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Frame-to-frame standard deviations of differential centroid between asteroid and reference stars as function of the angular separation.
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Accurate astrometry is crucial for determining orbits of near-Earth-asteroids (NEAs) and therefore better tracking them. This paper reports on a demonstration of 10 mas level astrometric precision on a dozen NEAs using the Pomona College 40 inch telescope, at the JPL's Table Mountain Facility. We used the technique of synthetic tracking (ST), in wh...
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... illustrate this, we estimate the centroid positions of a bright (apparent magnitude of ∼13.2) asteroid 1983 TB, observed on 2017 December 20, at distance of ∼0.09 au from the Earth, with respect to reference stars in each of the 1 Hz frames. Figure 3 shows the frame-to-frame standard deviations of the differential centroids between stars (blue plus sign for R. A. and red dot for decl. respectively) as function of the angular distances. ...
Context 2
... "moving PSF fitting" gives a similar performance to estimates from averaging centroids estimated using individual frames. Because we're using individual short-exposure frames, the centroiding of asteroids and stars has similar performance as shown in Figure 3, and the integration down follows the inverse of square root of integration time behavior; thus, ST yields NEA astrometry with accuracy similar to that of stellar astrometry. The "moving PSF fitting" to the whole data cube is useful when the asteroid is dim because centroiding individual short- exposure frames may become too noisy to converge reliably. ...
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... ST can track both the target and stars, thus, producing more accurate astrometry than the traditional approach that has to deal with centroiding streaked objects leading to degraded precision as the rate increases (Vereš et al. 2012). We have demonstrated 10 mas level NEO accuracy using ST (Zhai et al. 2018) with typically better than 10 mas astrometric solutions. To achieve 10 mas level NEO astrometry, we found it necessary to correct the differential chromatic refraction (DCR) effect of the atmosphere to account for the wavelength dependency of air refraction. ...
... This system does not have any refractive elements, thus its field distortion is insensitive to color making astrometric calibration easier. We have used it to achieve 10 mas level NEO astrometry (Zhai et al. 2018). ...
... The framework and procedural stages of data processing have been outlined in Zhai et al. (2014). For follow-up observation data processing, Zhai et al. (2018) provides a thorough description of how to generate astrometry for observing known NEOs. Here we give an overview of the data processing, highlight how ST identifies targets, and detail in generating highly accurate astrometry by correcting the DCR effect of the atmosphere as well as accounting for accurate timing when stacking up frames. ...
Synthetic tracking (ST) has emerged as a potent technique for observing fast-moving near-Earth objects (NEOs), offering enhanced detection sensitivity and astrometric accuracy by avoiding trailing loss. This approach also empowers small telescopes to use prolonged integration times to achieve high sensitivity for NEO surveys and follow-up observations. In this study, we present the outcomes of ST observations conducted with Pomona College’s 1 m telescope at the Table Mountain Facility and JPL’s robotic telescopes at the Sierra Remote Observatory. The results showcase astrometric accuracy statistics comparable to stellar astrometry, irrespective of an object’s rate of motion, and the capability to detect faint asteroids beyond 20.5th magnitude using 11 inch telescopes. Furthermore, we detail the technical aspects of data processing, including the correction of differential chromatic refraction in the atmosphere and accurate timing for image stacking, which contribute to achieving precise astrometry. We also provide compelling examples that showcase the robustness of ST even when asteroids closely approach stars or bright satellites cause disturbances. Moreover, we illustrate the proficiency of ST in recovering NEO candidates with highly uncertain ephemerides. As a glimpse of the potential of NEO surveys utilizing small robotic telescopes with ST, we present significant statistics from our NEO survey conducted for testing purposes. These findings underscore the promise and effectiveness of ST as a powerful tool for observing fast-moving NEOs, offering valuable insights into their trajectories and characteristics. Overall, the adoption of ST stands to revolutionize fast-moving NEO observations for planetary defense and studying these celestial bodies.
... Shao et al. ( 2014 ) developed the technique of synthetic tracking to obtain accurate positions for NEAs. Later, Zhai et al. ( 2018 ) reported the precision can reach the level of 10 mas using this technique. Moreo v er, the CCD distortion influences the astrometry of asteroids (Peng et al. 2012 ;Wang et al. 2015 ), which should be also taken account. ...
