共查询到20条相似文献，搜索用时 48 毫秒
1.
The paper presents an efficient algorithm for the study of satellite and space debris orbits on long time intervals. The averaged equations of motion are integrated by means of the implicit midpoint method. This approach is known as a symplectic mapping technique. The perturbing forces included in the mapping are: the geopotential, the atmospheric drag, lunisolar perturbations and the direct radiation pressure (without shadow effects). The influence of the atmosphere is approximated by simple methods for the estimation of integrals. The described mapping is valid for the wide range of orbits including the resonant and the eccentric ones; it can be helpful in practical and theoretical problems. The lifetime of GPS transfer orbits is discussed as an exemplary application. 相似文献
2.
William H. Jefferys 《Celestial Mechanics and Dynamical Astronomy》1971,3(3):390-394
In some perturbation theories it is possible to avoid expansion of the perturbations in powers of the eccentricity, obtaining results in closed form by using the true or eccentric anomaly instead of the mean anomaly. This paper describes an algorithm (which has been programmed for the 6600 computer using the formula manipulation system TRIGMAN) for automatically performing the integrals which arise in these theories. 相似文献
3.
K. Aksnes 《Celestial Mechanics and Dynamical Astronomy》1976,13(1):89-104
On the basis of expressions derived by Kozai, and new ones developed here, a detailed, semianalytic algorithm is presented for calculating radiation-pressure perturbations in the Keplerian elements. Through some simple modifications, the algorithm is also made to hold whene=0 and/ori=0. The perturbations are obtained by summing over the sunlit segment of the satellite's orbit during each revolution or part thereof. The end points of this segment are evaluated numerically once per revolution. The effect of the inherent uncertainties in the boundaries of the Earth's shadow is discussed. The algorithm is tested by means of numerical integration of the equations of motion and through comparisons with observations of the balloon satellite 1963 30D during a 200-day interval. 相似文献
4.
Davide Farnocchia Giacomo Tommei Andrea Milani Alessandro Rossi 《Celestial Mechanics and Dynamical Astronomy》2010,107(1-2):169-185
We propose two algorithms to provide a full preliminary orbit of an Earth-orbiting object with a number of observations lower than the classical methods, such as those by Laplace and Gauss. The first one is the Virtual debris algorithm, based upon the admissible region, that is the set of the unknown quantities corresponding to possible orbits for a given observation for objects in Earth orbit (as opposed to both interplanetary orbits and ballistic ones). A similar method has already been successfully used in recent years for the asteroidal case. The second algorithm uses the integrals of the geocentric 2-body motion, which must have the same values at the times of the different observations for a common orbit to exist. We also discuss how to account for the perturbations of the 2-body motion, e.g., the J 2 effect. 相似文献
5.
Expressions are given for the first order node-to-node perturbations in the orbital elements of a satellite due to an arbitrary zonal harmonic of the geopotential. Accurate and efficient procedures for computing such perturbations are necessary for orbit determination methods which will fully utilize the highly accurate observations now available.Comparison with a double precision numerical integration is made for an intermediate altitude satellite, TELSTAR I. (Second order perturbations due to the second harmonic, derived elsewhere, are included, as are the first order perturbations due to the zonals through fourteenth order.) Discrepancies in semi-major axis after 1 period are of the order of 0.1 mm. Discrepancies in timing are of the order of 0.03 msec. A detailed discussion of computational efficiency is included. 相似文献
6.
D. Standaert 《Celestial Mechanics and Dynamical Astronomy》1980,22(4):357-369
The aim of the present paper is to present the theoretical background of a method to compute the planetary perturbations on the Moon's motion. We formulate an algorithm based upon the Lie transform method and well-suited to the particular problem at hand.This algorithm is being implemented using Henrard's Semi-Analytical Lunar Ephemeris (SALE) as solution of the Main Problem and Bretagnon's planetary theory. The accuracy of the solution is intended to be about 0".001 for terms of period up to 2000 years.To illustrate the interest of our approach, we comment on some preliminary results obtained about the direct perturbations due to Venus on the Moon's longitude. The final results will be the subject of another paper. 相似文献
7.
Vacheslav Emel'yanenko 《Celestial Mechanics and Dynamical Astronomy》2002,84(4):331-341
A new symplectic algorithm is developed for cometary orbit integrations. The integrator can handle both high-eccentricity orbits and close encounters with planets. The method is based on time transformations for Hamiltonians separated into Keplerian and perturbation parts. The adaptive time-step of this algorithm depends on the distance from a centre and the magnitude of perturbations. The explicit leapfrog technique is simple and efficient. 相似文献
8.
