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1.
The main problem in the orbit determination of the space debris population orbiting our planet is identifying which separate sets of data belong to the same physical object. The observations of a given object during a passage above an observing station are collectively called a Too Short Arc (TSA): data from a TSA cannot allow for a complete determination of an orbit. Therefore, we have to solve first the identification problem, finding two or more TSAs belonging to the same physical object and an orbit fitting all the observations. This problem is well known for the determination of orbits of asteroids: we shall show how to apply the methods developed for preliminary orbit determination of heliocentric objects to geocentric objects. We shall focus on the definition of an admissible region for space debris, both in the case of optical observations and radar observations; then we shall outline a strategy to perform a full orbit determination.  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.
J. TicháM. Tichý  M. Ko?er 《Icarus》2002,159(2):351-357
The number of known near-Earth asteroids (NEAs) has increased rapidly in recent years due to large surveys. This discovery process has to be followed by follow-up observations to obtain a sufficient number of precise astrometric data needed for an accurate orbit determination of newly discovered bodies.Accurate orbit determination requires observations from at least two oppositions. If asteroids are not found in the next apparition, different from the discovery apparition, then they can be considered lost. This is particularly embarrassing for NEAs. If data for different apparitions are not found in the course of precovery surveys or in other archive data, then it is necessary to prepare targeted observations of a particular NEA in the second convenient apparition. Therefore NEA recovery is a very important part of NEA follow-up.We discuss here methods, techniques, and results of planned recoveries at the Klet' Observatory using a 0.57-m telescope equipped with a CCD detector. The Klet' NEA recovery subprogram has brought 21 planned NEA recoveries since 1997, including seven NEAs belonging to the potentially hazardous asteroid category.We briefly mention the overall work on NEA recoveries provided by several NEO follow-up programs as well as the need for communication resources supporting astrometric observers. Finally we present here a planned extension of the Klet' NEA recovery subprogram to fainter objects by means of a new 1.06-m reflector.  相似文献   

4.
Asteroid 1984 AB, discovered in January 1984, proved to be a unique object with a close dynamical relationship to Mars. A brief history of the discovery and subsequent “evolution” of the orbit as it was refined is presented. The preliminary orbit of 1984 AB indicated that it might be a Mars Trojan, and an extended discussion of this interesting possibility is presented, but this hypothesis had to be dismissed after further observations had refined the orbit. The semimajor axis and orbital eccentricity are very similar to that of Mars. No other known Mars-crossing asteroid exists with an orbit as closely associated to Mars.  相似文献   

5.
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   

6.
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7.
Sakurai's object(V4334 Sgr) in all likelihood is a star undergoing a final helium flash.Since its discovery in 1996 observers have been trying to keep up a monitoring of the amazingly fast changes of its stellar properties;changes occuring on time scales of a few weeks or months. By enabling us to follow the evolution of one object in `real time' it relieves us of the need to painstakingly assemble a consistent understanding from different objects, at the various stages of evolution that they have reached from differing starting conditions.Sakurai's object thereby offers a unique opportunity to study an important but short-lived aspect of regular stellar evolution, the final helium flash.  相似文献   

8.
Taking the re-entry object CZ-3B R/B (COSPAR identifier 2012-018D, NORAD catalog number 38253) as an example, retrieval of atmospheric mass densities in lower thermosphere below 200 km from its rebuilt precise orbit is studied in this paper. Two methodologies, i.e. analytical and numerical methods, are adopted in the retrieval. Basic principles of these two methodologies are briefly introduced. Based on the short-arc sparse observational data accumulated in the high accuracy re-entry prediction, orbit determinations of re-entry object CZ-3B R/B are performed sectionally, and then its precise orbit is rebuilt. According to the orbit theory, the variation of orbital semi-major axis of re-entry object CZ-3B R/B induced by atmospheric drag perturbation only is derived from the rebuilt precise orbit. In the derivation of secular change of the orbital semi-major axis of re-entry object CZ-3B R/B induced by atmospheric drag perturbation only, the time-span is set as one minute tentatively. And then retrieval results of atmospheric mass densities in lower thermosphere below 200 km by analytical and numerical methods are presented, as well as their bias deviations from the calculated results of the NRLMSISE-00 empirical model of the atmosphere. Setting bias deviation bands, the corresponding ‘confidence coefficients’ of the retrieved atmospheric mass densities with respect to the model values are given. Average bias deviations of the retrieved atmospheric mass densities by analytical and numerical methods from the model values are also calculated respectively. On the whole, the retrieved atmospheric mass densities by numerical method approach to the model values more closely; the differences between the retrieved results and the model values are relatively smaller at the peaks of atmospheric mass densities than the other places.  相似文献   

