PLEASE NOTE:
*
CCNet 87/2003 - 16 October 2003
NEW SNAPSHOTS OF WELSH 'FIREBALL' EVENT
---------------------------------------
(1) NEW TWIST IN WELSH 'FIREBALL' SAGA
Benny Peiser b.j.peiser@livjm.ac.uk
(2) NEW IMAGES OF WELSH 'FIREBALL' EVENT
Robert Nemiroff <nemiroff@mtu.edu>
(3) NEW SNAPS OF WELSH 'FIREBALL' EVENT
by way of Robert Nemiroff <nemiroff@mtu.edu>
(4) 'METEOR' OVER SOUTH WALES
by way of Robert Nemiroff <nemiroff@mtu.edu>
(5) A CAMBRIDGE OBSERVER OF THE WELSH 'FIREBALL' EVENT
by way of Robert Nemiroff <nemiroff@mtu.edu>
(6) HERMES IS FOUND
Roger W. Sinnott
(7) MPC ANNOUNCEMENT OF HERMES RECOVERY
MPEC 2003-774
(8) BACKGROUND INFO: EFFORTS ON 1937 UB "HERMES", A
LOST ASTEROID
Rechenzentrum Heidelberg
==========
(1) NEW TWIST IN WELSH 'FIREBALL' SAGA
Benny Peiser <b.j.peiser@livjm.ac.uk>
New digital snapshots have emerged of the 'fiery' object that was
observed in
the skies over South Wales on Sept. 24. The new images together
with an account
from an eyewitness as far away as Cambridge are posted in today's
CCNet.
The new evidence raise new questions and re-open the debate about
the nature
of the perplexing event.
As if the photos, taken by Welsh amateur photographer Gary Green,
were not baffling
enough, the account by John Lambert who says that he too observed
the 'fiery'
phenomenon from his garden in Cambridge raises doubts
whether the contrail of an airplane
flying over South Wales can be observed in far away
Cambridge, some 150 miles
to the east of Pencoed.
I have received the attached photos and comments from Robert
Nemiroff, one of the two
editors of "Astronomy Picture of the Day" (http://antwrp.gsfc.nasa.gov/apod/astropix.html).
He posted Jon Burnett's photo on the APOD website and wrote the
original text and updates.
He has asked me to circulate the new images, the accompanying
comments, and John Lambert's
comments on CCNet, stressing that they are not to be distributed
or published without
proper consent.
Robert and Jerry Bonnell are planning another update of the whole
story for the APOD
website. They are as curious as I am to learn what the analyses
of the new evidence may
reveal.
BTW: At Monday 's NEO meeting at the UK Spaceguard Centre in
Wales, Jay Tate presented
additional snapshots of the event taken by yet another
photographer (that's the 4th by
now) which show more puzzlingly features of the luminary
phenomenon.
Benny Peiser
=========
(2) NEW IMAGES OF WELSH 'FIREBALL' EVENT
Robert Nemiroff <nemiroff@mtu.edu>
Hi Benny,
I was the one who posted that APOD, wrote the original text,
and updated the text when another credible explanation was
suggested. I have had extensive e-mail correspondences with
several people, including meteor and contrail experts, so it
looks like we were living parallel lives and even arriving at
similar conclusions. I have forwarded to you some images and
personal witness accounts that apparently you did not have.
I hope you find them useful. Please do keep me informed of
your conclusions, as we will likely write another APOD
on this strange event in the near future.
- Robert Nemiroff
http://www.staff.livjm.ac.uk/spsbpeis/wales1.jpg
taken by Gary Green ((c) MMIII) on Sept. 24 2003, 19.06.36 BST
http://www.staff.livjm.ac.uk/spsbpeis/wales2.jpg
taken by Gary Green (© MMIII) on Sept. 24 2003, 19.08.02 BST
http://www.staff.livjm.ac.uk/spsbpeis/wales3.jpg
taken by Gary Green (© MMIII) on Sept. 24 2003, 19.10.24
BST
========
(3) NEW SNAPS OF WELSH 'FIREBALL' EVENT
by way of Robert Nemiroff <nemiroff@mtu.edu>
[mailto:gg@opobs.co.uk]
G.P.Green
4 Hafod Las
Pencoed
Bridgend
CF35 5NB
Home Phone 01656 860503
Astronomy Photograph of the day October 1st
Meteor over South Wales?