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
9.
Sławomir Breiter 《Celestial Mechanics and Dynamical Astronomy》1998,71(4):229-241
An explicit symplectic integrator is constructed for perturbed elliptic orbits of an arbitrary eccentricity. The perturbation
should be Hamiltonian, but it may depend on time explicitly. The main feature of the integrator is the use of KS variables
in the ten-dimensional extended phase space. As an example of its application the motion of an Earth satellite under the action
of the planet's oblateness and of lunar perturbations is studied. The results confirm the superiority of the method over a
classical Wisdom–Holman algorithm in both accuracy and computation time.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
10.
The problem of finding natural bounded relative trajectories between the different units of a distributed space system is of great interest to the astrodynamics community. This is because most popular initialization methods still fail to establish long-term bounded relative motion when gravitational perturbations are involved. Recent numerical searches based on dynamical systems theory and ergodic maps have demonstrated that bounded relative trajectories not only exist but may extend up to hundreds of kilometers, i.e., well beyond the reach of currently available techniques. To remedy this, we introduce a novel approach that relies on neither linearized equations nor mean-to-osculating orbit element mappings. The proposed algorithm applies to rotationally symmetric bodies and is based on a numerical method for computing quasi-periodic invariant tori via stroboscopic maps, including extra constraints to fix the average of the nodal period and RAAN drift between two consecutive equatorial plane crossings of the quasi-periodic solutions. In this way, bounded relative trajectories of arbitrary size can be found with great accuracy as long as these are allowed by the natural dynamics and the physical constraints of the system (e.g., the surface of the gravitational attractor). This holds under any number of zonal harmonics perturbations and for arbitrary time intervals as demonstrated by numerical simulations about an Earth-like planet and the highly oblate primary of the binary asteroid (66391) 1999 KW4. 相似文献
11.
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
12.
The motion of a lunar satellite 总被引：2，自引：0，他引：2
Claus Oesterwinter 《Celestial Mechanics and Dynamical Astronomy》1970,1(3-4):368-436
Presented in this theory is a semianalytical solution for the problem of the motion of a satellite in orbit around the moon. The principal perturbations on such a body are due to the nonspherical gravity field of the moon, the attraction of the earth, and, to a lesser degree, the attraction of the sun. The major part of the problem is solved by means of the celebrated von Zeipel Method, first successfully applied to the motion of an artificial earth satellite by Brouwer in 1959. After eliminating from the Hamiltonian all terms with the period of the satellite and those with the period of the moon, it is suggested to solve the remaining problem with the aid of numerical integration of the modified equations of motion.This theory was written in 1964 and presented as a dissertation to Yale University in 1965. Since then a great deal has been learned about the gravity field of the moon. It seems that quite a number of recently determined gravity coefficients would qualify as small quantities of order two. Hence, according to the truncation criteria employed, they should be considered in the present theory. However, the author has not endeavored to update the work accordingly. The final results, therefore, are incomplete in the lunar gravitational perturbations. Nevertheless, the theory does give the largest such variations and it does present the methods by which perturbations may be derived for any gravity terms not actually developed. 相似文献
13.
Dou-Xing Cui 《Celestial Mechanics and Dynamical Astronomy》1984,32(1):1-13
The perturbations of artificial satellite are derived here by a new method, somewhat similar to that of Poisson.The novel feature of the method is that the right-hand member f(t;x) of the differential equations need not be developed in series, as it is done in the von Zeipel and other methods. 相似文献
14.
This paper analyzes transversal small-scale perturbations in arbitrary three-dimensional (3D) spatially nonuniform space plasma
systems with magnetic surfaces and deduces a system of equations for these perturbations. It shows that a dipole magnetic
field can have perturbations of two different polarizations. Within dipole geometry, it derives equations for MHD-eigenmodes
and investigates stability of the perturbations. 相似文献
15.
P. Moore 《Celestial Mechanics and Dynamical Astronomy》1979,20(2):125-142
The orbital accelerations of certain balloon satellites exhibit marked oscillations caused by solar radiation impinging on the surface of the satellites, which, once spherical, have assumed a spheroidal shape producing a component of force at right-angles to the Sun-satellite direction. Given the characteristics and orientation of the satellite, the equations of force are determined by the formulae of Lucas. Otherwise the phase-angle and magnitude of the right-angle force are determined by trial and error, or best-fit techniques. Using a variation of the approach developed by Aksnes, a semi-analytical algorithm is presented for evaluating the perturbations of the Keplerian elements by direct solar radiation pressure on a spheroidal satellite. The perturbations are obtained by summing over the sunlit part of each orbit and allow for a linear variation in the phase-angle. The algorithm is used to determine the orbital accelerations of 1963-30D due to direct solar radiation pressure, and these results are compared to the observed values over two separate periods of the satellite's lifetime. 相似文献
16.
