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

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4. General solution of the basic equations with [FORMULA][FORMULA]

Eliminating mass between Eqs. (1) and (2) we arrive at

[EQUATION]

where

[FORMULA]          is the ablation term and

[FORMULA]  is the deceleration term.

Here [FORMULA] means natural logarithm. If the ablation term is identically (for all time instants) equal to the deceleration term, then K = constant.

Eq. (10) and [FORMULA] represent a complete solution. Similar numerical procedure as for the case with constant [FORMULA] and K can be applied to fit the computed distances along the trajectory to the observed distances, except that the partial derivatives cannot be written in a close form and have to be computed by numerical procedures only.

Eq. (10) contains two unknown functions [FORMULA], [FORMULA]. Assuming one of them, the other is resulting from (10). If we could determine [FORMULA] as well as [FORMULA] from the observed distances, we would be able to compute [FORMULA] and then from Eq. (10) also [FORMULA]. This will be described in details in the next section.

Once we have solved Eq. (10), mass and ablation are given as

[EQUATION]

and

[EQUATION]

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© European Southern Observatory (ESO) 2000

Online publication: June 5, 2000
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