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*Astron. Astrophys. 357, 1115-1122 (2000)*
## 3. Solutions of the basic equations with constant and *K*
These solutions for ,
can be found in Pecina &
Ceplecha (1983, 1984). They contain 4 parameters of unknown
values to be determined from observations:
, ,
, ,
i.e. initial velocity, ablation coefficient, velocity at
, distance along the trajectory at
, 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
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
,
before fragmentation, after
fragmentation, was published by Ceplecha et al. (1993), and contains 6
parameters of unknown values to be determined from observations, i.e.
, ,
, ,
, .
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:
More about these two solutions and about their application to
observations can be found also in Ceplecha et al. (1998).
© European Southern Observatory (ESO) 2000
Online publication: June 5, 2000
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