**Orbital links between
the Marsden and between the Kracht group comets**

Several links have been found between the Marsden group comets showing orbital periods of 5.5 to 6.1 years.

C/1999 J6 = C/2004 V9 (P = 5.5 years) Marsden

C/1999 N5 = C/2005 E4 (P = 5.7 years) Marsden

C/1999 N5 = C/2005 G2 (P = 5.8 years) Marsden

C/1996 V2 = C/2002 V5 (P = 6.0 years) Sekanina and Chodas this comet should return about 2008 Nov 09 (from integration with SOLEX)

C/2000 C4 = C/2005 W1 (P = 5.8 years) Marsden

C/1999 U2 = C/2005 W5 (P = 6.1 years) Marsden

Only one link had been found for the Kracht
group comets until 2005 December:

C/2000 O3 = C/2005 W4 (P = 5.3 years) Marsden

I searched for precursors of the known Kracht
group comets in archival SOHO LASCO data and finally found (2005
December 29 and 2006 January 02) three Kracht group comets in
images of 1996 December 05 - 07. An animated GIF of the two
brighter ones (found Dec 29) is here (LASCO C3). They cross a bright solar streamer and seem
to be caught by a solar coronal mass ejection.

These three comets got official designations C/1996 X3, X4, X5.
Brian Marsden added to MPEC 2006-C49: "**R. Kracht
suggests that one or both of the Kracht-group comets C/1996 X4
and C/1996 X5 (and more questionably C/1996 X3) returned as some
or all of C/2002 S4, C/2002 S5, C/2002 S7 and C/2002 S11.**".

The orbital elements of these comets taken from the MPECs are shown here:

Designation | T | q | peri | node | incl | Source | LASCO |

C/1996 X3 | 1996 Dec 06.17 | 0.0426 | 63.68 | 51.00 | 14.78 | MPEC 2006-C49 | C2 |

C/1996 X4 | 1996 Dec 06.28 | 0.0492 | 51.86 | 50.79 | 13.70 | MPEC 2006-C49 | C2/C3 |

C/1996 X5 | 1996 Dec 06.33 | 0.0490 | 51.17 | 51.28 | 13.78 | MPEC 2006-C49 | C2/C3 |

C/2002 S4 | 2002 Sep 18.22 | 0.0484 | 50.98 | 50.81 | 13.51 | MPEC 2002-T16 | C2/C3 |

C/2002 S5 | 2002 Sep 19.33 | 0.0467 | 52.01 | 49.01 | 14.03 | MPEC 2002-T16 | C2 |

C/2002 S7 | 2002 Sep 21.06 | 0.0483 | 51.38 | 50.57 | 13.53 | MPEC 2002-T25 | C2/C3 |

C/2002 S11 | 2002 Sep 30.34 | 0.0482 | 51.84 | 50.70 | 13.68 | MPEC 2002-T75 | C2/C3 |

All comets were observed with LASCO C2, the brighter comets were also observed with LASCO C3.

The orbital elements of C/1996 X4 and C/2002 S11 are looking quite similar:

Designation | T | q | peri | node | incl |

C/1996 X4 | 1996 Dec 06.28 | 0.0492 | 51.86 | 50.79 | 13.70 |

C/2002 S11 | 2002 Sep 30.34 | 0.0482 | 51.84 | 50.70 | 13.68 |

If these are two apparitions of the same comet, then the
orbital period is close to 2118 days (5.82 years). From this, we
can derive approximate values for a (3.234), e (0.985) and Q
(6.4).