The release of Gaia catalog is revolutionary to the astronomy of solar system objects. After some effects such as atmospheric refraction and CCD geometric distortion have been taken into account, the astrometric precision for ground-based telescopes can reach the level of tens of milli-arcseconds. If an object approaches a reference star in a small relative angular distance (less than 100 arcseconds), which is called close approach event in this work, the relative positional precision between the object and reference star will be further improved since the systematic effects of atmospheric turbulence and local telescope optics can be reduced. To obtain the precise position of a main-belt asteroid in an close approach event, a second-order angular velocity model with time is supposed in the sky plane. By fitting the relationship between the relative angular distance and observed time, we can derive the time of maximum approximation and calculate the corresponding position of the asteroid. In practice, 5 nights’ CCD observations including 15 close approach events of main-belt asteroid (702) Alauda are taken for testing by the 1m telescope at Yunnan Observatory, China. Compared with conventional solutions, our results show that the positional precision significantly improves, which reaches better than 4 milli-arcseconds, and 1 milli-arcsecond in the best case when referenced for JPL ephemeris in both right ascension and declination.
... 亮度暗指绝大多数近地小行星的可观测能量暗 弱 [17] . 以50 m目标为例, 平均绝对星等约为24等, 当前 绝大部分地基监测设备均无法在1个天文单位(约1.5亿 千米)距离探测. ...
... When not limited by photon noises, our NEO astrometry using ST has an accuracy of 10-20 mas. We have used images taken by an Andor's Zyla 5.5 CMOS camera on the Pomona College's 40 inch telescope to achieve 10 mas NEO astrometry comparable with the accuracy of stellar astrometry (Zhai et al. 2018). Note that this accuracy does not degrade with the increase of the rate of the motion, very suitable for observing NEOs at the closest approach. ...
Near-Earth Object (NEO) initial orbit determination typically uses astrometric measurements during a close approach over a time window much shorter than the orbital period of the NEO. The initial orbit is only weakly determined with dominant uncertainties in the distance of the NEO from the Earth. Topocentric astrometric measurements allow us to estimate NEO distances using observed nonlinear motions of the NEOs relative to observers, which come from the relative orbital motion of the NEOs to the Earth plus the topocentric parallax (parallax) from the diversity of observatory locations relative to the Earth center. We calculate the ratio of the contributions to the nonlinear motion from the relative orbital motion and the parallax to be approximately ( T Δ/(day au)) ² , where T is the arc length measured in days and Δ is the distance of close approach. The dominant nonlinear motion for ranging the NEO comes from the relative orbital motion of the NEO to the Earth center, due to mainly the differential solar gravitational acceleration, when T Δ ≳ 1 day au and the parallax when T Δ ≲ 1 day au. This is confirmed by simulation data and supported by observational data of real NEOs. In the regime T Δ ≲ 1 day au, the orbit determination uncertainties are inversely proportional to the amplitude of the parallax. Introducing diversities of hour angles and observatory latitudes (especially alternating between extreme values) into scheduled follow-up observations can improve the parallax amplitude, thus the orbit accuracy. Most of the newly discovered NEOs are in this regime, we recommend optimizing parallax by properly scheduling observations when the NEO is very close to the Earth and using synthetic tracking to improve astrometry accuracy for initial orbit determination.
... Using the traditional long-exposure methods to observe fastmoving faint and small objects, such as fixed star tacking mode or moving object tracking mode (Ryan & Ryan 2008;Zhang & Zhang 2019), we obtain the streaked images of targets that affect the accuracy of the astrometry. Many method are available to avoid streaks in a single image, such as the "shiftand-stack" technique for tracking Kuiper Belt objects (Tyson et al. 1992;Bernstein et al. 2004), and the synthetic tracking technique for searching NEOs Zhai et al. 2014Zhai et al. , 2018Zhai et al. , 2020. Image fusion is to superimpose multiple images into an image, in which the information complementarity, temporal, and spatial correlation in different images are used, the superimposed image contains more comprehensive and detailed information than original images. ...
The precise astrometric observation of small near-Earth objects (NEOs) is an important observational research topic in the astrometric discipline, which greatly promotes multidisciplinary research, such as the origin and evolution of the solar system, the detection and early warning of small NEOs, and deep-space navigation. The characteristics of small NEOs, such as faintness and fast moving speed, restrict the accuracy and precision of their astrometric observations. In the paper, we present a method to improve the accurate and precise astrometric positions of NEOs based on image fusion technique. The noise analysis and astrometric test from the observed images of the open cluster M23 are given. Using the image fusion technique, we obtain the sets of superimposed images and original images containing reference stars and moving targets, respectively. The final fused image set includes background stars with high signal-to-noise ratios and ideal NEO images simultaneously and avoids the saturation of background stars. Using the fused images, we can reduce the influence of telescope tracking and NEO ephemeris errors on astrometric observations, and our results indicate that the accuracy and precision of NEO Eros astrometry are improved obviously after we choose suitable image fuse mode.