9.
In a recent paper Fuhrmann et al. presented radial-velocity measurements of HD 75767 and derived an orbit that was an improvement on the one published by Sanford in 1931; an orbit published in 1991 was, however, overlooked, and the actual calculation of the new elements is open to criticism. A joint solution of all the available data provides a better result than any of the three constituent sets separately; the period is determined to a precision more than 100 times better than in the recent orbit, and a very small but definite eccentricity is reliably documented for the first time. The eccentricity is probably caused (or maintained) by the visual companion. Fuhrmann et al.'s conclusion that the secondary object in the spectroscopic orbit is a white dwarf does not seem inescapable; indeed, the object appears quite likely to be a lower-main-sequence star.  相似文献   

10.
Numerical tests are the basis of a study about the effects caused in the orbits of the planets (1)–(4) by possible errors in the system of planetary masses. The masses of five major and three minor planets are considered. Especially, the effects caused by (1) Ceres in the orbit of (2) Pallas since the time of discovery are found to be large enough for a determination of the mass of Ceres. A first result for this mass is (6.7±0.4)×10–10 solar masses.  相似文献   

11.
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   

12.
For satellite conjunction prediction containing many objects, timely processing can be a concern. Various filters are used to identify orbiting pairs that cannot come close enough over a prescribed time period to be considered hazardous. Such pairings can then be eliminated from further computation to quicken the overall processing time. One such filter is the orbit path filter (also known as the geometric pre-filter), designed to eliminate pairs of objects based on characteristics of orbital motion. The goal of this filter is to eliminate pairings where the distance (geometry) between their orbits remains above some user-defined threshold, irrespective of the actual locations of the satellites along their paths. Rather than using a single distance bound, this work presents a toroid approach, providing a measure of versatility by allowing the user to specify different in-plane and out-of-plane bounds for the path filter. The primary orbit is used to define a focus-centered elliptical ring torus with user-defined thresholds. An assessment is then made to determine if the secondary orbit can touch or penetrate this torus. The method detailed here can be used on coplanar, as well as non-coplanar, orbits.  相似文献   

13.
At the hundredth anniversary of the Tunguska event in Siberia it is appropriate to discuss measures to avoid such occurrences in the future. Recent discussions about detecting, tracking, cataloguing, and characterizing near-Earth objects (NEOs) center on objects larger than about 140 m in size. However, objects smaller than 100 m are more frequent and can cause significant regional destruction of civil infrastructures and population centers. The cosmic object responsible for the Tunguska event provides a graphic example: although it is thought to have been only about 50 to 60 m in size, it devastated an area of about 2000 km2. Ongoing surveys aimed at early detection of a potentially hazardous object (PHO: asteroid or comet nucleus that approaches the Earth’s orbit within 0.05 AU) are only a first step toward applying countermeasures to prevent an impact on Earth. Because “early” may mean only a few weeks or days in the case of a Tunguska-sized object or a longperiod comet, deflecting the object by changing its orbit is beyond the means of current technology, and destruction and dispersal of its fragments may be the only reasonable solution. Highly capable countermeasures- always at the ready—are essential to defending against an object with such short warning time, and therefore short reaction time between discovery and impending impact. We present an outline for a comprehensive plan for countermeasures that includes smaller (Tunguska-sized) objects and long-period comets, focuses on short warning times, uses non-nuclear methods (e.g., hyper-velocity impactor devices and conventional explosives) whenever possible, uses nuclear munitions only when needed, and launches from the ground. The plan calls for international collaboration for action against a truly global threat.  相似文献   

14.
双行根数(Two Line Element, TLE)作为一类广泛使用的空间物体编目数据, 其预报精度和误差特性是TLE编目 在空间碎片研究中所要关注的问题之一. TLE编目需要配合SGP4/SDP4 (Simplified General Perturbations 4/Simplified Deep Space 4)模型进行轨道预报, 对深空物体来说, 主要考虑带谐项$J_2$、$J_3$、$J_4$摄动、 第三体日月摄动和特殊轨道共振问题修正等. 其中, SGP4/SDP4模型第三体摄动计算时, 对日月轨道近似采用了长期进动根数和 简单平运动的方式, 在外推10d时存在约2$^\circ$--3${^\circ  相似文献   

15.
Laplace’s method is a standard for the calculation of a preliminary orbit. Certain modifications, briefly summarized, enhance its efficacy. At least one differential correction is recommended, and sometimes becomes essential, to increase the accuracy of the computed orbital elements. Difficult problems, lack of convergence of the differential corrections, for example, can be handled by total least squares or ridge regression. The differential corrections represent more than just getting better agreement with the observations, but a means by which a satisfactory orbit can be calculated. The method is applied to three examples of differing difficulty: to calculate a preliminary orbit of Comet 122/P de Vico from 59 observations made during five days in 1995; a more difficult calculation of a possible new object with a poor distribution of observations; Herget’s method fails for this example; and finally a really difficult object, the Amor type minor planet 1982 DV (3288 Seleucus). For this last object use of L1 regression becomes essential to calculate a preliminary orbit. For this orbit Laplace’s method compares favorably with Gauss’s.  相似文献   