Such a comet would spent much time around aphelion close to the
orbit of Jupiter. A better comparison of the two orbits can be
made with including the perturbations induced by Jupiter and the
other planets. I integrated the orbit of C/1996 X4 to 2002 Sep 30
with SOLEX
by forcing e to an appropriate value to meet the perihelion time
of 2002 Sep 30 and got with e = 0.9847956:

Designation | T | q | peri | node | incl |

C/1996 X4 | 2002 Sep 30.34 | 0.0484 | 52.06 | 50.62 | 13.67 |

C/2002 S11 | 2002 Sep 30.34 | 0.0482 | 51.84 | 50.70 | 13.68 |

The orbital elements remain similar and the perihelion
distance of C/1996 X4 is now very close that of C/2002 S11.
Further integration of this simple link predicts the next
perihelion at 2008 July 23.0.

To show that both comets are the same, a common orbit must be
computed.

SOLEX comes with EXORB an orbit determination program from the
same author, Aldo Vitagliano. He kindly extended the MPEC import
of EXORB to accept the spacebased observations of SOHO.

The orbit of C/1996 X4 with EXORB

Starting with the orbit from MPEC 2006-C49 EXORB converges to an orbit which shows a very large residual of 129" at the last C2 observation (pixel size 12"). Excluding this observation returns an orbit for C/1996 X4, which is very close to the orbit on MPEC 2006-C49:

Designation | T | q | peri | node | incl | Source |

C/1996 X4 | 1996 Dec 06.28 | 0.0492 | 51.86 | 50.79 | 13.70 | MPEC 2006-C49 |

C/1996 X4 | 1996 Dec 06.28 | 0.0492 | 51.89 | 50.79 | 13.70 | Kracht/EXORB |

The residuals of the remaining six C2 observations are:

JD | dRA* (") | dDec (") | dAng (") |

2450423.312560 | -25.1 | -17.4 | 29.0 |

2450423.408410 | +12.0 | -08.2 | 13.8 |

2450423.454930 | -00.3 | +60.9 | 60.9 |

2450423.711870 | +12.5 | -06.7 | 13.4 |

2450423.757010 | +38.8 | -27.4 | 45.3 |

2450423.791760 | +17.2 | -29.6 | 33.6 |

The bad results in C2 seem to be caused by a lack of suitable reference stars. In 1996 most of the C2 observations were done not with the whole field of 1024 x 1024 pixel, but with a cropped field of 1024 x 512 pixel centered on the sun and showing the equatorial region around the sun with many bright coronal streamers making the identifation of reference stars difficult. From the seven C2 observations of C/1996 X4 six were made with 1024 x 512 pixel. The astrometry file shows that only 5 - 7 reference stars were used for the cropped images (a description of the format of the SOHO comet astronomy text files is here).

The residuals for C3 look normal, with a worst residual of 50" and the second worst of 34". There are 14 C3 observations, pixel size is about 55". Under these circumstances, I decided not to give a greater weight to the C2 observations but to use them with the same weight as the C3 observations.

For the next iterations, I used a constrained value of a =
3.23 and removed each time the observation with the worst
residual before the next iteration. The RMSs were 30.3",
26.7", 24.4", 22.5", 21.2". At this point,
four of the seven C2 observations were removed (and only one C3
observation), showing again that the C2 astrometry in 1996
December was very difficult to do.

The next worst observation was in C3 with an acceptable residual
of 28", so I stopped the iterations here. The resulting
orbit, compared with the orbit on MPEC 2006-C49 is shown here:

Designation | T | q | peri | node | incl | Source |

C/1996 X4 | 1996 Dec 06.28 | 0.0492 | 51.86 | 50.79 | 13.70 | MPEC 2006-C49 |

C/1996 X4 | 1996 Dec 06.28 | 0.0490 | 51.28 | 50.75 | 13.72 | Kracht/EXORB |

The orbit of C/2002 S11 with EXORB

Starting with the orbit from MPEC 2002-T75 EXORB converged (with e = 1) to an orbit in excellent agreement with the MPEC (but with RMS of 36") using all observations:

