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1.
Florent Deleflie Gilles Métris Pierre Exertier 《Celestial Mechanics and Dynamical Astronomy》2006,94(1):83-104
This paper studies the long period variations of the eccentricity vector of the orbit of an artificial satellite, under the
influence of the gravity field of a central body. We use modified orbital elements which are non-singular at zero eccentricity.
We expand the long periodic part of the corresponding Lagrange equations as power series of the eccentricity. The coefficients
characterizing the differential system depend on the zonal coefficients of the geopotential, and on initial semi-major axis,
inclination, and eccentricity. The differential equations for the components of the eccentricity vector are then integrated
analytically, with a definition of the period of the perigee based on the notion of “free eccentricity”, and which is also
valid for circular orbits. The analytical solution is compared to a numerical integration. This study is a generalization
of (Cook, Planet. Space Sci., 14, 1966): first, the coefficients involved in the differential equations depend on all zonal coefficients (and not only on
the very first ones); second, our method applies to nearly circular orbits as well as to not too eccentric orbits. Except
for the critical inclination, our solution is valid for all kinds of long period motions of the perigee, i.e., circulations
or librations around an equilibrium point. 相似文献
2.
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
3.
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
4.
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
5.
HUANG Yong HU Xiaogong HUANG Cheng 《中国科学院上海天文台年刊》2005,(1):14-21
从解析形式出发,利用月球重力场模型JGL165P1,分析了月球重力场(带谐项)对绕月低轨卫星的长期影响。为了减少计算误差,保证计算精度,在分析解中使用循环公式来计算倾角函数。结果指出对于一个高度为100km的极月轨道卫星,冻结轨道存在的可能性不大,但是当轨道倾角在i=90°附近或者高度再高一些,则有可能存在冻结轨道;对于100km高的初始圆轨道,卫星在无控的情况下半年内将会坠落到月球表面,如果高度增加到200km,则不进行轨道控制也不会坠落到月面上。利用仿真软件GEODYN解算出来的结果证实了上述结论。 相似文献
6.
D.G. King-Hele 《Planetary and Space Science》1977,25(4):343-352
The satellite 1966-51C was launched in June 1966 into a polar orbit with perigee height 180 km, apogee height 3600 km, and orbital period 125 min. The orbit contracted rapidly under the influence of air drag, and the satellite decayed in March 1967. The only available observations are from the NASA Minitrack system, and 825 of these have been used with PROP6 orbit refinement program, to determine orbital parameters at 20 epochs. For most of these orbits the standard deviations in inclination and right ascension of the node are less than 0.002° (corresponding to about 200 m cross-track) and the standard deviations in eccentricity are less than 0.00002 (150 m in height).The variation in inclination is analysed to determine upper-atmosphere zonal wind speeds, with excellent resolution in local time. The results, for heights near 210 km and a representative latitude near 30°, indicate west-to-east winds of 100 ± 40 m/s for local time 18–21 h, and east-to-west winds of 80 ± 25 m/s for 02–04 h and 09–12 h local time. The values of the right ascension of the node are also analysed, and provide independent confirmation of the wind speeds obtained from the inclination. Analysis of the decrease in perigree distance indicates values of density scale height within 5% of those predicted by the COSPAR International Reference Atmosphere 1972, for the conditions experienced by 1966-51C. 相似文献
7.
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
8.
The smallness parameter of the approximation method is defined in terms of the non-dimensional initial distance between target and chaser satellite. In the case of a circular target orbit, compact analytical expressions are obtained for the interception travel time up to third order. For eccentric target orbits, an explicit result is worked out to first order, and the tools are prepared for numerical evaluation of higher order contributions. The possible transfer orbits are examined within Lambert’s theorem. For an eventual rendezvous it is assumed that the directions of the angular momenta of the two orbits enclose an acute angle. This assumption, together with the property that the travel time should vanish with vanishing initial distance, leads to a condition on the admissible initial positions of the chaser satellite. The condition is worked out explicitly in the general case of an eccentric target orbit and a non-coplanar transfer orbit. The condition is local. However, since during a rendezvous maneuver, the chaser eventually passes through the local space, the condition propagates to non-local initial distances. As to quantitative accuracy, the third order approximation reproduces the elements of Mars, in the historical problem treated by Gauss, to seven decimals accuracy, and in the case of the International Space Station, the method predicts an encounter error of about 12 m for an initial distance of 70 km. 相似文献
9.