... Many method are available to avoid streaks in a single image, such as the "shift-and-stack" technique for tracking Kuiper Belt objects (Tyson et al. 1992;Bernstein et al. 2004), and the synthetic zhyg@ynao.ac.cn jcwang@ynao.ac.cn * Released on 2021 October 29, and this manuscript has been accepted by AJ. arXiv:2111.01494v1 [astro-ph.IM] 2 Nov 2021 tracking technique for searching NEOs Zhai et al. 2014Zhai et al. , 2018Zhai et al. , 2020. Image fusion is to superimpose multiple images into an image, in which the information complementarity, temporal, and spatial correlation in different images are used, the superimposed image contains more comprehensive and detailed information than original images. ...
The precise astrometric observation of small near-Earth objects (NEOs) is an important observational research topic in the astrometric discipline, which greatly promotes multidisciplinary research, such as the origin and evolution of the solar system, the detection and early warning of small NEOs, and deep-space navigation. The characteristics of small NEOs, such as faintness and fast moving speed, restrict the accuracy and precision of their astrometric observations. In the paper, we present a method to improve the accurate and precise astrometric positions of NEOs based on image fusion technique. The noise analysis and astrometric test from the observed images of the open cluster M23 are given. Using the image fusion technique, we obtain the sets of superimposed images and original images containing reference stars and moving targets respectively. The final fused image set includes background stars with high signal-to-noise ratios and ideal NEO images simultaneously and avoids the saturation of background stars. Using the fused images, we can reduce the influence of telescope tracking and NEO ephemeris errors on astrometric observations, and our results indicate that the accuracy and precision of NEO Eros astrometry are improved obviously after we choose suitable image fuse mode.
... Although GD can be expressed by a high-order polynomial if there are sufficient Gaia stars in the field of view (FOV), a GD pattern of the CCD camera in a certain time is still desirable. For example, when performing Synthetic Tracking (Zhai et al. 2018) for detecting and tracking near-Earth objects (NEO), it is convenient and timesaving to transform the pixel positions to the distortionfree positions by utilizing GD solution, instead of building a high order distortion model (Equations 3 and 4 in Zhai et al. 2018). ...
... Although GD can be expressed by a high-order polynomial if there are sufficient Gaia stars in the field of view (FOV), a GD pattern of the CCD camera in a certain time is still desirable. For example, when performing Synthetic Tracking (Zhai et al. 2018) for detecting and tracking near-Earth objects (NEO), it is convenient and timesaving to transform the pixel positions to the distortionfree positions by utilizing GD solution, instead of building a high order distortion model (Equations 3 and 4 in Zhai et al. 2018). ...
Gaia Data Release 2 (Gaia DR2) provides high accuracy and precision astrometric parameters (position, parallax, and proper motion) for more than 1 billion sources and is revolutionizing astrometry. For a fast-moving target such as an asteroid, with many stars in the field of view that are brighter than the faint limit magnitude of Gaia (21 Gmag), its measurement accuracy and precision can be greatly improved by taking advantage of Gaia reference stars. However, if we want to study the relative motions of cluster members, we could cross-match them in different epochs based on pixel positions. For both types of targets, the determination of optical field-angle distortion or called geometric distortion (GD) in this paper is important for image calibration especially when there are few reference stars to build a high-order plate model. For the former, the GD solution can be derived based on the astrometric catalogue's position, while for the latter, a reference system called 'master frame' is constructed from these observations in pixel coordinates, and then the GD solution is derived. But, are the two GD solutions in agreement with each other? In this paper, two types of GD solutions, which are derived either from the Gaia DR2 catalogue or from the self-constructed master frame, are applied respectively for the observations taken by 1-m telescope at Yunnan Observatory. It is found that two GD solutions enable the precision to achieve a comparable level (~10 mas) but their GD patterns are different. Synthetic distorted positions are generated for further investigation into the discrepancy between the two GD solutions. We aim to find the correlation and distinction between the two types of GD solutions and their applicability in high precision astrometry.
... ). High dynamic range synthetic tracking (ST) offers a means of avoiding the streak limit in asteroid surveys, and of substantially improving the detectability of small fast-moving bodies (Zhai et al. 2018); our analysis suggests that these surveys should try to accommodate as high an incoming velocity as possible, ideally up to hundreds of km s −1 . ...
