共查询到20条相似文献，搜索用时 46 毫秒
1.
Zhang Fei-peng Huang Cheng Feng Chu-gang Dong Xiao-jun Liao Xin-hao 《Chinese Astronomy and Astrophysics》2001,25(4):641-489
Variance component estimation (VCE) is applied to precise orbit determination (POD) of the ERS-2 satellite. Twenty 5-day long arcs in the early three months in 1998 were calculated using the SLR and PRARE data. In the data the adjacent arcs overlap for two days except the intervals for orbit maneuver. The effect of VCE orbit determination on the calculation is investigated by an analysis of residuals and comparison of overlapping arcs, and the mean a posteriori standard deviation of each group of measured residuals is given. It is shown by the residuals analysis that the fitting of the measurements is significantly improved by VCD. However, according to Abbey criterion, VCD is not able to eliminate the systematic errors due to errors in the dynamic and geometric models. The results of the comparison of the overlapping arcs show that (1) VCE reduces the mean range deviation of overlapping arcs, especially where there are obviously unreasonable deviations, so that the orbit obtained has a more uniform precision; (2) By using VCE, adjacent arcs tend to close up and this is more apparent in the transverse direction. From the mean a posteriori standard error of each group of measurements, it can be seen that as far as the single normal point measurement is concerned, the data of some SLR stations are more important than other measurements in POD calculation. Generally speaking, determination of weighting by using VCE is more reasonable than by using initial standard deviation. 相似文献
2.
Contemporary surveys provide a huge number of detections of small solar system bodies, mostly asteroids. Typically, the reported astrometry is not enough to compute an orbit and/or perform an identification with an already discovered object. The classical methods for preliminary orbit determination fail in such cases: a new approach is necessary. When the observations are not enough to compute an orbit we represent the data with an attributable (two angles and their time derivatives). The undetermined variables range and range rate span an admissible region of solar system orbits, which can be sampled by a set of Virtual Asteroids (VAs) selected by an optimal triangulation. The attributable results from a fit and has an uncertainty represented by a covariance matrix, thus the predictions of future observations can be described by a quasi-product structure (admissible region times confidence ellipsoid), which can be approximated by a triangulation with each node surrounded by a confidence ellipsoid. The problem of identifying two independent short arcs of observations has been solved. For each VA in the admissible region of the first arc we consider prediction at the time of the second arc and the corresponding covariance matrix, and we compare them with the attributable of the second arc with its own covariance. By using the penalty (increase in the sum of squares, as in the algorithms for identification) we select the VAs which can fit together both arcs and compute a preliminary orbit. Even two attributables may not be enough to compute an orbit with a convergent differential corrections algorithm. The preliminary orbits are used as first guess for constrained differential corrections, providing solutions along the Line Of Variations (LOV) which can be used as second generation VAs to further predict the observations at the time of a third arc. In general the identification with a third arc will ensure a least squares orbit, with uncertainty described by the covariance matrix. 相似文献
3.
Bruno Bertotti 《Celestial Mechanics and Dynamical Astronomy》2001,80(1):21-38
We show that, when a natural satellite like Titan is invisible (e.g., due to an opaque atmosphere) its planetary orbit and its mass can be determined by tracking a spacecraft in close flybys. This is an important problem in the Cassini mission to the Saturnian system, which will be greatly improved by a good astrometric model for all its main components; in particular, an accuracy of a few hundred meters for the orbit of Titan is necessary to allow a measurement of its moment of inertia. The orbit of the spacecraft is the union of elliptical arcs, joined by short hyperbolic transitions: a problem of singular perturbation theory, whose solution leads to a matching condition between the inner hyperbolic orbit and the elliptical orbital elements. Since the inner elements are given in terms of the relative position and velocity of the spacecraft, accurate Doppler measurements in both regions can provide a satisfactory determination of Titan's position and velocity, hence of its Keplerian elements. The errors in this determination are discussed on the basis of the expected Allan deviation of the Doppler method; it is found that the driving errors are those in the elliptical arcs; the fractional errors in Titan's orbital elements are expected to be 10–7. It is also possible to measure the mass of the satellite; however, when the eccentricity e of the flybys is large, the mass and a scaling transformation are highly correlated and the fractional error in the mass is expected to be e times worse. 相似文献
4.