We develop a new and fast method to estimate perturbations by a planet on cometary orbits. This method allows us to identify accurately the cases of large perturbations in a set of fictitious orbits. Hence, it can be used in constructing perturbation samples for Monte Carlo simulations in order to maximize the amount of information. Furthermore, the estimated perturbations are found to yield a good approximation to the real perturbation sample. This is shown by a comparison of the perturbations obtained by the new estimator with the results of numerical integration of regularized equations of motion for the same orbits in the same dynamical model: the three-dimensional elliptic restricted three-body problem (Sun-Jupiter-comet). 相似文献
17.
Trent Jansen‐Sturgeon Eleanor K. Sansom Philip A. Bland 《Meteoritics & planetary science》2019,54(9):2149-2162
Fireball networks establish the trajectories of meteoritic material passing through Earth's atmosphere, from which they can derive pre‐entry orbits. Triangulated atmospheric trajectory data require different orbit determination methods to those applied to observational data beyond the Earth's sphere of influence, such as telescopic observations of asteroids. Currently, the vast majority of fireball networks determine and publish orbital data using an analytical approach, with little flexibility to include orbital perturbations. Here, we present a novel numerical technique for determining meteoroid orbits from fireball network data and compare it to previously established methods. The re‐entry of the Hayabusa spacecraft, with its known pre‐Earth orbit, provides a unique opportunity to perform this comparison as it was observed by fireball network cameras. As initial sightings of the Hayabusa spacecraft and capsule were made at different altitudes, we are able to quantify the atmosphere's influence on the determined pre‐Earth orbit. Considering these trajectories independently, we found the orbits determined by the novel numerical approach to align closer to JAXA's telemetry in both cases. Using simulations, we determine the atmospheric perturbation to become significant at ~90 km—higher than the first observations of typical meteorite dropping events. Using further simulations, we find the most substantial differences between techniques to occur at both low entry velocities and Moon passing trajectories. These regions of comparative divergence demonstrate the need for perturbation inclusion within the chosen orbit determination algorithm. 相似文献
18.
近地小行星轨道演化的数值研究与辛算法有效性的探讨 总被引：2，自引：0，他引：2
本文采用改进的显式辛算法（symplecticalgorithm）和嵌套的RKF7（8）积分器对43颗已命名（或编号）的近地小行星的轨道演化进行数值研究．在力学模型上,除考虑各大行星的引力振动外,还增加了后牛顿效应,而在算法上则着重探索辛算法在近地小行星轨道演化研究中的应用前景,特别是当小行星与某一大行星靠近时辛算法的有效性．本文的结果可为了解近地小行星的轨道演化状况和对它们进行监测提供可靠的信息． 相似文献
19.
The methods for analytical determination of partial derivatives of the current parameters of motion with respect to their initial values are described. The methods take into account principal perturbations and are based on the use of the osculating and superosculating intermediate orbits constructed earlier by the author. These orbits ensure the first-, second-, and third-order contact to the real trajectory at the initial time. The solution for parameters of the intermediate motion and partial derivatives of these parameters is given in a universal closed form. The partial derivatives on long time intervals are computed using a step-by-step procedure combined with the Encke method of special perturbations, in which the intermediate orbits are used as the reference. The numerical results show that the new approach can be efficiently used for solving the problem of differential correction of orbits of asteroids and comets on the basis of observational data. 相似文献
20.
Continuing a work initiated in an earlier publication (Yamada et al. in Phys Rev D 91:124016, 2015), we reexamine the linear stability of the triangular solution in the relativistic three-body problem for general masses by the standard linear algebraic analysis. In this paper, we start with the Einstein–Infeld–Hoffmann form of equations of motion for N-body systems in the uniformly rotating frame. As an extension of the previous work, we consider general perturbations to the equilibrium, i.e., we take account of perturbations orthogonal to the orbital plane, as well as perturbations lying on it. It is found that the orthogonal perturbations depend on each other by the first post-Newtonian (1PN) three-body interactions, though these are independent of the lying ones likewise the Newtonian case. We also show that the orthogonal perturbations do not affect the condition of stability. This is because these do not grow with time, but always precess with two frequency modes, namely, the same with the orbital frequency and the slightly different one due to the 1PN effect. The condition of stability, which is identical to that obtained by the previous work (Yamada et al. 2015) and is valid for the general perturbations, is obtained from the lying perturbations. 相似文献