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Astron. Astrophys. 357, 1115-1122 (2000)

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6. Application of our model to precise photographic data on individual meteoroids

It is not easy to find out observational data with enough precision for application of Eq. (10) using the procedure described in the preceding section. We inspected several photographic archives of double- and multi-station meteor photographs with the aim not only to find out precise records (with geometrical precision of the trajectory better than [FORMULA] m), but also records which yielded either no solution for the gross-fragmentation model (or single-body model), or a solution with significant time dependence of residuals, or an "unrealistic" solution. From inspecting over 1000 events by using the gross-fragmentation model (mainly in European and the U.S. archives; McCrosky et al. 1976, 1977; Ceplecha & McCrosky 1997; Spurny 1997), we were able to find out 22 such cases. The results on them are summarized in Table 2. Meaning of individual symbols in Table 2 are as follows: [FORMULA] is the standard deviation for one measured point as derived by application of the gross-fragmentation model (constant [FORMULA] and K): residuals show large systematic changes with time for all meteors in Table 2. [FORMULA] is the standard deviation for one observed point according to solutions presented in this paper, i.e. with [FORMULA] and K as functions of time: these residuals are almost random with time for all meteors in Table 2. [FORMULA], [FORMULA], and [FORMULA] are velocity at the first point, velocity at the last point, and mass at the first point, respectively. Trajectory parts are denoted: B the beginning-, C the central-, and E the end-part. H stands for relatively "high" value, L stands for relatively "low" value, and V stands for "very". "dec-abl" contains the difference between the deceleration term and the ablation term (it reflects the difference of our present solution against solution with constant [FORMULA] and K. Symbol "-" means that deceleration term is less than the ablation term, symbol "+" means that the deceleration term is greater than the ablation term, and symbol "=" means that both terms are about equal.

In all computations we used CIRA 72 (1972) model of atmospheric densities using them according to the months in which the meteor was recorded. We found also several cases with precise data, which clearly exhibit large positive (and oscillating) values of [FORMULA], and cannot be explained in scope of Eqs. (1) to (7) (Fig. 10).

Because [FORMULA] cannot be computed for the beginning parts of a trajectory from observations at all, at such points we assumed average [FORMULA] value corresponding to the meteoroid type. As standard deviation of so-defined [FORMULA] value we took 50% of its value (corresponding to statistical uncertainties of the group definitions). Such average values of [FORMULA] were also used at extreme end of a trajectory in case they were not available from observations (the precision of v and [FORMULA] is also low at extreme end of a trajectory and may not be sufficient for determination of [FORMULA]). We defined [FORMULA] as corresponding to the meteoroid type, and we started integration of Eq. (10) at a point, where [FORMULA] corresponded also to the meteoroid type. The numerical values used are in Table 1.


Table 1. Average values of [FORMULA] and K for different meteoroid types (groups) on assumption of [FORMULA]


Table 2. Survey of results on photographic meteors with precise data.

Publishing detailed results would need about 10 plots of different values as function of time for each case. Thus we decided to put all these plots on the Web (Ceplecha et al. 2000). As an example of our results we present data on meteoroid O 27471 in Figs. 1 to 9. In Fig. 10 we present [FORMULA] for one of the cases we found with positive and oscillating values of acceleration. There is not possible any interpretation of these [FORMULA] in the scope of our basic equations.

[FIGURE] Fig. 1. Residuals for model with constant [FORMULA] and K. Strong time dependence of residuals is evident. Horizontal lines are the average [FORMULA] m (the standard deviation for one observed value).

[FIGURE] Fig. 2. Residuals for model with [FORMULA] and K as function of time. Residuals are random with time. Standard deviation for one observed value is [FORMULA] m.

[FIGURE] Fig. 3. Velocity as function of time. Standard deviation for each value is given.

[FIGURE] Fig. 4. Deceleration as function of time. Standard deviation for each value is given.

[FIGURE] Fig. 5. Ablation coefficient as function of time. Standard deviation for each value is given.

[FIGURE] Fig. 6. Shape-density coefficient K as function of time. Standard deviation for each value is given.

[FIGURE] Fig. 7. Comparison of ablation and deceleration terms.

[FIGURE] Fig. 8. Height as function of time.

[FIGURE] Fig. 9. Mass as function of time. Standard deviation for each value is given.

[FIGURE] Fig. 10. Acceleration for meteor O 63511 shows regular oscillations outside standard deviations, and into positive values. The smooth line corresponds to solution with [FORMULA] and K constant. This solution is far from reality. Eq. (1) and procedures of this paper cannot be used for explaining the atmospheric interaction of this meteor.

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© European Southern Observatory (ESO) 2000

Online publication: June 5, 2000