According to the optimal control theory, the optimal control problem of the low-thrust tra jectory can be converted into a solution of nonlinear two- point boundary-value problem (TPBVP). To solve the TPBVP, the repeated random guesses for the initial costate variables and iterative computations are needed. In order to enhance the convergence of the iterations, we select an appropriate performance index, and then linearize the equations of the TPBVP around a Keplerian orbit. For multi-revolution transfers, instead of the multi- revolution Lambert tra jectory, multiple segmented Keplerian arcs are used to ensure the effectiveness of the linearization. The method is totally automatic with multiple iterations. With this method, we can get the results within 3 ∼ 5 iterations, and the random guess of the initial costates is unnecessary. Finally by the iterative optimization of the performance index, a better control strategy approaching to the bang-bang control is obtained. 相似文献
5.
Diana W. Scott 《Planetary and Space Science》1967,15(12):1895-1911
An Earth satellite can only be observed by optical methods when it is illuminated by sunlight and the observing station is in darkness, with the result that the satellite is in general only visible on two fairly small arcs of its orbit.
In this paper, a graphical method has been developed for predicting the latitudes from which a satellite in a circular orbit is visible, with the particular aim of discovering periods when a satellite may be observed in mid-latitudes in both the northern and southern hemispheres. For near-polar orbits the occurrence of such periods depends critically on the position of the ascending node of the orbit; but for lower inclinations, the periods of visibility become shorter and more frequent, and the orientation of the orbit is less significant. 相似文献
6.
In this paper, a method to capture near-Earth objects (NEOs) incorporating low-thrust propulsion into the invariant manifolds technique is investigated. Assuming that a tugboat-spacecraft is in a rendez-vous condition with the candidate asteroid, the aim is to take the joint spacecraft-asteroid system to a selected periodic orbit of the Sun–Earth restricted three-body system: the orbit can be either a libration point periodic orbit (LPO) or a distant prograde periodic orbit (DPO) around the Earth. In detail, low-thrust propulsion is used to bring the joint spacecraft-asteroid system from the initial condition to a point belonging to the stable manifold associated to the final periodic orbit: from here onward, thanks to the intrinsic dynamics of the physical model adopted, the flight is purely ballistic. Dedicated guided and capture sets are introduced to exploit the combined use of low-thrust propulsion with stable manifolds trajectories, aiming at defining feasible first guess solutions. Then, an optimal control problem is formulated to refine and improve them. This approach enables a new class of missions, whose solutions are not obtainable neither through the patched-conics method nor through the classic invariant manifolds technique. 相似文献
7.
When the observational data are not enough to compute a meaningful orbit for an asteroid/comet we can represent the data with an attributable, i.e., two angles and their time derivatives. The undetermined variables range and range rate span an admissible region of Solar System orbits, which can be sampled by a set of Virtual Asteroids (VAs) selected by means of an optimal triangulation [Milani, A., Gronchi, G.F., de' Michieli Vitturi, M., Kne?evi?, Z., 2004. Celest. Mech. Dyn. Astron. 90, 59-87]. The attributable 4 coordinates are the result of a fit and they have an uncertainty, represented by a covariance matrix. Two short arcs of observations, represented by two attributables, can be linked by considering for each VA (in the admissible region of the first arc) the covariance matrix for the prediction at the time of the second arc, and by comparing it with the attributable of the second arc with its own covariance. By defining an identification penalty we can select the VAs allowing to fit together both arcs and compute a preliminary orbit. Two attributables may not be enough to compute an orbit with convergent differential corrections. Thus the preliminary orbit is used in a constrained differential correction, providing solutions along the Line Of Variation which can be used as second generation VAs to further predict the observations at the time of a third arc. In general the identification with a third arc will ensure a well determined orbit, to which additional sets of observations can be attributed. To test these algorithms we use a large scale simulation and measure the completeness, the reliability and the efficiency of the overall procedure to build up orbits by accumulating identifications. Under the conditions expected for the next generation asteroid surveys, the methods developed in this and in the preceding papers are efficient enough to be used as primary identification methods, with very good results. One important property is that the completeness in finding the possible identifications is as good for comparatively rare orbits, such as the ones of Near-Earth Objects, as for main belt orbits. 相似文献
8.
