5 Atmospheric trajectory from the video-record combined with visual observations

The location of the video camera and the apparent trail given by Eq. (1) defines a plane, in which the atmospheric trajectory had to be located. Visual sightings of casual observers were necessary to derive the atmospheric trajectory in this plane. We have used a method and computer code by Borovicka (1990) to do this. Each visual observation can be checked not only against the others, but against the video recorded apparent trail, which makes the decision on what visual observations are realistic more objective. In the final reduction we have used the following visual observations of Table 1 combined with the video recorded trail from station 2: stations 1,3,4,5,6,7,8,9,10, 12,14,15,16,18,19,21,24,26,31,32,and 33.
The first observed point from station 12 was located at
$\lambda = 352.94^\circ \pm 0.05^\circ$ E, $\varphi = 41.43^\circ \pm 0.03$ N,
$h = 52.4 \pm 3.2$ km.
Video recorded frame 2 was located at
$\lambda = 352.20^\circ \pm 0.04^\circ$ E, $\varphi = 42.92^\circ \pm 0.03$ N,
$h = 38.9 \pm 3.0$ km.
The last point observed (video recorded frame 191) was located at
$\lambda = 351.78^\circ \pm 0.04^\circ$ E, $\varphi = 43.72^\circ \pm 0.03$ N,
$h = 34.0 \pm 2.9$ km.
Azimuth and zenith distance of the radiant for this terminal point (frame 191) were
$a_{\rm R} = 339.0^\circ \pm 1.2^\circ$, $z_{\rm R} = 87.3^\circ \pm 1.5^\circ$,
and the right ascension and declination of the apparent radiant were
$\alpha_{\rm R}= 250.1^\circ \pm 1.5^\circ$, $\delta_{\rm R}= -39.9^\circ \pm 1.5^\circ$.

The trajectory was very shallow, almost tangential to the Earth's surface. The Earth-grazing character of the trajectory is also the main reason that there was enough time to take the video record of the bolide. On the other hand, the standard deviation of distances along the trajectory are rather high, i.e. $\pm 5.3$ km for one point. Thus also the velocities derived directly from the end part of the trajectory using distances of only about 20 km are inaccurate. This will be dealt with in the next section. Because the final data on velocity and thus also for location of individual video frames can be improved by using combination of the geometrical solution of this section. with modeling the motion, ablation (including discrete fragmentation), and luminosity of the bolide, we present also the final data on locations together with velocities in Table 4 of the next section.