## 2. Relative motion of the nucleiA total of 124 positions of nucleus A with respect to B has been collected from the available astrometric data, covering a period of time from May 5, 1997 to Jan. 23, 1998, or 8 months. The major contributors were Gajdo et al. (1997, 1998), Sugie (1997), Yamanishi et al. (1997, 1998), and Nakamura (1997, 1998). Positional data were likewise reported by Kojima (1997), by Kobayashi (1997), by Manca and Cavagna (1997), by Holvorcem (1997), by Hergenrother and Spahr (1997), and by Pravec and arounová (1997). The maximum angular separation between the two components, about 3 arcmin, occurred in October 1997. Analysis of the positional offsets has followed the standard technique for split comets. As described by Sekanina (1982a), this iterative least-squares differential-correction orbital procedure solves for up to five separation parameters: the time of splitting, ; three components of the separation velocity, , in the cardinal directions; and the companion's relative radial nongravitational deceleration, . The separation-velocity components in the directions referred to the plane of the parent comet's heliocentric orbit are, respectively, the radial (away from the Sun), transverse, and normal velocities, , , and , in the right-handed RTN coordinate system. The deceleration is assumed to vary inversely as a square of heliocentric distance and is usually expressed in units of 10the solar gravitational acceleration. The mutual gravitational attraction of the fragment nuclei is ignored. Unless the comet experiences a grazing approach to a planet, the planetary perturbations can safely be neglected. The orbital elements by Nakano (1998), calculated for an osculating epoch of Dec. 23, 1996, have been used below, after they were precessed to equinox B1950.0. Because of the diffuse nature of the nuclear condensations, their astrometric positions are measured with a nontrivial uncertainty, usually a fraction of 1 arcsec. It is therefore necessary to prescribe a rejection cutoff for the residuals of the offsets in right ascension and declination. In this investigation, the separation parameters were computed for six assumed rejection cutoffs that vary from 1.2 arcsec down to 0.2 arcsec in steps of 0.2 arcsec. The sets of separation parameters from the orbital solutions constrained by each of the six rejection cutoffs are listed in Table 1. The apparent, expected decrease in the nominal mean residual with decreasing rejection cutoff is diagnostically meaningless. In fact, an excessively tight rejection cutoff requires that most observations be discarded (e.g., 90% for a cutoff of 0.2 arcsec), including many at either end of the time span covered, thus shortening the orbital arc to be used in the computations and leading necessarily to relatively inferior solutions. In truth, the most constraining rejection cutoff is yielded by its minimum value that is expressed in terms of the standard deviation of a fitted Gaussian distribution law.
A discriminating search criterion can appropriately be formulated
on the basis of a simple consideration that follows. Let
- c be the residual between the observed value
of a offset of nucleus A from nucleus B and its value calculated from
the chosen solution. Let be the absolute value
of an intrinsic rejection cutoff. Since the offset residuals for each
solution's output are given to 0.01 arcsec, the intrinsic
rejection cutoff equals its nominal value (as listed in
Table 1) + 0.005
arcsec. Similarly, the intrinsic number of the
offset residuals equals to , where where Since, furthermore, the squares of residuals summed up over the
a ratio (o - c) can be written in the form It can be shown that Table 2 compares the six solutions in terms of
. It is apparent that the condition
is satisfied by each of the tabulated values of
The magnitude of the nongravitational deceleration classifies
nucleus A as a typical The excellent match to the measured offsets of nucleus A is apparent from Fig. 1, which also shows the computed motion of the companion prior to its discovery. Unfortunately, the comet's appearance at the time of splitting will never be known, as the object was then only from the Sun, heading for conjunction with it on Feb. 10, 1997, 6 weeks after perihelion. In fact, the comet was not at all observed between July 18, 1996 and May 5, 1997. Even though its perihelion distance was 1.3 AU, it was never seen at heliocentric distances under 2.2 AU!
© European Southern Observatory (ESO) 1998 Online publication: September 30, 1998 |