Dear Sirs,
I noted with interest the above on your website. Coincidentally I
to photographed the event and even more coincidentally I'm from
the
same village as the Oct 1st photographer, although I don't know
him.
Attached are the sequence of three photos I took. They were taken
over
a three minute period just after 7 p.m. (Sunset) British Summer
time
on the 24th September. In view of the differing opinions
expressed
on your website as to what the original photos represented then I
wonder if the attached can shed any further light. For
information
the photos attached are full frame shots taken on a digital SLR.
The close up shot was taken on a 300mm lens which as it was on a
Canon digital camera would equate to 480 mm ordinary lens.
(Because
of the CCD chip giving 1.6 magnification).
I look forward to your reply.
Gary Green
===========
(4) 'METEOR' OVER SOUTH WALES
by way of Robert Nemiroff <nemiroff@mtu.edu>
[mailto Gary Green:gg@opobs.co.uk]
Dear Sirs,
Meteor South Wales
Thank you for your reply. The background to this incident is as
follows.
I am a 46 year old ex Bank manager whose interest in photography
stems
back over 15 years. Having only a matter of days earlier
purchased a
new Digital SLR I was naturally wishing to try it out, although
not
wishing to take anything serious or worthwhile with it on the
evening
in question.
Having found a car park locally which had a largely uninterrupted
view
of the western skyline. I set about running off a few frames as
the sun
was setting. It was one of those nights when the horizon promised
much
but delivered little. This being the case in-between shots I cast
an eye
around to try the camera on any interesting general cloud
formations to
take. After all being a digital camera there wasn't any film to
be wasted.
One of the bugbears of taking any decent shots that have a sky in
them is
the occurrence of aircraft contrails slashing uninteresting and
distracting
white lines through your photo. You then either have to wait for
the
contrail to disperse or actively incorporate it in your shot. On
this
instance because the setting sun was lighting the trail I went
ahead and
took the shots. Over a short period of time three shots were
taken interspersed
with uninteresting shots of the sunset.
Because the camera is digital it stores the technical data of the
photo at the
time of taking. Camera type, lens shutter speed, etc., and
importantly time.
This data may be on the tiff files sent to you and viewable if
accessed
through Adobe Photoshop 7 browser. I've looked it up on the
original files and
the order of the shots is, 1). Portrait format, straight
contrail. Time 19.06.36.
2) Landscape format, bent contrail. Time 19.08.02. 3)
Expanded contrail,
Time 19.10.24.
To answer your questions.
Shots 1 and 2 were taken as the contrail was being formed. There
was no sign
of an aircraft at the leading edge of the contrail. Magnifying
the leading edge
does show some kind of indefinite black blob there but you can't
tell what
it is. Shot three was not witnessed forming as I'd been looking
the other way.
As such I couldn't tell you how quickly this event occurred.
After shot three
the plume lingered there for quite a while but no further trail
developed coming
out of the plume.
While South Wales is on the general London to U.S. flight path,
throughout there
were no sounds of aircraft in the air. Given that we are in the
area of the flight
path you do get used to seeing contrails forming. However what
struck me as
slightly odd on this occasion was the speed that the leading edge
was progressing
across the sky. It seemed slow compared to the size of the
contrail. Normally a slow
contrail indicates a high aircraft. At the greater height the
aircraft seems to
move less distance but in being high the trail is also smaller to
the human eye.
The other thing that caught my eye was the sharp deviation in the
trail in photo 2.
I don't know whether my stomach would have appreciated being in
any plane that
changed direction in that sharp a fashion.
It would be quite something if this was a meteor and hell it
beats banking.
If you want to use the shots the website I that's ok.
If there is any other information you think would assist then
don't hesitate
to ask.
