. For instance the product c(1 – cos i) where c is the modulus of the angular momentum and i the inclination. (D) The large perturbations affect essentially the difference “mean longitude of the Trojan asteroid minus mean longitude of Jupiter”. That difference can have very large perturbations that are characteristics of the “horseshoes orbit”. For small inclinations it is well known that this difference has two stable points near ±60° (Lagange equilibrium points L4 and L5) and an unstable point at 180° (L3). The stable longitude differences are function of the inclination and reach 180° for an inclination of 145°41′. Beyond that inclination only one equilibrium remains: a stable difference at 180°. 相似文献
4.
J2 Invariant Relative Orbits for Spacecraft Formations 总被引：1，自引：0，他引：1
An analytic method is presented to establish J
2 invariant relative orbits. Working with mean orbit elements, the secular drift of the longitude of the ascending node and the sum of the argument of perigee and mean anomaly are set equal between two neighboring orbits. By having both orbits drift at equal angular rates on the average, they will not separate over time due to the J2 influence. Two first order conditions are established between the differences in momenta elements (semi-major axis, eccentricity and inclination angle) that guarantee that the drift rates of two neighboring orbits are equal on the average. Differences in the longitude of the ascending node, argument of perigee and initial mean anomaly can be set at will, as long as they are setup in mean element space. For near polar orbits, enforcing both momenta element constraints may result in impractically large relative orbits. It this case it is shown that dropping the equal ascending node rate requirement still avoids considerable relative orbit drift and provides substantial fuel savings.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
5.
研究了在高空电离层中运动的带电荷的卫星受电感应阻力后对轨道根数产生的摄动影响。研究结果表明 ,电感应阻力对带电卫星的轨道半长轴、轨道偏心率、近地点赤经、历元平赤经均有周期摄动影响 ,但除对半长轴有长期摄动效应外对其它轨道根数均无长期摄动。轨道倾角和升交点赤经不受摄动影响。文中以飞行在高度 1 50 0km的电离层中的导体卫星作为算例。计算结果显示 :带电导体卫星在高空电离层中带有一定电量时电感应阻力对轨道半长轴的缩短产生显著效应 相似文献
6.
The Effect of C22 on Orbit Energy and Angular Momentum 总被引：1，自引：0，他引：1
D.J. Scheeres 《Celestial Mechanics and Dynamical Astronomy》1999,73(1-4):339-348
The effect of the C22 gravity field term on a particle is evaluated analytically over one orbit to find the change in orbit energy and angular
momentum as an explicit function of the orbital inclination, argument of pericenter, longitude of the ascending node, orbit
parameter and eccentricity. Changes in orbit energy and angular momentum are shown to be proportional to a family of integrals
which can be parameterized in terms of eccentricity and non-dimensional pericenter radius.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
7.
V. Kudielka 《Celestial Mechanics and Dynamical Astronomy》1994,60(4):455-470
An analytic model for third-body perturbations and for the second zonal harmonic of the central body's gravitational field is presented. A simplified version of this model applied to the Earth-Moon-Sun system indicates the existence of high-altitude and highly-inclined orbits with their apsides in the equator plane, for which the apsidal as well as the nodal motion ceases. For special positions of the node, secular changes of eccentricity and inclination disappear too (balanced orbits). For an ascending node at vernal equinox, the inclination of balanced orbits is 94.56°, for a node at autumnal equinox 85.44°, independent of the eccentricity of the orbit. For a node perpendicular to the equinox, there exist circular balanced orbits at 90° inclination. By slightly adjusting the initial inclination as suggested by the simplified model, orbits can be found — calculated by the full model or by different methods — that show only minor variations in eccentricity, inclination, argument of perigee, and longitude of the ascending node for 105 revolutions and more. Orbits near the unstable equilibria at 94.56° and 85.44° inclination show very long periodic librations and oscillations between retrogade and prograde motion.Retired from IBM Vienna Software Development Laboratory. 相似文献
8.
Up to now, 17 Neptune Trojan asteroids have been detected with their orbits being well determined by continuous observations. This paper analyzes systematically their orbital dynamics. Our results show that except for two temporary members with relatively short lifespans on Trojan orbits, the vast majority of Neptune Trojans located within their orbital uncertainties may survive in the solar system age. The escaping probability of Neptune Trojans, through slow diffusion in the orbital element space in 4.5 billion years, is estimated to be ～50%. The asteroid 2012 UW177 classified as a Centaur asteroid by the IAU Minor Planet Center currently is in fact a Neptune Trojan. Numerical simulations indicate that it is librating on the tadpole-shaped orbit around the Neptune's L4 point. It was captured into the current orbit approximately 0.23 million years ago, and will stay there for at least another 1.3 million years in the future. Its high inclination of i ≈ 54° not only makes it the most inclined Neptune Trojan, but also makes it exhibit the complicated and interesting co-orbital transitions between the leading and trailing Trojans via the quasi-satellite orbit phase. 相似文献
9.
