To improve upon the trajectories from yesterday I have now actually numerically integrated some trajectories to find one that both explains the positions in Jan Hattenbach's images as well as impacting in the Broadcast Warning area. To do this I chose the first and third positions from my earlier message (http://satobs.org/seesat/Sep-2013/0183.html); this gives me the observer position and the RA and Dec. The two observations are 14s apart. By now picking a range for both these observations as a start and end point I can compute XYZ positions for them, take the difference of the two and divide by the time between them to get the velocity of the object. Numerically integrating the trajectory based on this position and velocity (treating the Earth as a point mass, no drag) gives an impact position on the Earth surface. By varying the range of the start and end point the impact point varies and some of them are within the Broadcast Warning area. Selecting only those gives the following results: Impact point r1 r2 t v lat lng 3650 km 3640 km 1620 s 5.73 km/s -9.56 3.20 3660 km 3650 km 1632 s 5.74 km/s -9.83 3.57 3670 km 3660 km 1644 s 5.75 km/s -10.10 3.93 3780 km 3780 km 1770 s 5.62 km/s -13.00 -0.81 3790 km 3790 km 1783 s 5.63 km/s -13.28 -0.45 3800 km 3800 km 1796 s 5.64 km/s -13.55 -0.09 3810 km 3810 km 1809 s 5.65 km/s -13.82 0.27 Launch point r1 r2 t v lat lng 3650 km 3640 km -436 s 5.73 km/s 27.96 -69.60 3660 km 3650 km -438 s 5.74 km/s 27.97 -69.81 3670 km 3660 km -440 s 5.75 km/s 27.98 -70.01 3780 km 3780 km -396 s 5.62 km/s 28.37 -66.95 3790 km 3790 km -398 s 5.63 km/s 28.39 -67.15 3800 km 3800 km -399 s 5.64 km/s 28.38 -67.30 3810 km 3810 km -401 s 5.65 km/s 28.40 -67.50 The columns here give the range of the start and end point, the time of flight from the start point until impact, the velocity at the start point and the latitude and longitude of the impact point in degrees. The first set of rows gives the impact point by integrating forward in time, the second set of rows gives the impact point when integrating backward in time, which estimates the point from where the object was launched. By adding the time of flight of both segments the total time of flight is found. Now the big caveat is that this model only computes a ballistic trajectory and does not treat the drag during reentry nor model the boost phase during launch. However, to first order it should be representative of the actual trajectory flown. It confirms that trajectories can be found that explain both the object in the images in Jan Hattenbach's images and impact the Broadcast Warning area. It is comforting that the velocity is below but near the reported maximum velocity of 6000 m/s and that all launch points group closely to near 28 deg North and 68 deg West. I've converted the first trajectory in a kml file that can be loaded with Google-Earth: https://db.tt/siN47hhn Regards, Cees _______________________________________________ Seesat-l mailing list http://mailman.satobs.org/mailman/listinfo/seesat-l
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