YOURS TRULY,
Gary
===========
(5) A CAMBRIDGE OBSERVER OF THE WELSH 'FIREBALL' EVENT
by way of Robert Nemiroff <nemiroff@mtu.edu>
[mailto:John.Lambert@arm.com]
Hi Robert,
I found this page from following a link from the BBC website, and
as soon
as I saw the picture recognised that I saw this event as well. I
live in
Cambridge, England and saw it from my back garden. I must object
to the statement
"perhaps a better hypothesis is an unusual airplane contrail
reflecting the
setting Sun" because that it certainly wasn't. I thought it
looked like a meteor,
although it was a lot lower in the sky than I would have
expected. The only
difference from where I was is that it looked to me to be
descending at a very
steep angle compared to the photo. That could be because I was
closer in line
with its line of flight.
Hope that helps.
John Lambert
==============
A CAMBRIDGE OBSERVER OF THE WELSH 'FIREBALL' EVENT
by way of Robert Nemiroff <nemiroff@mtu.edu>
[mailto:John.Lambert@arm.com]
Hi Robert,
I have seen meteors before but this struck me as being unusual
for a couple
of reasons. I first caught sight of it between two houses just
above the
roof line and it looked like a normal meteor except that I've
never seen a
meteor that low in the sky before. It seemed to burn up much
quicker and more
spectacularly than I expected and it was much brighter than a
normal meteor.
It seemed to completely burn up just before my horizon level.
After seeing it,
my first reaction was to listen for a bang because its brightness
suggested
that it was quite close, but then I thought about its trajectory
and realised
that it was probably going to hit somewhere out in the Atlantic.
I then formed
the opinion that the most likely explanation was that it could
have been a piece
of space debris burning up rather than a meteor.
I then forgot about it till I saw the picture and then recognised
it
straight away. It was only the possible explanation of a vapour
trail
that caused me to e-mail you to try and put the record straight.
Hope that helps.
John Lambert
=======
(6) HERMES IS FOUND
From: Roger W. Sinnott
Sent: Wednesday, October 15, 2003 10:03 PM
To: asteroid@SkyandTelescope.com
==================================================================
This Is SKY & TELESCOPE's AstroAlert for Minor Planets
==================================================================
After eluding astronomers for 66 years, the long-lost asteroid
Hermes has finally been retrieved.
Early on October 15th, Brian A. Skiff (Lowell Observatory
Near-Earth Object Search, Arizona) sent measurements of four CCD
images obtained with the 23-inch Catalina Schmidt telescope to
the Minor Planet Center in Cambridge, Massachusetts. At the
center, Timothy B. Spahr identified the suspect with other
measurements submitted in the past seven weeks -- but not
recognized as unusual -- by LONEOS and by the Lincoln Near Earth
Asteroid Research (LINEAR) project in New Mexico. In addition,
quick action by James Young (Table Mountain Observatory,
California) secured a confirmation just before dawn on the 15th.
Judging by its brightness, Hermes is a minor planet about 1 to 2
kilometers across. So it could be somewhat larger than the 1937
estimates. In a famous exhibit at the American Museum of Natural
History, New York, Hermes was depicted as a sphere about the size
of Central Park.
Hermes is by no means the last of the "lost asteroids"
-- many thousands of others in the Minor Planet Center's database
fall in this category because they could not be followed long
enough for an accurate orbit to be determined. But Hermes is by
far the most famous. It was discovered by Karl Reinmuth at
Heidelberg, Germany, on October 28, 1937, and tracked for only
five days. Although never officially numbered, it has been known
by the name Hermes ever since.
In late October 2003, Hermes will be bright enough (magnitude 13)
to be seen in 8-inch and larger amateur telescopes as it races
westward across Cetus, Pisces, and Aquarius. By month's end it
will be moving 7 degrees per day and gaining. Unlike the
situation in 1937, when Hermes skimmed to within 800,000 km of
our planet (two Earth-Moon distances), it will pass about nine
times that far on November 4, 2003. Nevertheless, the possibility
of future close encounters definitely puts this object in the PHA
(potentially hazardous asteroid) class.