Giorgio E. O. Giacaglia 《Celestial Mechanics and Dynamical Astronomy》1974,9(2):239-267
Lunisolar perturbations of an artificial satellite for general terms of the disturbing function were derived by Kaula (1962). However, his formulas use equatorial elements for the Moon and do not give a definite algorithm for computational procedures. As Kozai (1966, 1973) noted, both inclination and node of the Moon's orbit with respect to the equator of the Earth are not simple functions of time, while the same elements with respect to the ecliptic are well approximated by a constant and a linear function of time, respectively. In the present work, we obtain the disturbing function for the Lunar perturbations using ecliptic elements for the Moon and equatorial elements for the satellite. Secular, long-period, and short-period perturbations are then computed, with the expressions kept in closed form in both inclination and eccentricity of the satellite. Alternative expressions for short-period perturbations of high satellites are also given, assuming small values of the eccentricity. The Moon's position is specified by the inclination, node, argument of perigee, true (or mean) longitude, and its radius vector from the center of the Earth. We can then apply the results to numerical integration by using coordinates of the Moon from ephemeris tapes or to analytical representation by using results from lunar theory, with the Moon's motion represented by a precessing and rotating elliptical orbit. 相似文献
10.
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
11.
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
12.
D.G. King-Hele 《Planetary and Space Science》1974,22(4):509-524
Cosmos 387 (1970-111A) was launched on 16 December 1970 into a near-circular orbit with an average height of 540 km and an inclination of 74.0°. On 5 November 1971 the orbit, in its slow contraction under the influence of air drag, passed through 15th-order resonance, when the ground track repeats after 15 revolutions. The orbit has been determined with the aid of the RAE orbit refinement program PROP at 19 epochs between May 1971 and June 1972, using 1500 optical and radar observations. The average accuracy is about 70 m in perigee height and 0.001° in inclination.The variation of orbital inclination while the satellite was experiencing 15th-order resonance, as given by these 19 orbits and 55 U.S. Navy orbits, has been analysed to obtain equations accurate to 4 per cent for the geopotential coefficients of order 15 and odd degree (15, 17, 19 …). These equations have subsequently been used (with others) in determining individual coefficients of order 15 and odd degree.The variation of eccentricity with argument of perigee showed unexpected complexity, including a tight loop near resonance (Fig. 4). Analysis of the variation in eccentricity has yielded, for the first time, accurate equations for the geopotential coefficients of order 15 and even degree (16, 18 …), thus opening the way to the evaluation of individual coefficients of this type. The variations in the argument of perigee and right ascension of the node have also been analysed. 相似文献
13.
D.G. King-Hele 《Planetary and Space Science》1976,24(1):1-16
The satellite 1970-114F, the final-stage rocket of the Molniya 1S communications satellite, decayed in the atmosphere on 3 March 1973. During the last 20 days of its life the orbit suffered exceptionally rapid decay, with the apogee height decreasing from 7000 to 1000 km while the perigee height remained near 110 km. About 650 observations, made by visual observers in Britain and by U.S. Navy sensors, have been used with the PROP6 orbit refinement program to determine orbits at 14 epochs. Although the decay rate was more than ten times greater than in any previous orbit determination with PROP, good orbits were obtained, the standard deviation in inclination being less than 0.002° on eight orbits.The combination of high drag and good accuracy allows three techniques in orbital analysis to be successfully applied for the first time. Since zonal winds have little effect on the orbit, the changes in inclination are analysed to determine meridional winds near perigee, at heights of 110–120 km, latitudes of 63–65°S, and 6–12 hr LT. The changes in right ascension of the node are also successfully analysed for the same purpose. The two methods agree in indicating a south-to-north wind of 40 ± 30 m/sec from 11 to 21 February, a geomagnetically quiet period, and a south-to-north wind averaging 150 ± 30 m/sec from 22 February to 3 March, a geomagnetically disturbed period. Thirdly, the changes in the argument of perigee are analysed to determine atmospheric oblateness, which is found to be equal to the Earth's oblateness, to within ±20%. Lastly, the drag coefficient in transition flow is evaluated and found to be 0.85 ± 0.20. 相似文献
14.
A. Abdel Aziz Bakry 《Earth, Moon, and Planets》1988,41(1):77-88
In this paper, an algorithm is constructed for the determination of the perturbed motion, in both, the rectangular and the orbital elements of highly eccentric orbits in Earth's gravitational field with axial symmetry whatever the number N of the zonal harmonic coefficients may be. An application of the algorithm for the Explorer 28 satellite (e > 0.94) is given for two geopotential models corresponding to N = 2 and N = 36. In both examples extremely accurate predictions during the satellite life time are obtained. 相似文献
15.
16.