Designation | T | q | peri | node | incl | Source |

C/2002 S11 | 2002 Sep 30.34 | 0.0482 | 51.84 | 50.70 | 13.68 | MPEC 2002-T75 |

C/2002 S11 | 2002 Sep 30.34 | 0.0482 | 51.83 | 50.70 | 13.68 | Kracht/EXORB |

But again here is a problem with the C2 observations showing
very large residuals (up to 112" on JD 2452548.395900).
Conspicious is an accumulation of large residuals when the comet
entered the C2 field of view in the upper right quadrant of the
images. The astrometry
file shows that 11 reference stars were used for the first C2
image (2002 September 30 19.9050 h). No reference star is in the
upper right quadrant of the image, 3 are at lower right, 3 at
upper left and 5 at lower left! The reference star situated
closest to the comet is 364 pixel away. Essentially the same
reference stars were used for the next images. It seems that the
large residuals in C2 are due to poor astrometry.

As in the case of C/1996 X4, I decided to use all observations
with the same weight. The residuals for the C3 observations
looked again normal, with a worst residual of 47" and the
second worst of 36".

To get a better orbit I excluded first all C2 observations with residuals >50", then all C2 observations with residuals >30" and finally all C2 observations with residuals >20" (always constraining a = 3.23). The residuals of the worst C3 observations dropped to 45" and 35". The RMS of the resulting orbit is 22.4" (comparable with the RMS of the C/1996 X4 orbit: 21.2"). From the 21 C2 observations from MPEC 2002-T75 only 9 remained. The resulting orbit, compared with the orbit on MPEC 2002-T75 is shown here:

Designation | T | q | peri | node | incl | Source |

C/2002 S11 | 2002 Sep 30.34 | 0.0482 | 51.84 | 50.70 | 13.68 | MPEC 2002-T75 |

C/2002 S11 | 2002 Sep 30.34 | 0.0482 | 51.64 | 50.78 | 13.66 | Kracht/EXORB |

Linking the orbits of C/1996 X4 and C/2002 S11 with EXORB

The actual link was done with the orbit of
C/2002 S11 as the starting orbit and constraining the semimajor
axis a to match the orbit of C/1996 X4.

With a = 3.235869 the RMS dropped to a minimum of 23.7"
using all observations of C/1996 X4 and C/2002 S11, which were
left by the processes described above.

The RMS from 16 observations of C/1996 X4 is
21.2 ", the RMS from 41 observations of C/2002 S11 is
22.4" and the RMS from 57 observations from C/1996 X4 and
C/2002 S11 is 23.7". The residuals show no systematic trend in the observations of C/1996
X4 or C/2002 S11, so the identification C/1996 X4 = C/2002 S11
seems to be quite probable.

Orbital elements for the link (C/1996 X4 = C/2002 S11) together with a prediction for the next perihelion passage in 2008 are shown here:

Designation | T | q | e | peri | node | incl | epoch |

C/1996 X4 | 1996 Dec 06.28 | 0.04904 | 0.984845 | 51.289 | 50.971 | 13.682 | 2450423.5 |

C/2002 S11 | 2002 Sep 30.33 | 0.04820 | 0.985085 | 51.476 | 50.805 | 13.650 | 2452547.5 |

C/2008 Ox | 2008 Jul 22.95 | 0.04806 | 0.985127 | 52.341 | 50.004 | 13.522 | 2454669.5 |

This comet will return to perihelion in the second half of
2008 July, close to July 22/23. The exact time could be
influenced by further fragmention events.

Next, I will search for more potential 1996-2002 linkages.

Rainer Kracht, 2007 October 04

The orbit of C/1996 X5

Starting with the orbit from MPEC 2006-C49 EXORB converges to an orbit which shows a large residual of 79" at the last C2 observation (pixel size 12"). Excluding this observation returns an orbit (with RMS 16.8") for C/1996 X5, which is very close to the orbit on MPEC 2006-C49:

Designation | T | q | peri | node | incl | Source |

C/1996 X5 | 1996 Dec 06.33 | 0.0490 | 51.17 | 51.28 | 13.78 | MPEC 2006-C49 |

C/1996 X5 | 1996 Dec 06.33 | 0.0490 | 51.20 | 51.27 | 13.79 | Kracht/EXORB |

The orbit is similar to the orbit of C/1996 X4 and can also be linked with the orbit of C/2002 S11.