The preliminary ephemeris below has been calculated from the
orbital elements by Brian G. Marsden on Minor Planet Electronic
Circular 2003-T74, issued October 15th. It gives Hermes's right
ascension and declination (equinox 2000.0) at 0 hours Universal
Time on each date, its distance from the Earth (Delta) and Sun
(r) in astronomical units, its elongation angle from the Sun,
visual magnitude, and the constellation through which it is
passing. (View or print the table with a fixed-space font like
Courier.)
Sky & Telescope plans to issue another AstroAlert with a more
detailed ephemeris later.
Roger W. Sinnott
Senior Editor
Sky & Telescope
==================================================================
AstroAlert is a free service of SKY & TELESCOPE, the
Essential
Magazine of Astronomy (http://SkyandTelescope.com/).
This e-mail
was sent to AstroAlert subscribers. If you feel you received it
in error, or to unsubscribe from AstroAlert, please send a plain-
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with the following
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replacing "e-mail@address.com"
with your actual e-mail address.
=========
(7) MPC ANNOUNCEMENT OF HERMES RECOVERY
MPEC 2003-774
http://cfa-www.harvard.edu/mpec/K03/K03T74.html
M.P.E.C.
2003-T74
Issued 2003 Oct. 15, 17:10 UT
The Minor Planet Electronic Circulars
contain information on unusual
minor planets
and routine data on comets. They are published
on behalf of Commission 20 of the International
Astronomical Union by the
Minor
Planet Center, Smithsonian Astrophysical Observatory,
Cambridge, MA 02138, U.S.A.
Supported in
part by the Steven and Michele Kirsch Foundation
Prepared using the Tamkin Foundation Computer Network
MPC@CFA.HARVARD.EDU
URL http://cfa-www.harvard.edu/iau/mpc.html
ISSN 1523-6714
1937 UB (HERMES)
Observations:
J37U00B C2003 08 26.35985 01 52
54.33 +04 08
41.6
18.8 704
J37U00B C2003 08 26.37269 01 52
54.87 +04 08
44.8
19.6 704
J37U00B C2003 08 26.38603 01 52
55.52 +04 08
46.6
19.3 704
J37U00B C2003 08 26.41142 01 52
56.62 +04 08
52.1
19.2 704
J37U00B C2003 09 03.37679 01 58
49.08 +04 23
54.8
19.0 704
J37U00B C2003 09 03.38860 01 58
49.59 +04 23
55.5
19.1 704
J37U00B C2003 09 03.40035 01 58
49.96 +04 23
55.8
18.6 704
J37U00B C2003 09 03.41219 01 58
50.36 +04 23
57.0
19.3 704
J37U00B C2003 09 28.29353 02 05
19.55 +04 12
35.4
16.9 704
J37U00B C2003 09 28.30707 02 05
19.22 +04 12
32.1
18.5 704
J37U00B C2003 09 28.31989 02 05
18.78 +04 12
30.5
18.0 704
J37U00B C2003 09 28.34613 02 05
18.17 +04 12
26.7
17.0 704
J37U00B C2003 09 28.37929 02 05
17.41 +04 12
21.0 17.1
R 699
J37U00B C2003 09 28.39356 02 05
17.02 +04 12
18.8
699
J37U00B C2003 09 28.40779 02 05
16.65 +04 12
15.9
699
J37U00B C2003 09 28.42207 02 05
16.31 +04 12
14.2
699
J37U00B C2003 10 05.59036 02 01
02.22 +03 46
56.7
16.7 608
J37U00B C2003 10 05.60121 02 01
01.55 +03 46
53.9
16.8 608
J37U00B C2003 10 05.61168 02 01
00.90 +03 46
50.5
16.8 608
J37U00B C2003 10 15.30771 01 45
29.04 +02 45
15.7 14.4
R 699
J37U00B C2003 10 15.32432 01 45
26.23 +02 45
06.8
699
J37U00B C2003 10 15.34094 01 45
23.44 +02 44
57.8
699
J37U00B C2003 10 15.35751 01 45
20.63 +02 44
48.9
699
J37U00B C2003 10 15.51076 01 44
55.17 +02 43
26.6 14.5
R 673
J37U00B C2003 10 15.51215 01 44
54.94 +02 43
25.8
673
J37U00B C2003 10 15.51354 01 44
54.72 +02 43
24.9
673
J37U00B C2003 10 15.51516 01 44
54.47 +02 43
24.2
673
J37U00B C2003 10 15.51725 01 44
54.14 +02 43
23.1
673
Observer details:
