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Corresponding author: S. R. Proud, Department of Geosciences and Natural Resource Management, University of Copenhagen, Oester Voldgade 10, DK-1350 Copenhagen, Denmark. (firstname.lastname@example.org)
 The large number of objects in a range of orbits around the Sun means that some will inevitably intersect the Earth, becoming a meteor. These objects are commonly comet fragments or asteroids. To determine the type of a particular meteor requires knowledge of its trajectory and orbital path that is typically estimated by using ground-based observations such as images or radar measurements. A lack of data can, however, make this difficult and create large uncertainties in the reconstructed orbit. Here I show a new method for estimating a meteor's trajectory, and hence allowing computation of the orbit, based upon measurements from satellite sensors. The meteor that fell on 15 February 2013 is used as an example and the resulting orbit is in broad agreement with estimates from other observations. This new technique represents an alternative method for trajectory determination that may be particularly useful in areas where ground-based observations are sparse.
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 The orbit of an object is described by its orbital elements and particular classes of objects will have orbital elements that, while different, display common properties such as similar semimajor axes or inclinations relative to the Sun [Shoemaker et al., 1979]. When a new object is discovered, its orbital elements can therefore be compared to the typical elements for a given class to determine its classification. For a meteor, this process is complex as the object is no longer in orbit. Instead, numerical methods must be used to solve the n-body gravitational problem backward in time to simulate a point where the object was far from the Earth and in orbit around the Sun [Whipple and Jacchie, 1957]. The initial state for this problem is usually an observed position and velocity of the meteor during its passage through the atmosphere, but because of the simulation's sensitivity to the initial state, small uncertainties can propagate to become relatively large uncertainties in the computed orbital elements. It is therefore important to gain as accurate a measurement of the meteor's path as possible [Koschny and Diaz del Rio, 2002]. Currently, there are three common techniques for determining the trajectory: Radar observations provide measurements of the range and azimuth between a ground station and the meteor, so giving the meteor's position, and the Doppler shift in the returning signal can be used to estimate speed. Multiple observations can provide accurate estimates for a meteor's trajectory [Jones et al., 2005]. However, there are many regions not covered by radar and therefore no observations will be available for a meteor if it falls such an area. An alternative approach is to analyze the low-frequency sound waves (infrasound) produced by the passage of a meteor through the atmosphere. Data from infrasound stations can be used to estimate the meteor's kinetic energy and—by using multiple microphones and several stations—helps provide data on the meteor's trajectory [Edwards, 2010; Brown et al., 2011, 2002; Silber et al., 2011]. Because stations are spread across the globe, there is a much greater chance of detecting a meteor using infrasound than by radar. There are, however, larger uncertainties in infrasound measurements and therefore the computed orbital elements will also be more uncertain, particularly as it is hard to estimate the trajectory unless combining infrasound with a secondary source of data. In many cases, this is not possible, meaning that the trajectory estimate will either be very inaccurate or entirely missing. A third approach is to use optical data from images or videos to estimate the trajectory [Betlem et al., 1998; Brown et al., 1994; Boroviĉka et al., 2003]. If two or more cameras capture images of a meteor, then the camera positions and meteor azimuth and elevation within the images can be used to triangulate the meteor's position. As with infrasound, a second set of measurements at a different time can be used to estimate the velocity. This method is attractive as it requires no specialized equipment and, in some conditions, can be based upon a significant number of source cameras. In addition to amateur camera footage, there are numerous professional camera networks that are specifically designed to capture images of objects entering the atmosphere [Oberst et al., 1998; Cooke and Moser, 2011]. These “fireball networks” are set up in numerous countries and are frequently used in meteor analysis [Kokhirova and Borovicka, 2011].