Linking the orbits of C/1996 X5 and C/2002 S11

With a = 3.235833 the RMS dropped to a minimum of 25.2" using all observations of C/1996 X5 and C/2002 S11, which were left by the processes described above.

The RMS from 20 observations of C/1996 X5 is
16.8 ", the RMS from 41 observations of C/2002 S11 is
22.4" and the RMS from 61 observations from C/1996 X5 and
C/2002 S11 is 25.2". The residuals show a small systematic trend in dDec of C/1996 X5, but
the identification C/1996 X5 = C/2002 S11 seems to be possible
(but it's less probable).

Orbital elements for the link (C/1996 X5 = C/2002 S11) together with a prediction for the next perihelion passage in 2008 are shown here:

Designation | T | q | e | peri | node | incl | epoch |

C/1996 X5 | 1996 Dec 06.33 | 0.04904 | 0.984845 | 51.133 | 51.074 | 13.698 | 2450423.5 |

C/2002 S11 | 2002 Sep 30.33 | 0.04820 | 0.985085 | 51.318 | 50.910 | 13.667 | 2452547.5 |

C/2008 Ox | 2008 Jul 22.89 | 0.04805 | 0.985129 | 52.182 | 50.110 | 13.538 | 2454669.5 |

The orbit of C/1996 X3

Starting with the orbit from MPEC 2006-C49 EXORB converges to a very similar orbit (RMS 31.7"):

Designation | T | q | peri | node | incl | Source |

C/1996 X3 | 1996 Dec 06.17 | 0.0426 | 63.68 | 51.00 | 14.78 | MPEC 2006-C49 |

C/1996 X3 | 1996 Dec 06.17 | 0.0426 | 63.77 | 50.98 | 14.79 | Kracht/EXORB |

There are only six C2 observations, the first with a residual of 51.4". Removing this observation, the RMS drops to 13.0". The resulting orbit, compared with the orbit on MPEC 2006-C49 is shown here:

Designation | T | q | peri | node | incl | Source |

C/1996 X3 | 1996 Dec 06.17 | 0.0426 | 63.68 | 51.00 | 14.78 | MPEC 2006-C49 |

C/1996 X3 | 1996 Dec 06.17 | 0.0427 | 63.62 | 50.55 | 14.68 | Kracht/EXORB |

This orbit can also be linked with the orbit of C/2002 S11!

Linking the orbits of C/1996 X3 and C/2002 S11

With a = 3.236027 the RMS dropped to a minimum of 22.1" using all observations of C/1996 X3 and C/2002 S11, which were left by the processes described above.

The RMS from 5 observations of C/1996 X5 is
13.0", the RMS from 41 observations of C/2002 S11 is
22.4" and the RMS from 46 observations from C/1996 X3 and
C/2002 S11 is 22.1". The residuals show no systematic trend. The residuals of the linked
orbit are even slightly better than the residuals from the
original orbit of C/2002 S11.

Orbital elements for the link (C/1996 X3 = C/2002 S11) together
with a prediction for the next perihelion passage in 2008 are
shown here:

Designation | T | q | e | peri | node | incl | epoch |

C/1996 X3 | 1996 Dec 06.12 | 0.04904 | 0.984847 | 51.369 | 50.993 | 13.682 | 2450423.5 |

C/2002 S11 | 2002 Sep 30.33 | 0.04820 | 0.985086 | 51.558 | 50.826 | 13.650 | 2452547.5 |

C/2008 Ox | 2008 Jul 23.11 | 0.04806 | 0.985128 | 52.420 | 50.028 | 13.523 | 2454669.5 |

Rainer Kracht, 2007 October 05

While it seems difficult to identify the immediate precursor of C/2002 S11 with these results, it seems quite probable that C/2002 S11 will return to perihelion next on 2008 July 22/23 (the computed perihelion times are 2008 July 22.89/22.95/23.11).

