Electronic Telegram No. 3642
Central Bureau for Astronomical Telegrams
INTERNATIONAL ASTRONOMICAL UNION
CBAT Director:  Daniel W. E. Green; Hoffman Lab 209; Harvard University;
 20 Oxford St.; Cambridge, MA  02138; U.S.A.
e-mail:  cbatiau@eps.harvard.edu (alternate cbat@iau.org)
URL http://www.cbat.eps.harvard.edu/index.html
Prepared using the Tamkin Foundation Computer Network


COMET 96P/MACHHOLZ
     Z. Sekanina, Jet Propulsion Laboratory, provides the results of his study
of this comet's splitting, based on the detection of fragment B in nineteen
SOHO/LASCO C2 images obtained during 2012 July 14.5-14.7 UT, as reported on
CBET 3631 and MPEC 2013-Q08.  Nearly 100 computer runs employing 16 of the 19
astrometric observations showed that no single "best" solution for the
separation of B from the primary nucleus A can be offered because versions of
the applied fragmentation model (Sekanina 1982, in Comets, ed. by L. L.
Wilkening; Tucson: University of Arizona Press, p. 251) with three, four, or
five parameters (fragmentation time, relative nongravtitational deceleration,
and three separation-velocity components) failed to converge to physically
plausible values.  The primary problem was with the normal component of the
separation velocity, which in such runs always exceeded 10 m/s, a limit that
was deemed unacceptable.  The search was eventually directed to solutions with
the lowest possible separation velocity by forcing its normal component to be
below 4 m/s.  The range of solutions was thus cut down substantially, with
further reduction achieved by requiring that the deceleration equal 5 x
10^{-5} the solar gravitational acceleration, an average that is close to
common values among the companions persisting over periods of at least several
years.  Extra test runs indicated, in addition, that the results were not
sensitive to the deceleration's exact value.  On these assumptions, the most
acceptable solutions were centered on mid-2008 as the probable fragmentation
time, when the comet was about 14 months past its 2007 perihelion, 4.7 AU
from the sun, and 0.4 AU below the ecliptic.  The minimum separation velocity
came out to be 4.9 m/s, with the radial, transverse, and normal components of,
respectively, -2.4 m/s (toward the sun), +3.5 m/s (in the direction of orbital
motion), and -2.5 m/s (below the orbit plane).  A wide range of such similar
solutions fitted the observations with an RMS residual of +/- 4".7.  Less
attractive solutions with gradually increasing separation velocities were
obtained for fragmentation times closer to the 2007 perihelion because of
higher orbital velocities and for those closer to aphelion because the same
separation distance between the components had to be bridged during a shorter
period of time.


NOTE: These 'Central Bureau Electronic Telegrams' are sometimes
      superseded by text appearing later in the printed IAU Circulars.

                         (C) Copyright 2013 CBAT
2013 August 30                   (CBET 3642)              Daniel W. E. Green