4 Azimuths and zenith distances of the bolide trail from the video record

We used individual digitized frames for deriving azimuths and elevations of the bolide at different time instants. With reasonable precision, this was possible only for those frames, where fiducial objects of known coordinates were available. There are no stars or other celestial objects in the field of view throughout the whole video record, i.e. from frame 1 to frame 191 (we will refer to frames just only by their numbers: MET001$\equiv 1$, etc.). Thus we had to limit these computations only to the last part of the trail, where terrestrial objects are present in the field of view of the video camera. Also the beginning part of the recorded trail was calibrated using terrestrial objects in the field of view just before the start of the quick motion of the camera toward the bolide, and following then quantitatively this quick motion. The azimuths and elevations of fiducial points we used in the final calibration are given in Table 2. Their precision is around $\pm 0.1^\circ$.

We measured rectangular coordinates of the bolide main body in pixels of the digitized frames. All the frames from 1 to 191 were measured. Only main body is dealt with in this section. Also 13 fragments and the wake phenomenon were measured and results on them are presented in the last section.

  

Table 2: Azimuths and elevations of fiducial points used for calibration of the video frames

4.1 Calibration of the end part of the video-record

Rectangular coordinates of the main body were transformed to azimuths, a, and elevations, h, by using a newly developed least squares version of the old method for positional reductions on wide field images (Ceplecha 1951, 1954a,b). Three objects define this transformation uniquely, but we rather used 4 of them as the lower limit, just to have an additional check. This seems well grounded, because terrestrial objects on the video record are visible only marginally being very close to the sensitivity limit of the camera, and thus hard to measure. This way only the frames from 147 to 176 were reduced, all with fiducial objects A, B, D, E, and some with additional object C. The resulting azimuths and elevations are given in Table 3 with their standard deviations. They were derived for "average" points (i.e. smoothed over 5 frames centered at the given frame). We used only these 6 positions (a, h) in Table 3 to define the great circle of the apparent trail of the bolide from the video frames. The resulting great circle is given by Eq. (1).  

$$\sin(164.052 - a) = -1.56256 \tan (h).$$ (1)

Standard deviation of one position in Table 3 from the average apparent trail given by Eq. (1) is $\pm 0.16^\circ$. Using the great circle defined by Eq. (1) and the measured position of the body in frame 191 (the last record of the body), we can derive the terminal point of the video recorded trail as $a=195.50^\circ$ and $h=18.46^\circ$.

  

Table 3: Azimuths and elevations of the bolide apparent trail from the video frames

4.2 Calibration of the beginning part of the video-record

The cameraman documented a students party, which took place at a wide open balcony with clear skies overhead. When he saw the bolide, he quickly and smoothly moved the camera onto the bolide and followed its motion also quite smoothly until the bolide ceased to be visible (frame 191). The camera was still in motion during the exposure time of frame 1, while frame 2 is the first with almost no smear effect, the bolide image being already nicely pointed. We have chosen position of the bolide in frame 2 and projected it (computational way) onto the frame with scenery of the student party just one frame before the camera started to move quickly to the bolide: in our system of frame numbers, this was frame no.-14. Fiducial objects F, G, H were used to derive this starting position of the camera as $a=303.3^\circ$, $h=-14.1^\circ$, using the same method as in previous section. We measured then differences proportional to the differences in azimuth and elevation, from a frame to the next frame, $\Delta a$, $\Delta h$, starting from frame -14 to frame -13, from frame -13 to frame -12, and so on until frame 2. These differences were measured relatively to terrestrial objects on frames -14 to -8, and relatively to the bolide itself on frames -4 to 2; frames -7, -6, and -5, where there were no objects to compare with, were interpolated. Having the great circle of the apparent trail as given by Eq. (1), and starting at $a=303.3^\circ$, $h=-14.1^\circ$, we added all the differences $\Delta a$, $\Delta h$, and we had to match this great circle just at frame 2. This condition defined the proportionality constant, and so defined also the position of the bolide on frame 2 as $a=264.96^\circ$, $h=32.15^\circ$. The derived motion of the camera is given in Fig. 2, where also the position of the great circle of the trajectory as defined by Eq. (1) is given.

  

Figure 2: Quick motion of the video camera from terrestrial objects (frame -14) to the bolide frame 2; a is the azimuth and h the elevation. Thick line is the bolide apparent trail as given by Eq. (1); thin line with numbered points is the camera motion; the points correspond to the position of the video camera at individual frames during the quick motion