9.
将方差分量估计（VCE）方法应用于ERS－2卫星的精密定轨,用SLR和PRARE资料计算了1998年前3个月的23个长度为5天的弧段（除了调整轨道的时段外,相邻弧段有两天的重叠）,从观测值残差分析和重叠弧段比较两个方面,考察VCE方法对定轨计算的影响,并给出了各组观测值的平均验后均方差,对观测值残差的分析表明,使用VCE方法明显地改善了观测值的拟合程度,但从阿卑（Abbey)标准对观测值残差的检验结果来看,使用VCE方法不能消除轨道中由力学模型和几何模型误差引入的系统差,重叠弧段比较的结果表明：（1）使用VCE方法缩小了重叠弧段的平均距离差,并改善了一部分权段明显不合理的偏离,使最后得到的轨道具有更均匀的精度,（2）相比较而言,VCE方法使相邻弧段靠拢的趋势在轨道切向体现得较为明显,由各组观测值的平均验后方差可见,说单个标准点观测值而言,部分SLR台站的观测资料在定轨计算中占有比其他观测资料更重的地位,纵观全文,使用VCE后得到的观测值的平衡验后均方差来确定资料的双重将比使用均方差更为合理。 相似文献
10.
Modern asteroid surveys produce an increasingly large number of observations, which are grouped into very short arcs (VSAs) each containing a few observations of the same object in one single night. To decide whether two VSAs collected in different nights correspond to the same observed object we can attempt to compute an orbit with the observations of both arcs: this is called the linkage problem. Since the number of linkages to be attempted is very large, we need efficient methods of orbit determination. Using the first integrals of Kepler’s motion we can write algebraic equations for the linkage problem, which can be put in polynomial form. In Gronchi et al. (Celest Mech Dyn Astron 123(2):105–122, 2015) these equations are reduced to a polynomial equation of degree 9: the unknown is the topocentric distance of the observed body at the mean epoch of one VSA. Here we derive the same equations in a more concise way, and show that the degree 9 is optimal in a sense that will be specified in Sect. 3.3. We also introduce a procedure to join three VSAs: from the conservation of angular momentum we obtain a polynomial equation of degree 8 in the topocentric distance at the mean epoch of the second VSA. For both identification methods, with two and three VSAs, we discuss how to discard solutions. Finally, we present some numerical tests showing that the new methods give satisfactory results and can be used also when the time separation between the VSAs is large. The low polynomial degree of the new methods makes them well suited to deal with the very large number of asteroid observations collected by the modern surveys. 相似文献
11.