The angle between planetary spin and the normal direction of an orbital plane is supposed to reveal a range of information about the associated planetary formation and evolution. Since the orbit's eccentricity and inclination oscillate periodically in a hierarchical triple body and tidal friction makes the spin parallel to the normal orientation of the orbital plane with a short timescale in an isolated binary system, we focus on the comprehensive effect of third body perturbation and tidal mechanism on the angle. Firstly, we extend the Hut tidal model(1981) to the general spatial case, adopting the equilibrium tide and weak friction hypothesis with constant delay time, which is suitable for arbitrary eccentricity and any angle ? between the planetary spin and normal orientation of the orbital plane. Furthermore, under the constraint of angular momentum conservation, the equations of orbital and ratational motion are given. Secondly, considering the coupled effects of tidal dissipation and third body perturbation, and adopting the quadrupole approximation as the third body perturbation effect, a comprehensive model is established by this work. Finally, we find that the ultimate evolution depends on the timescales of the third body and tidal friction. When the timescale of the third body is much shorter than that of tidal friction, the angle ? will oscillate for a long time,even over the whole evolution; when the timescale of the third body is observably larger than that of the tidal friction, the system may enter stable states, with the angle ? decaying to zero ultimately, and some cases may have a stable inclination beyond the critical value of Lidov-Kozai resonance. In addition, these dynamical evolutions depend on the initial values of the orbital elements and may aid in understanding the characteristics of the orbits of exoplanets. 相似文献
17.
M. A. Vashkov’yak 《Astronomy Letters》2001,27(7):455-463
Based on data for twelve recently discovered outer satellites of Saturn, we investigate their orbital evolution on long time scales. For our analysis, we use the previously obtained general solution of Hill’s double-averaged problem, which was refined for libration orbits, and numerical integration of the averaged system of equations in elements with allowance for Saturn’s orbital evolution. The following basic quantitative parameters of evolving orbits are determined: extreme eccentricities and inclinations, as well as circulation periods of the pericenter arguments and of the longitudes of the ascending nodes. For four new satellite orbits, we have revealed the libration pattern of variations in pericenter arguments and determined the ranges and periods of their variations. Based on characteristic features of the orbits of Saturn’s new satellites, we propose their natural classification. 相似文献
18.
Eva Tresaco Jean Paulo S. Carvalho Antonio F. B. A. Prado Antonio Elipe Rodolpho Vilhena de Moraes 《Celestial Mechanics and Dynamical Astronomy》2018,130(2):9
This paper provides a method for finding initial conditions of frozen orbits for a probe around Mercury. Frozen orbits are those whose orbital elements remain constant on average. Thus, at the same point in each orbit, the satellite always passes at the same altitude. This is very interesting for scientific missions that require close inspection of any celestial body. The orbital dynamics of an artificial satellite about Mercury is governed by the potential attraction of the main body. Besides the Keplerian attraction, we consider the inhomogeneities of the potential of the central body. We include secondary terms of Mercury gravity field from \(J_2\) up to \(J_6\), and the tesseral harmonics \(\overline{C}_{22}\) that is of the same magnitude than zonal \(J_2\). In the case of science missions about Mercury, it is also important to consider third-body perturbation (Sun). Circular restricted three body problem can not be applied to Mercury–Sun system due to its non-negligible orbital eccentricity. Besides the harmonics coefficients of Mercury’s gravitational potential, and the Sun gravitational perturbation, our average model also includes Solar acceleration pressure. This simplified model captures the majority of the dynamics of low and high orbits about Mercury. In order to capture the dominant characteristics of the dynamics, short-period terms of the system are removed applying a double-averaging technique. This algorithm is a two-fold process which firstly averages over the period of the satellite, and secondly averages with respect to the period of the third body. This simplified Hamiltonian model is introduced in the Lagrange Planetary equations. Thus, frozen orbits are characterized by a surface depending on three variables: the orbital semimajor axis, eccentricity and inclination. We find frozen orbits for an average altitude of 400 and 1000 km, which are the predicted values for the BepiColombo mission. Finally, the paper delves into the orbital stability of frozen orbits and the temporal evolution of the eccentricity of these orbits. 相似文献
19.
M. A. Vashkov’yak 《Solar System Research》2016,50(6):390-401
The problem of the secular perturbations of the orbit of a test satellite with a negligible mass caused by the joint influence of the oblateness of the central planet and the attraction by its most massive (or main) satellites and the Sun is considered. In contrast to the previous studies of this problem, an analytical expression for the full averaged perturbing function has been derived for an arbitrary orbital inclination of the test satellite. A numerical method has been used to solve the evolution system at arbitrary values of the constant parameters and initial elements. The behavior of some set of orbits in the region of an approximately equal influence of the perturbing factors under consideration has been studied for the satellite system of Uranus on time scales of the order of tens of thousands of years. The key role of the Lidov–Kozai effect for a qualitative explanation of the absence of small bodies in nearly circular equatorial orbits with semimajor axes exceeding ~1.8 million km has been revealed. 相似文献
20.
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