## 4. Nongravitational motion of comet 43P/Wolf-HarringtonThe orbital motion of the comet has been investigated based on astrometric observations made during its nine observable apparitions from 1924 to 1998. The total number of the collected observations amounted to 415. From the last return of the comet to the Sun, 212 observations are available. For this dominated apparition the numbers of observations were decreased by taking into account so called normal places i.e. if more than two observations were made at the same day, they were replaced by one average comet position. For each apparition the observations were selected separately according to the mathematically objective criteria elaborated by Bielicki (Bielicki & Sitarski 1991). The mean residuals for each apparition have been calculated. The results from every apparitions have been combined and the "a priori" mean residual of , representing accuracy of the whole observational set, was obtained. Global characteristics of the observations are given in Table 1.
## 4.1. Symmetrical modelsThe reasonably linkage of all astrometric observations of the comet 43P/Wolf-Harrington was impossible using the standard Marsden's model. This model was explicitly inconsistent with the real motion of the comet giving the mean residual . To examine temporal variations of the nongravitational effects the constant nongravitational parameters have been determined for each three successive observable apparitions. Values of parameters for such observational intervals are listed in Table 2. The first interval of time has spanned six real apparitions of the comet because it was not observed during its three succesive returns to the Sun after 1924. A particular behaviour of the parametr connected with the transverse component of the nongravitational force should be noticed. The nongravitational acceleration was slowly decreasing over a long period of time from 1924 to 1978 and then felt down reaching a small value close to zero. It is interesting to see that the acceleration did not switched into deceleration after the 1984 apparition but it started to increase. The parameter is very poorly determined for almost all intervals of time.
An employment of the model (see Sect. 2) in which
are expressed in terms of angular
parameters ,
## 4.2. Asymmetrical modelAsymmetrical model of the nongravitational acceleration understood as a perihelion shift of the function (see Sect. 2) provided a much better orbital solution than the standard model. The orbital linkage of all comet's apparitions with the mean residual equal to was obtained. However, it was necessary to introduce a linear variation of two parameters: the describing the time shift of with respect to the perihelion and the angle connected with the comet's orientation. According to this orbital fit the function reached peak 23 days before perihelion passage in 1925 and due to the linear evolution its maximum occured about 57 days after perihelion of the 1997 apparition. Linear variations of parameters remarkably limit the physical meaning of the model especially for the prediction of the future orbit. To study a behaviour of the perihelion shift of in shorter intervals of time, the asymmetric model was applied for each four successively observable apparitions of the comet. In Table 4, the values of and in the appropriate observational intervals are presented. The last interval includes only three apparitions, because of difficulty in linking of the observations from 1977 to 1998. One can see that a form of variations is different than that for the symmetrical model. The maximum of the function significantly peaks before perihelion passages for the comet's returns until the 1972. Then the acceleration decreases and the parameter reaches positive values. The second change of takes place after the 1991 apparition and the maximum of is shifted again before perihelion. Nonlinear variations of explain the poor accuracy of the orbital linkage of all comet's observations where the linear change of was assumed. However, a general evolution of the shift of the maximum cometary activity, from negative to positive number of days in consecutive returns of the comet, has been confirmed.
## 4.3. Forced precession modelThe analysis of the nongravitational parameters determined as
constant values within sets of three or four consecutive apparitions
has shown long-term variations of the nongravitational perturbations
in the orbital motion of Comet Wolf-Harrington. One of the posssible
explanation of these temporal variations could be forced precession of
a rotating nonspherical cometary nucleus. Therefore the orbital
version of the forced precession model (see Sect. 2) was applied.
The model has been preliminary employed to link all of the comet
apparitions (Krolikowska et al. 1998a), where the last return was
represented by observations made only till December 1997. Values of
six model parameters has been found for a prolate spheroid nucleus of
the comet. The comparison of the mean residual of that orbital
solution which reached with the `a
priori' residual of indicated that
the forced precession model needs some additional parameters to give
better approximation to the real motion of the comet. As it follows
from Table 2 the nongravitational perturbations exibit some
irregular behaviour represented by unexpected changes not only in
but in
, too. Time shift of the function
described by
can be determined together with the
basic parameters of the forced precession model. To model
discontinuities in the nongravitational motion of the comet changes of
values of close to the selected
moments of aphelion passage has been assumed. After some numerical
calculations two moments of discontinuities in 1975 and in 1988 has
been established. The model parameters:
Based on discontinuities in the nongravitational perturbations the comet 43P/Wolf-Harrington may be classified as an "erratic" comet. Its orbital motion was compared with that of five comets which exhibit strongly variable nongravitational effects (Krolikowska et al. 1999, 2000). The satisfactory precessional models were found for all of these comets. ## 4.4. Spotty nucleus modelTime dependent shifts of a maximum activity seem to play essential
role in the nongravitational motion of the comet Wolf-Harrington.
Attemps to model the nongravitational acceleration as a result of the
outgassing from one emission source which is active in the same degree
over the whole interval motion of the comet 43P/Wolf-Harrington, have
not been successful even taking into account a linear precession of
the spin axis. Extensive numerical experiments with using a model of
the spotty-nucleus described in Sect. 3, allowed to ascertain
that processes of activation and/or deactivation of emission sources
on the nucleus surface took place at least three times. From numerical
fitting of the model parameters to positional observations, the lag
angle, , the orientation of the
nucleus in space described by the angles
In both cases the first region ( Taking into account that the activation of new regions could
disturb the nucleus spin axis, the orbital programme was run to search
for the possible change of the angles In Fig. 2 variations of three orbital components of the nongravitational acceleration during the whole investigated period of the comet's motion resulting from the Model A are shown. One easily recognizes that in the case of the forced precession model the component is always negative or close to zero, whereas for the spotty - nucleus model is strongly variable near perihelions and reaches either positive and negative values. © European Southern Observatory (ESO) 2000 Online publication: December 5, 2000 |