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

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3. Solutions of the basic equations with constant [FORMULA] and K

These solutions for [FORMULA], [FORMULA] can be found in Pecina & Ceplecha (1983, 1984). They contain 4 parameters of unknown values to be determined from observations: [FORMULA], [FORMULA], [FORMULA], [FORMULA], i.e. initial velocity, ablation coefficient, velocity at [FORMULA], distance along the trajectory at [FORMULA], respectively. We can transform the problem of computing them from the observed distances along the trajectory as function of time into the following linear equation for small increments of these unknowns parameters

[EQUATION]

The partial derivatives in (8) can be written as closed expressions and can be found in Pecina & Ceplecha (1983, 1984).

The solution for one gross-fragmentation point, i.e. with [FORMULA], [FORMULA] before fragmentation, [FORMULA] after fragmentation, was published by Ceplecha et al. (1993), and contains 6 parameters of unknown values to be determined from observations, i.e. [FORMULA], [FORMULA], [FORMULA], [FORMULA], [FORMULA], [FORMULA]. In addition two more parameters emerge during the computational procedure, i.e. the position of the fragmentation point on the trajectory, and the relative amount of the fragmented mass, making the total number of parameters to be determined equal to 8. We can once more again convert the problem of computing these parameters into linear equation for their small increments (equations defining the partial derivatives: see Ceplecha et al. 1993) as follows:

[EQUATION]


[TABLE]

More about these two solutions and about their application to observations can be found also in Ceplecha et al. (1998).

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© European Southern Observatory (ESO) 2000

Online publication: June 5, 2000
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