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
10.
The dynamic evolution of sun-synchronous orbits at a time interval of 20 years is considered. The numerical motion simulation has been carried out using the Celestial Mechanics software package developed at the Institute of Astronomy of the University of Bern. The dependence of the dynamic evolution on the initial value of the ascending node longitude is examined for two families of sun-synchronous orbits with altitudes of 751 and 1191 km. Variations of the semimajor axis and orbit inclination are obtained depending on the initial value of the ascending node longitude. Recommendations on the selection of orbits, in which spent sun-synchronous satellites can be moved, are formulated. Minimal changes of elements over a time interval of 20 years have been observed for orbits in which at the initial time the angle between the orbit ascending node and the direction of the Sun measured along the equator have been close to 90° or 270°. In this case, the semimajor axis of the orbit is not experiencing secular perturbations arising from the satellite’s passage through the Earth’s shadow. 相似文献
11.
Li-Yong Zhou Rudolf Dvorak Yi-Sui Sun 《Monthly notices of the Royal Astronomical Society》2009,398(3):1217-1227
The stability of Trojan type orbits around Neptune is studied. As the first part of our investigation, we present in this paper a global view of the stability of Trojans on inclined orbits. Using the frequency analysis method based on the fast Fourier transform technique, we construct high-resolution dynamical maps on the plane of initial semimajor axis a 0 versus inclination i 0 . These maps show three most stable regions, with i 0 in the range of (0°, 12°), (22°, 36°) and (51°, 59°), respectively, where the Trojans are most probably expected to be found. The similarity between the maps for the leading and trailing triangular Lagrange points L 4 and L 5 confirms the dynamical symmetry between these two points. By computing the power spectrum and the proper frequencies of the Trojan motion, we figure out the mechanisms that trigger chaos in the motion. The Kozai resonance found at high inclination varies the eccentricity and inclination of orbits, while the ν8 secular resonance around i 0 ∼ 44° pumps up the eccentricity. Both mechanisms lead to eccentric orbits and encounters with Uranus that introduce strong perturbation and drive the objects away from the Trojan like orbits. This explains the clearance of Trojan at high inclination (>60°) and an unstable gap around 44° on the dynamical map. An empirical theory is derived from the numerical results, with which the main secular resonances are located on the initial plane of ( a 0 , i 0 ) . The fine structures in the dynamical maps can be explained by these secular resonances. 相似文献
12.
本文利用天体力学中的摄动理论和天体物理学中的气体星多方模型理论研究了太阳多方模型对行星轨道要素变化的长期摄动影响。文中给出了太阳日多方指数ｎ＝３的模型由于自转、扁度和内部密度分布等因素对行星轨道要素变化的长期摄动效应的理论结果。研究结果表明：行星轨道要素除长轴、偏心率和轨道倾角不受长期摄动外升交点经度、近日点经度以及平近点角均受长期摄动的影响。最后利用理论结果对行星轨道要素的长期投动效应做了数值计算，数值结果在表１中给出。 相似文献
13.
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
14.
F. MarzariH. Scholl 《Icarus》2002,159(2):328-338
We have numerically explored the mechanisms that destabilize Jupiter's Trojan orbits outside the stability region defined by Levison et al. (1997, Nature385, 42-44). Different models have been exploited to test various possible sources of instability on timescales on the order of ∼108 years.In the restricted three-body model, only a few Trojan orbits become unstable within 108 years. This intrinsic instability contributes only marginally to the overall instability found by Levison et al.In a model where the orbital parameters of both Jupiter and Saturn are fixed, we have investigated the role of Saturn and its gravitational influence. We find that a large fraction of Trojan orbits become unstable because of the direct nonresonant perturbations by Saturn. By shifting its semimajor axis at constant intervals around its present value we find that the near 5:2 mean motion resonance between the two giant planets (the Great Inequality) is not responsible for the gross instability of Jupiter's Trojans since short-term perturbations by Saturn destabilize Trojans, even when the two planets are far out of the resonance.Secular resonances are an additional source of instability. In the full six-body model with the four major planets included in the numerical integration, we have analyzed the effects of secular resonances with the node of the planets. Trojan asteroids have relevant inclinations, and nodal secular resonances play an important role. When a Trojan orbit becomes unstable, in most cases the libration amplitude of the critical argument of the 1:1 mean motion resonance grows until the asteroid encounters the planet. Libration amplitude, eccentricity, and nodal rate are linked for Trojan orbits by an algebraic relation so that when one of the three parameters is perturbed, the other two are affected as well. There are numerous secular resonances with the nodal rate of Jupiter that fall inside the region of instability and contribute to destabilize Trojans, in particular the ν16. Indeed, in the full model the escape rate over 50 Myr is higher compared to the fixed model.Some secular resonances even cross the stability region delimited by Levison et al. and cause instability. This is the case of the 3:2 and 1:2 nodal resonances with Jupiter. In particular the 1:2 is responsible for the instability of some clones of the L4 Trojan (3540) Protesilaos. 相似文献
15.