Xiangyuan Zeng Hexi Baoyin Junfeng Li Shengping Gong 《Celestial Mechanics and Dynamical Astronomy》2011,111(4):415-430
A new concept of three dimensional non-Keplerian trajectories with double angular momentum reversal is investigated with high
performance solar sails. The main discussion of this paper is about such 3D solar inverse orbits with inner constraints. The
problem is addressed in a time optimal control framework solved by an indirect method. Two typical solar inverse orbits have
been achieved and presented in a 3D non-dimensional dynamic model in the Heliocentric Inertial Frame. Starting from the Earth
orbit ecliptic plane, a sailcraft in the inverse orbit exhibits a butterfly shape trajectory. As such, the new orbits are
symmetrical with respect to a plane which contains the Sun-perihelion line. The relation of the sail attitude angles between
the two symmetrical parts of the orbits are used to reduce the simulation effort. The quasi-heliostationary property at its
aphelia is demonstrated with variation of the orbital radius. Evolutions of the orbital velocity and optimal sail orientations
are also outlined and discussed to benefit future design work. As is suited for space observation guaranteed by its butterfly
shape, the inverse orbits are thoroughly studied in terms of the concerned parameters. The discussion of the parametric influence
is ranked in order as perihelion distance r
E
, required maximum position z
max, perihelion position z
f
and the sail lightness number β. Suitable ranges of each parameter are adopted to illustrate the orbital variation trend. Through numerical simulations the
features of such inverse orbits are further emphasized to provide an initial reference for future researchers. 相似文献
12.
The process of calculating a good orbit from astrometric observations of the same object involves three main steps: preliminary orbit determination, least squares orbit fitting, and quality control assessing the orbit's uncertainty and reliability. For the next generation sky surveys, with much larger number density of observations, new algorithms, or at least substantial revisions of the classical ones, are needed. The classical theory of preliminary orbit algorithms was incomplete in that the consequences of the topocentric correction had not been fully studied. We show that it is possible to rigorously account for topocentric observations and that this correction may increase the number of alternate preliminary orbits without impairing the overall performance. We have developed modified least squares algorithms including the capability of fitting the orbit to a reduced number of parameters. The restricted fitting techniques can be used to improve the reliability of the orbit computing procedure when the observed arcs have small curvature. False identification (where observations of different objects are incorrectly linked together) can be discarded with a quality control on the residuals and a ‘normalization’ procedure removing duplications and contradictions. We have tested our algorithms on two simulations based on the expected performance of Pan-STARRS—one of the next generation all-sky surveys. The results confirm that large sets of discoveries can be handled very efficiently resulting in good quality orbits. In these tests we lost only 0.6 to 1.3% of the possible objects, with a false identification rate in the range 0.02 to 0.06%. 相似文献
13.
14.
Orbits around Mercury are influenced by the strong elliptic third-body perturbation, especially for high eccentricity orbits, the periapsis altitude changes dramatically. Frozen orbits whose mean eccentricity and argument of perigee remain constants are obviously a good choice for space missions, but the forming conditions are too harsh to meet practical needs. To deal with this problem, a continuous control method that combines analytical theory and parameter optimization is proposed to build an artificial frozen orbit. The artificial frozen orbits are investigated on the basis of double averaged Hamiltonian, of which the second and third zonal harmonics and the perturbation of elliptic third-body gravity are considered. In this paper, coefficients of perturbations which satisfy the conditions of frozen orbits are involved as control parameters, and the relevant artificial perturbations are compensated by the control strategy. So probes around Mercury can be kept on frozen orbit under the influence of continuous control force. Then complex method of optimization is used to search for the energy optimized artificial frozen orbits. The choosing of optimal parameters, the objective function setting and other issues are also discussed in the study. Evolution of optimal control parameters are given in large ranges of semi-major axis and eccentricity, through the variation of these curves, the fuel efficiency is discussed. The result shows that the control method proposed in this paper can effectively maintain the eccentricity and argument of perigee frozen. 相似文献
15.
16.
初轨计算的参考矢量法 总被引：3，自引：0，他引：3
本文从最优估计角度研究短弧资料定初轨问题，提出一种最小二乘估计算法，同时提出一种符合实用的参考矢量法．仿真结果显示，参考矢量法克服了现有初轨算法所承受病态影响，把定轨精度提高到接近最佳水平． 相似文献
17.