The links C/1996 X4 = C/2002 S4 and C/1996 X4 = C/2002 S7

Next, I have linked C/1996 X4 with C/2002 S4 (residuals) and C/1996 X4 with C/2002 S7 (residuals). Orbital elements together with a prediction for the next perihelion passage in 2008 are shown here:

Designation | T | q | e | peri | node | incl | epoch |

C/1996 X4 | 1996 Dec 06.28 | 0.04916 | 0.984749 | 51.127 | 50.909 | 13.629 | 2450423.5 |

C/2002 S4 | 2002 Sep 18.22 | 0.04833 | 0.984988 | 51.308 | 50.752 | 13.599 | 2452535.5 |

C/2008 Mx | 2008 Jun 28.37 | 0.04826 | 0.985007 | 52.083 | 50.037 | 13.482 | 2454645.5 |

The predicted next perihelion passage for C/2002 S4 is 2008 June 28.

Designation | T | q | e | peri | node | incl | epoch |

C/1996 X4 | 1996 Dec 06.28 | 0.04909 | 0.984786 | 51.086 | 50.972 | 13.646 | 2450423.5 |

C/2002 S7 | 2002 Sep 21.07 | 0.04825 | 0.985025 | 51.270 | 50.812 | 13.615 | 2452538.5 |

C/2008 Nx | 2008 Jul 04.03 | 0.04817 | 0.985049 | 52.065 | 50.079 | 13.496 | 2454651.5 |

The predicted next perihelion passage for C/2002 S7 is 2008 July 03/04.

Rainer Kracht, 2007 October 06

Linking the smaller (C2 only) comets of 2002 with 1996

The link C/1996 X4 = C/2002 S5 shows a strong
trend in the residuals of C/2002 S5. The
same is true for the residuals of the link C/1996
X5 = C2002 S5.

The residuals of the link C/1996 X3 = C/2002 S5 show no such trend
(RMS 10.6"). Orbital elements together
with a prediction for the next perihelion passage in 2008 are
shown here:

Designation | T | q | e | peri | node | incl | epoch |

C/1996 X3 | 1996 Dec 06.12 | 0.04916 | 0.984756 | 51.128 | 50.979 | 13.590 | 2450423.5 |

C/2002 S5 | 2002 Sep 19.31 | 0.04833 | 0.984994 | 51.310 | 50.820 | 13.559 | 2452536.5 |

C/2008 Mx | 2008 Jun 30.70 | 0.04826 | 0.985014 | 52.091 | 50.100 | 13.442 | 2454647.5 |

The link C/1996 X4 = C/2002 Q10 shows a trend in the residuals of C/2002 Q10, which
is similar to the trend in the residuals of C/2002 S5 from the
link with C/1996 X4.

The residuals of the link C/1996
X3 = C/2002 Q10 show no such trend (RMS 11.4"). Orbital
elements together with a prediction for the next
perihelion passage in 2008 are shown here:

Designation | T | q | e | peri | node | incl | epoch |

C/1996 X3 | 1996 Dec 06.12 | 0.04912 | 0.984657 | 51.197 | 51.018 | 13.617 | 2450423.5 |

C/2002 Q10 | 2002 Aug 27.50 | 0.04830 | 0.984893 | 51.376 | 50.864 | 13.587 | 2452513.5 |

C/2008 Kx | 2008 Mai 16.21 | 0.04840 | 0.984866 | 52.019 | 50.274 | 13.487 | 2454602.5 |