 I propose a fourth method that relies upon data from geostationary satellites that typically generate images of the Earth across multiple wavelengths—both in the visible and infrared regions of the spectrum—with a relatively frequent image capture time of between 5 and 30 min [Schmetz et al., 2002; Menzel and Purdom, 1994]. Each pixel within a satellite image is “geolocated” so that it corresponds to a particular latitude and longitude on the Earth. This is useful when analyzing the land surface but problematic when examining features at high altitude because the parallax effect means that the geolocation for these features will be incorrect: The apparent position of the feature will be shifted relative to its actual position by an amount proportional to its altitude and the angle between it and the point directly below the satellite (the subsatellite point). Parallax correction tools exist for use within meteorological analysis of satellite images that use an estimate of cloud height to correct for this shift and display the cloud at its correct location above the Earth. For a meteor trail within a satellite image, only the apparent latitude and longitude are known. The actual latitude and longitude as well as the height are unknown and cannot be computed from one observation alone. However, by using data from two or more satellites that have different subsatellite points, this can be overcome as each satellite will give a different apparent position for the meteor trail. An iterative process that tests various trail altitudes can then be used with a parallax correction method until the corrected trail location from all the satellites converges—thus providing the meteor position and altitude at a given time. Repeating this process for several different locations along the trail then allows an estimate the azimuth and slope of the meteor's path through the atmosphere. Together with an estimate of speed, this produces both the position and velocity of the meteor and allows calculation of the orbital elements. The accuracy of the position retrieved by this method will be limited by a number of factors. First, each pixel within the satellite image will have a discrete size—meaning that it will not be possible to estimate the position of the meteor to an accuracy greater than that of the pixel size. Second, the geolocation applied to an image is not exact and there is a small uncertainty in the latitude and longitude associated with a given pixel. This is typically smaller than the pixel size, though.
 To test the validity of this new method, I computed the trajectory and orbital elements of the meteor that was seen over Chelyabinsk, Russia, on 15 February 2013. This meteor has been extensively documented within the media and attempts have been made to calculate its properties from both ground-based observations[Zuluaga et al., 2013; Borovicka et al., 2013] and space-based sensors (e.g., http://neo.jpl.nasa.gov/fireballs/). The trail produced by the meteor is clearly visible within images captured by all three of the Meteosat Second Generation (MSG) series of satellites [Schmetz et al., 2002], shown in Figure 1. These satellites all carry the same sensor, SEVIRI [Aminou, 2002], and produce one image of the Earth every 15 min. All three satellites are located above the equator, with MSG-1 positioned at 4.5°E, MSG-2 at 9.5°E, and MSG-3 at 0.0°E. Two clearly identifiable points on the meteor trail were picked out in these images and used for determining the position of the meteor with the parallax correction method. Before analyzing these points, the effect of the wind upon the trail location was accounted for: There was a delay of approximately 5 min between the meteor trail forming and the MSG image scan time. Over this time, the trail will be blown by the wind and this must be corrected in order to retrieve the true location of the trail. Here I used numerical weather predictions from the European Centre for Medium-Range Weather Forecasting to estimate the high-altitude wind. At both points, the cloud velocity vector due to wind was 109.9° at 13.51 m s−1and the meteor trail will therefore have moved by 4 km to the ESE in the time before the image scan. The raw image coordinates were therefore updated to negate this movement. The meteor trajectory can therefore be defined by an azimuth of and a slope of . The first point is located at 54.57±0.03°N, 62.66±0.03°E and the altitude was calculated to be 59.0±0.2 km. The second point is 54.65±0.02°N, 61.98±0.04°E with an altitude of 47.3±0.3 km. The uncertainties in latitude and longitude are calculated from the known uncertainty in the MSG pixel geolocation and pixel size. The altitude uncertainties are found from the range of altitudes that produced a corrected location within the bounds of the pixel uncertainties. One farther pixel on the trail was also analyzed but was at lower altitude (24 km) and less clearly defined between the images. This resulted in an uncertainty in the altitude of almost 1.5 km, and therefore this pixel was not used within the trajectory calculation. By using an estimate of the meteor's velocity, 17.6 km s−1, that is taken from an average of NASA's summary of the meteor and the two visual documentations [Zuluaga et al., 2013; Borovicka et al., 2013]—together with the two locations listed above the meteor-position and velocity vectors were calculated and used as an initial state for the n-body numerical integrator used to estimate the meteor's orbit. For this integration, I used the “sparvm” package [Atreya and Christou, 2007] in conjunction with the Jet Propulsion Laboratory SPICE software [Acton, 1996]. The final orbital elements are listed in Table 1 along with orbital elements computed by other groups based upon observations from the ground. Alternative elements bounded by the extreme minimum and maximum trajectories produced from the uncertainties in the meteor position and speed (minimum speed 17 km s−1, maximum 18.6 km s−1) are also listed.