With the increase in complexities of interplanetary missions, the main focus has shifted to reducing the total delta-V for the entire mission and hence increasing the payload capacity of the spacecraft. This paper develops a trajectory to Mars using the Lagrangian points of the Sun-Earth system and the Sun-Mars system. The whole trajectory can be broadly divided into three stages: (1) Trajectory from a near-Earth circular parking orbit to a halo orbit around Sun-Earth Lagrangian point L2. (2) Trajectory from Sun-Earth L2 halo orbit to Sun-Mars L1 halo orbit. (3) Sun-Mars L1 halo orbit to a circular orbit around Mars. The stable and unstable manifolds of the halo orbits are used for halo orbit insertion. The intermediate transfer arcs are designed using two-body Lambert’s problem. The total delta-V for the whole trajectory is computed and found to be lesser than that for the conventional trajectories. For a 480 km Earth parking orbit, the total delta-V is found to be 4.6203 km/s. Another advantage in the present approach is that delta-V does not depend upon the synodic period of Earth with respect to Mars. 相似文献
18.
Daniele Serra Federica Spoto Andrea Milani 《Celestial Mechanics and Dynamical Astronomy》2018,130(11):75
Chaotic dynamical systems are characterized by the existence of a predictability horizon, connected to the notion of Lyapunov time, beyond which predictions of the state of the system are meaningless. In order to study the main features of orbit determination in the presence of chaos, Spoto and Milani (Celest Mech Dyn Astron 124:295–309, 2016) applied the classical least-squares fit and differential correction algorithm to determine a chaotic orbit and a dynamical parameter of a simple discrete system—Chirikov standard map (cf. Chirikov in Phys Rep 52:263, 1979)—with observations distributed beyond the predictability horizon. They found a time limit beyond which numerical calculations are affected by numerical instability: the computability horizon. In this article, we aim at pushing forward such inherent obstacle to numerical calculations in chaotic orbit determination by applying the classical and the constrained multi-arc method (cf. Alessi et al. in Mon Not R Astron Soc 423:2270–2278, 2012) to the same dynamical system. These strategies entail the determination of an orbit when observations are grouped in separate observed arcs. For each arc, a set of initial conditions is determined and, in the case of the constrained multi-arc method, all subsequent arcs are constrained to belong to the same trajectory. We show that the use of these techniques in place of the standard least-squares method has significant advantages: Not only can we perform accurate numerical calculations well beyond the computability horizon, in particular, the constrained multi-arc strategy improves considerably the determination of the dynamical parameter. 相似文献
19.
Using statistical orbital ranging, we systematically study the orbit computation problem for transneptunian objects (TNOs). We have automated orbit computation for large numbers of objects, and, more importantly, we are able to obtain orbits even for the most sparsely observed objects (observational arcs of a few days). For such objects, the resulting orbit distributions include a large number of high-eccentricity orbits, in which TNOs can be perturbed by close encounters with Neptune. The stability of bodies on the computed orbits has therefore been ascertained by performing a study of close encounters with the major planets. We classify TNO orbit distributions statistically, and we study the evolution of their ephemeris uncertainties. We find that the orbital element distributions for the most numerous single-apparition TNOs do not support the existence of a postulated sharp edge to the belt beyond 50 AU. The technique of statistical ranging provides ephemeris predictions more generally than previously possible also for poorly observed TNOs. 相似文献
20.
We consider dynamics of a Sun–Jupiter–Asteroid system, and, under some simplifying assumptions, show the existence of instabilities in the motions of an asteroid. In particular, we show that an asteroid whose initial orbit is far from the orbit of Mars can be gradually perturbed into one that crosses Mars’ orbit. Properly formulated, the motion of the asteroid can be described as a Hamiltonian system with two degrees of freedom, with the dynamics restricted to a “large” open region of the phase space reduced to an exact area preserving map. Instabilities arise in regions where the map has no invariant curves. The method of MacKay and Percival is used to explicitly rule out the existence of these curves, and results of Mather abstractly guarantee the existence of diffusing orbits. We emphasize that finding such diffusing orbits numerically is quite difficult, and is outside the scope of this paper. 相似文献