Numerical integrations have been performed for orbits of Venus', Earth's and Mars' Trojan-asteroid test particles in a self consistent model of the solar system to study the stability of inclined Trojan orbits. In the case of Mars low inclination orbits tend to be unstable while the contrary seems to apply to Venus and Earth, although the stability of some very high inclination orbits may not be excluded on the basis of these computations. 相似文献
16.
The local magnetic structure of the heliospheric current sheet (HCS) is observed as a boundary through which the magnetic field inverts its direction toward or away from Sun. The local variability of the HCS has been studied by means of a comparison of its local orientation estimated from data of different spacecraft. With the aim of determining possible variations in the local orientation, the selected events have been grouped according to their magnetic connection. A rough estimate of the magnetic connection (C) between two observation points has been found by considering the absolute value of the difference between the elapsed and expected times (C=|??t el??C???t ex|/??t ex). Lower values of C imply better connections, and smaller variation in the HCS orientation is expected if variations, temporal or spatial, in the HCS shape are negligible. Two periods have been analyzed: the ascending phase of Solar Cycle 23 and the minimum of the cycle in 2007??C?2008. It has been observed that, during the ascending phase, changes in the local HCS shape are mainly due to spatial variations. During minimum, the results show an increasing trend of the variation of the HCS local inclination with distance between spacecraft up to 5000 Earth radii (R E). For larger distances the results show a downward tendency. This inversion could be related to a continuous interaction of the HCS with the solar wind and with a poor magnetic connection, which could lead to changes in the local HCS shape making it unrecognizable to analyze the evolution of the structure from one observation point to another. 相似文献
17.
Many asteroids with a semimajor axis close to that of Mars have been discovered in the last several years. Potentially some of these could be in 1:1 resonance with Mars, much as are the classic Trojan asteroids with Jupiter, and its lesser-known horseshoe companions with Earth. In the 1990s, two Trojan companions of Mars, 5261 Eureka and 1998 VF31, were discovered, librating about the L5 Lagrange point, 60° behind Mars in its orbit. Although several other potential Mars Trojans have been identified, our orbital calculations show only one other known asteroid, 1999 UJ7, to be a Trojan, associated with the L4 Lagrange point, 60° ahead of Mars in its orbit. We further find that asteroid 36017 (1999 ND43) is a horseshoe librator, alternating with periods of Trojan motion. This asteroid makes repeated close approaches to Earth and has a chaotic orbit whose behavior can be confidently predicted for less than 3000 years. We identify two objects, 2001 HW15 and 2000 TG2, within the resonant region capable of undergoing what we designate “circulation transition”, in which objects can pass between circulation outside the orbit of Mars and circulation inside it, or vice versa. The eccentricity of the orbit of Mars appears to play an important role in circulation transition and in horseshoe motion. Based on the orbits and on spectroscopic data, the Trojan asteroids of Mars may be primordial bodies, while some co-orbital bodies may be in a temporary state of motion. 相似文献
18.
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
19.
A. V. Melnikov 《Solar System Research》2017,51(4):327-334
The orbital dynamics of the single known planet in the binary star system HD 196885 has been considered. The Lyapunov characteristic exponents and Lyapunov time of the planetary system have been calculated for possible values of the planetary orbit parameters. It has been shown that the dynamics of the planetary system HD 196885 is regular with the Lyapunov time of more than 5 × 104 years (the orbital period of the planet is approximately 3.7 years), if the motion occurs at a distance from the separatrix of the Lidov–Kozai resonance. The values of the planet’s orbital inclination to the plane of the sky and longitude of the ascending node lie either within ranges 30° < i p < 90° and 30° < Ωp < 90°, or 90° < i p < 180° and 180° < Ωp < 300°. 相似文献