Table 1. The Orbital Elements of the Chelyabinsk Meteor as Computed by the Parallax Method and Two Other Methods That Used Ground-Based Observationsa
The MSG minimum and maximum bounds give the largest deviations in the orbital elements that are possible based upon the uncertainties in the meteor position and velocity. The columns in the table give the semimajor axis (SMa), eccentricity (Ecc), inclination (Inc), longitude of ascending node (LAN), and argument of periapsis (APe), respectively.
 Overall, there is a good agreement between the orbital elements produced from the new method presented here and the other methods. Some differences do exist, though. I estimate a semimajor axis that is approximately 0.02 AU larger than the average of the alternative methods, something that could be due to uncertainty in the speed estimate due to factors such as atmospheric drag acting upon the meteor. I also calculate a slightly different inclination of the orbit, most likely due to uncertainties in both the exact position of the meteor and its speed. Lastly, the value calculated here for the argument of periapsis is significantly different (approximately 12°) from that found by Borovicka et al.  but closely matches that found by Zuluaga et al. . It should be noted that both the Borovicka et al.  and Zuluaga et al.  results are preliminary and may be revised in the future. This could account for some of the differences in the orbital elements between each method. Despite these differences, the parallax method of computing a meteor trajectory appears successful and shows promise for future meteor events. Here I have only used data from satellites that are relatively close together—the maximum separation of longitude is 9.5°—and therefore it is likely that the method would be more accurate if data from a wider separation of satellites are used, China's Fengyun 2D [Jin et al., 2010] is a possible candidate, for example. In this study, I have also not accounted for atmospheric effects upon the satellite measurements. As light reflected by the meteor trail passes through the atmosphere to the satellite, it will be scattered by particles within the atmosphere—possibly leading to a further uncertainty in the trail position. Because of the low atmospheric density, this effect will be small at high altitudes but will be more significant when the trail is closer to the ground [Proud et al., 2010]. This was the case for the third pixel analyzed here that was not used for the trajectory reconstruction. While I have focused in this study upon the use of the parallax method in determining the location of a meteor trail, it is also possible to use the method to compute the altitude and position of water or ice clouds, particularly those at high altitude. This method could therefore also find use within meteorology as an alternative method of cloud height estimation. Lastly, although I have considered the parallax, infrasound, radar, and visual determination methods separately, it is possible to combine them when forming the meteor trajectory. This should be investigated to establish if it will result in a more accurate trajectory than using one method alone. Furthermore, there are several possibilities for increasing the accuracy of the method described here. For instance, including an estimate of atmospheric drag in the calculation of the meteor trajectory would result in more accurate orbital elements (particularly the semimajor axis). Another addition would be to use the capability of geostationary satellites to produce frequent repeat images to analyze the wind speed and direction: By calculating the motion of the meteor trail between two subsequent images, it will be possible to estimate the effect of the wind upon the trail. This will allow for a more accurate correction of the wind-induced motion between trail formation and image capture, hence reducing the uncertainty in the meteor trajectory.
 In this short paper, I have demonstrated how the parallax method can be used to transform multiple images of a meteor trail into an estimate of its trajectory and hence, by using an external estimate of velocity, its orbital elements. The retrieved orbital elements are similar to those retrieved from other sources and this gives confidence that the method is both useful and accurate. Some uncertainties do exist, though, and by correcting for effects such as atmospheric scattering and differential high-altitude winds, it may be possible to further improve the retrieved elements. Because of the location of the meteor trail, I have used data from the MSG satellites here, but in the case of future meteor events, there is no reason why, if they occur elsewhere in the world, the method would not be successful with data from other geostationary satellites such as GOES or MTSAT. Polar-orbiting sensors may also be useful, particularly as they are capable of producing images at a higher-spatial resolution, but their utility is limited by the less frequent revisit time—meaning that a polar satellite is less likely to image a meteor than a Geosat.
 The author wishes to thank EUMETSAT for their assistance in providing the Level 1.0 SEVIRI data and assisting in geolocating the images. The author also wishes to thank Radoslaw Guzinski for his thoughts on parallax correction of MSG images. The research presented in this paper was funded by the Danish Council for Independent Research | Natural Sciences.
 The Editor thanks an anonymous reviewer for assistance in evaluating this paper.