1I/'Oumuamua (or 1I) and 2I/Borisov (or 2I), the first InterStellar Objects (ISOs) discovered passing through the solar system, have opened up entirely new areas of exobody research. Finding additional ISOs and planning missions to intercept or rendezvous with these bodies will greatly benefit from knowledge of their likely orbits and arrival rates. Here, we use the local velocity distribution of stars from the Gaia Early Data Release 3 Catalogue of Nearby Stars and a standard gravitational focusing model to predict the velocity dependent flux of ISOs entering the solar system. With an 1I-type ISO number density of $\sim$0.1 AU$^{-3}$, we predict that a total of $\sim$6.9 such objects per year should pass within 1 AU of the Sun. There will be a fairly large high-velocity tail to this flux, with half of the incoming ISOs predicted to have a velocity at infinity, v$_{\infty}$, $>$ 40 km s$^{-1}$. Our model predicts that $\sim$92\% of incoming ISOs will be residents of the galactic thin disk, $\sim$6\% ($\sim$4 per decade) will be from the thick disk, $\sim$1 per decade will be from the halo and at most $\sim$3 per century will be unbound objects, ejected from our galaxy or entering the Milky Way from another galaxy. The rate of ISOs with very low v$_{\infty}$ $\lesssim$ 1.5 km s$^{-1}$ is so low in our model that any incoming very low velocity ISOs are likely to be previously lost solar system objects. Finally, we estimate a cometary ISO number density of $\sim$7 $\times$ 10$^{-5}$ AU$^{-3}$ for 2I type ISOs, leading to discovery rates for these objects possibly approaching once per decade with future telescopic surveys.
... It is bright enough to be detected as a streak as shown in the right plot in Figure 4 even with the trailing loss when coadding all the 133 frames to simulate an integration of about 1.5 hr for ZTF tracking the sidereal. Although this can be detected as a streak (blue line) in the co-added images, for accurate astrometry, the whole data cube is needed to take the advantage of ST (Zhai et al. 2018). Similarly, Figure 5 displays another main belt asteroid of magnitude of 20.8, whose signals only show in three sub-data cubes because it ran into a masked region due to a bright star. ...
... Note that ST enables to perform follow-up observations of multiple objects in a field conveniently because there is no need to track individual objects during observation. Another advantage of this approach is to produce more accurate astrometry (Zhai et al. 2018). ...
The Zwicky Transit Facility (ZTF) is a powerful time domain survey telescope with a large field of view of 47 deg 2 . We apply the synthetic tracking technique to integrate a ZTF’s deep drilling data set, which consists of 133 nominal 30 s exposure frames spanning about 1.5 hr, to search for slowly moving asteroids down to approximately 23rd magnitude. We found 1168 objects from searching 40 of the 64 CCD-quadrant subfields, each of which covers a field size of about 0.73 deg 2 . While most of the objects are in the core region of the asteroid belt, there are asteroids belonging to families of Trojan, Hilda, Hungaria, Phocaea, and near-Earth-asteroids. Such an approach is effective and productive for discovering new asteroids. Here we report the data processing and results as well as discuss a potential deep drilling operation mode using this approach for survey facilities.
... It is bright enough to be detected as a streak as shown in the right plot in Fig. 4 even with the trailing loss when co-adding all the 133 frames to simulate an integration of ∼ 1.5 hours for ZTF tracking the sidereal. Even though this can -9be detected as a streak in the co-added images, for accurate astrometry, the whole datacube is needed to take the advantage of synthetic tracking (Zhai et al. 2018). Fig. 5 displays similarly another main belt asteroid of magnitude of 20.8, whose signals only show in three sub-datacubes because it ran into a masked region due to a bright star. ...
The Zwicky Transit Factory (ZTF) is a powerful time domain survey facility with a large field of view. We apply the synthetic tracking technique to integrate a ZTF's long-dwell dataset, which consists of 133 nominal 30-second exposure frames spanning about 1.5 hours, to search for slowly moving asteroids down to approximately 23rd magnitude. We found more than one thousand objects from searching 40 CCD-quadrant subfields, each of which covers a field size of $\sim$0.73 deg$^2$. While most of the objects are main belt asteroids, there are asteroids belonging to families of Trojan, Hilda, Hungaria, Phocaea, and near-Earth-asteroids. Such an approach is effective and productive. Here we report the data process and results.
