2. Fitting the model for the split comets
The developed model for the split comets was shown in Paper 1 to have up to five parameters: the time of splitting, the differential nongravitational deceleration, and the three Cartesian components of the separation velocity. The deceleration is attributed to uneven effects that the sun-directed outgassing from the individual components is believed to exert on their orbital momenta, whereas the separation velocity is the result of an impulse acquired by the components in the course of their splitting.
For a split comet with two components, the model is fitted to a set of observed positional offsets between the companion, or the secondary nucleus, and the parent, or the principal (primary) nucleus. Mathematically it is unimportant which of the two components is the principal nucleus. However, since in practice only one component usually survives, it is appropriate to identify it with the principal nucleus, because it almost certainly must be by far the more massive one.
It was shown in Paper 1 that when the deceleration effects dominate, the principal nucleus is always the leading component, the secondary nucleus trailing behind, eventually along the orbit. On the other hand, when the separation-velocity effects prevail, there is no constraint on the relative positions of the components.
If a comet breaks up into more than two components, it is necessary to identify the principal nucleus and the companion of each split pair. This is accomplished by comparing the optimized solutions calculated from the sets of offsets that involve various fragment pairs. A secondary of one pair may become the principal nucleus in another pair, with a sequence of such breakups building up a complex hierarchy of fracture products.
In practice, the fitting of the multiparameter model is accomplished by applying an iterative least-squares differential-correction procedure, with an option to solve for any combination of fewer than the five unknowns in order to facilitate a reasonably rapid convergence. Consequently, 31 different variants of possible solutions are available, which is especially useful in early stages of the search for the best solution. This option also allows one to force the deceleration to be zero and thus to appraise its role in the motions of the fragments.
© European Southern Observatory (ESO) 1997
Online publication: July 8, 1998