The link C/1996 X4 = C/2002 Q8 shows worst residuals of 137" and 110" for C/2002 Q8. After removing these observations, the RMS of the residuals drops from 47.6" to 37.9". A slightly better result can be obtained with the link C/1996 X3 = C/2002 Q8. After removing the same two observations of C/2002 Q8 the RMS of the residuals is 33.5". Orbital elements together with a prediction for the next perihelion passage in 2008 are shown here:

Designation | T | q | e | peri | node | incl | epoch |

C/1996 X3 | 1996 Dec 06.12 | 0.04924 | 0.984612 | 50.951 | 50.818 | 13.435 | 2450423.5 |

C/2002 Q8 | 2002 Aug 25.92 | 0.04841 | 0.984849 | 51.125 | 50.668 | 13.406 | 2452511.5 |

C/2008 Jx | 2008 Mai 12.99 | 0.04850 | 0.984825 | 51.769 | 50.078 | 13.307 | 2454598.5 |

The first of the 2002 comets can be linked with the first of the1996 comets. The residuals for C/1996 X3 = C/2002 N2 look good (RMS 12.4"). Orbital elements together with a prediction for the next perihelion passage in 2008 are shown here:

Designation | T | q | e | peri | node | incl | epoch |

C/1996 X3 | 1996 Dec 06.12 | 0.04913 | 0.984423 | 51.270 | 50.998 | 13.648 | 2450423.5 |

C/2002 N2 | 2002 Jul 11.88 | 0.04834 | 0.984653 | 51.425 | 50.870 | 13.621 | 2452466.5 |

C/2008 Cx | 2008 Feb 13.02 | 0.04868 | 0.984552 | 51.909 | 50.423 | 13.537 | 2454509.5 |

A possible schedule for the Kracht group comets of 2008

Numerous orbital links can be made between the
comets of 1996 and 2002 with residuals comparable to the
residuals of the single orbits. So it seems almost certain that
they will return in 2008. Some of them could be already too faint
at their return in 2008 to be found again in the SOHO LASCO
images. Some of them could fragment further with unknown
consequences on their perihelion times.

From the work above the expected times of their next perihelion
passage are (with bold designations of C3 comets):

Designation | T |

C/2002 N2 | 2008 Feb 12/13 |

C/2002 Q8 | 2008 May 12/13 |

C/2002 Q10 | 2008 May 16 |

C/2002 S4 |
2008 Jun 28 |

C/2002 S5 | 2008 Jun 30 |

C/2002 S7 |
2008 Jul 03/04 |

C/2002 S11 |
2008 Jul 22/23 |

Rainer Kracht, 2007 October 08

News

Matthew M. Knight gave a talk about the "Recent Evolution of the Kracht Group of Comets" at the DPS meeting of the American Astronomical Society 7-12 October 2007 in Orlando, Florida (abstract). Details of his talk are not written up yet, but he agrees with my list of perihelion dates for the comets returning in 2008 in a personal mail from 2007 Nov 23.

Due to a LASCO C2 data gap on 2008 February 13 we don't know if C/2002 N2 returned as predicted.

C/2002 Q8 returned 2008 March 03 as C/2008 E4 showing that it's not directly related to the 1996 December cluster.

C/2002 S11 returned 2008 April 12/13 as C/2008 G6 showing that it's not directly related to the 1996 December cluster. It seems to be now very probable that C/1996 X3/X4/X5 have returned as 2002 S4/S5/S7.

C/2002 Q10 didn't return as predicted.

C/2002 S4 didn't return as predicted.

C/2002 S5 didn't return as predicted.

C/2002 S7 returned 2008 July 04 as C/2008 N4, but according to
the gravitational linkage the perihelion passage in 1996 was a
few hours before those of C/1996 X3, X4, X5.

Using nongravitational forces C/1996 X3 could be linked with 2002
S7 and 2008 N4!

C/2002 S4 (or C/2002 S11) returned 2008 September 06 as C/2008 R7, which was very bright - even visible in STEREO SECCHI COR2.