16.
The problem of the motion of a string attached to a satellite on a circular orbit, as treated by Singh and Demin, is reconsidered. In their paper they discuss problems of uniqueness and stability. In particular the radial equilibrium positions were found to be unstable in a certain sense. In the present paper it is shown that: (i) with the stability definition used by Singh and Demin the equilibrium of a string hanging in a uniform gravity field would also be unstable; (ii) a definition of stability more appropriate for continuous systems would establish the stability of the string both in orbit and in a uniform gravity field.The results reported in this note were obtained during a stay at Stanford University sponsored by the Volkswagen Foundation, Hannover, Germany.  相似文献   

17.
The object P/2010 TO20 LINEAR-Grauer, discovered at a heliocentric distance of over 5 AU, and at first classified as a Trojan, is now believed to be a comet. This paper reports special observations of the object that have allowed a significant refinement of its orbit and investigation of its dynamic evolution. It is shown that P/2010 TO20 LINEAR-Grauer is not a Trojan yet demonstrates unusual dynamic features. In particular, the object moves in a temporary satellite orbit relative to Jupiter over the observation interval. The comet has been in the Hill sphere for about two years and has made one revolution around the planet. The jovicentric distance function has two minima, and the smallest distance is 0.075 AU. Our estimates show that, with a probability of 0.76, the comet is likely to move in a Jupiter family orbit with a perihelion distance of less than 2.5 AU. The average time for such a transition is around forty thousand years.  相似文献   

18.
The properties of images of rings in Kerr geometry in each order are examined, showing that there are two principally different image types, depending on whether the extended emitting object has surface elements with larger declination relative to the equatorial plane than does the observer. In this case, the assumption of infinitesimal thinness of the emitting object as used for the general relativistic flux transformation until now, is an invalid approximation. Local images of a vertically extended accretion disc as seen by different observers are presented. They demonstrate the importance to take into account the first indirect image as well.  相似文献   

19.
We evaluate the asteroid impact risk from the discovery night onwards using six-dimensional statistical orbit computation techniques to examine the a posteriori probability density of the orbital elements. Close to the discovery moment the observational data of an object are typically exiguous: the number of observations is very small and/or the covered orbital arc is very short. For such data, the covariance matrices computed in the linear approximation (e.g., with the least-squares technique) are known to fail to describe the uncertainties in the orbital parameters. The technique of statistical ranging gives us rigorous means to assess the orbital uncertainties already on the discovery night. To examine the time evolution of orbital uncertainties, we make use of a new nonlinear Monte Carlo technique of phase-space sampling using volumes of variation, which complements the ranging technique for exiguous data and the least-squares technique for extensive observational data. We apply the statistical techniques to the near-Earth Asteroid 2004 AS1, which grabbed the attention of asteroid scientists because, for one day, it posed the highest and most immediate impact risk so far recorded. We take this extreme case to illustrate the ambiguities in the impact risk assessment for short arcs. We confirm that the weighted fraction of the collision orbits at discovery was large but conclude that this was mostly due to the discordance of the discovery-night observations. This case study highlights the need to introduce a regularization in terms of an a priori probability density to secure the invariance of the probabilistic analysis especially in the nonlinear orbital inversion for short arcs. We remark that a predominant role of the a priori can give indications of the feasibility of the probabilistic interpretation, that is, how reliable the results derived from the a posteriori probability density are. Nevertheless, the strict mathematical definition of, e.g., the collision probability remains valid, and our nonlinear statistical techniques give us the means to always deduce, at the very least, order-of-magnitude-estimates for the collision probability.  相似文献   

20.
Supernova (SN) 2002ap in M74 was discovered on 2002 January 29. Being one of the nearest (10 Mpc) SN events in the last decades, and spectroscopically similar to the so-called 'hypernovae' 1997ef and 1998bw, both possibly associated with gamma-ray bursts (GRBs), it is of great interest. Shortly after its discovery, we launched an intensive photometric and spectroscopic monitoring campaign of this event, and here we report the results of the first month of observations. We use our UBVRI photometry to estimate the magnitudes at, and dates of, peak brightness. Our data suggest that this object reached its peak B -band luminosity on February     . Based on its similarity to SN 1998bw, we estimate the range of possible dates for a GRB that may have been associated with SN 2002ap. We find that it may include dates outside the time frame for which all available gamma-ray data have been intensively scanned, according to recent reports. The absolute magnitude at peak brightness of SN 2002ap  ( M B =-16.9)  shows that it was significantly fainter than SN 1998bw, or normal Type Ia SNe, but similar to SN 1997ef. Our spectroscopic observations confirm that SN 2002ap is strikingly similar to SNe 1998bw and 1997ef. We briefly describe the spectral evolution of this object. To assist other observers and to stimulate theoretical models, we make our entire data set publicly available in digital form (http://wise-obs.tau.ac.il/∼avishay/local.html).  相似文献   

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