608 Haleakala-NEAT/MSSS. Observers R. Bambery, E. Helin, S.
Pravdo, M. Hicks,
K. Lawrence, P. Kervin, J. Africano, R.
Maeda. 1.2-m reflector + CCD.
673 Table Mountain Observatory, Wrightwood. Observer J.
Young. 0.6-m
reflector + CCD.
699 Lowell Observatory-LONEOS. Observers M. E. Van Ness, B.
A. Skiff. 0.59-m
LONEOS Schmidt + CCD.
704 Lincoln Laboratory ETS, New Mexico. Observers M.
Blythe, F. Shelly,
M. Bezpalko, R. Huber, L. Manguso, D. Torres,
R. Kracke, M. McCleary,
H. Stange, S. Adams, T. Brothers, S.
Partridge. Measurers J. Stuart,
R. Sayer, J. Evans, J. Kommers, P.
Hopman. 1.0-m f/2.15 reflector + CCD.
Orbital elements:
1937
UB
PHA 0.003
Epoch 2003 Dec. 27.0 TT = JDT
2453000.5
MPC
M
1.79614
(2000.0)
P
Q
n 0.46288738
Peri. 92.39541
-0.59740895 -0.79969615
a 1.6550806
Node 34.51615
+0.68733602 -0.54908819
e 0.6242226
Incl. 6.06865
+0.41312437 -0.24287492
P
2.13
H
17.1
G
0.15
U 6
Residuals in seconds of arc
030826 704 0.3+ 1.0- 030928
704 1.1- 0.4- 031015 699
0.1- 0.2-
030826 704 0.4- 0.3+ 030928
704 0.0 0.0 031015
699 0.2+ 0.3-
030826 704 0.2+ 0.2+ 030928
699 0.2+ 0.1+ 031015 699
0.0 0.4-
030826 704 (0.6- 2.1+) 030928 699
0.1- 0.2+ 031015 673 0.2-
0.1+
030903 704 0.7- 0.6+ 030928
699 0.0 0.4- 031015 673
0.2- 0.1+
030903 704 0.7+ 0.3+ 030928
699 0.5+ 0.3+ 031015 673
0.1- 0.0
030903 704 0.0 0.4- 031005
608 0.3- 0.5+ 031015 673
0.1+ 0.2+
030903 704 0.2- 0.2- 031005
608 0.2- 0.7+ 031015 673
0.3+ 0.2+
030928 704 0.4+ 0.4+ 031005
608 0.1- 0.2+
030928 704 0.6+ 0.8- 031015
699 0.1+ 0.2-
Ephemeris:
1937
UB
a,e,i = 1.66, 0.62,
6
q = 0.6219
Date TT R. A. (2000)
Decl. Delta
r Elong.
Phase V
2003 10 08 01 58.54 +03
35.4 0.287 1.277
163.4 12.9 15.7
2003 10 10 01 55.90 +03
24.3 0.264 1.256
165.7 11.3 15.4
2003 10 12 01 52.63 +03
11.4 0.242 1.236
168.0 9.7 15.1
2003 10 14 01 48.61 +02
56.6 0.221 1.216
170.2 8.0 14.8
2003 10 16 01 43.64 +02
39.3 0.200 1.195
172.0 6.7 14.5
2003 10 18 01 37.45 +02
18.9 0.179 1.174
172.7 6.2 14.2
2003 10 19 01 33.78 +02
07.2 0.169 1.164
172.4 6.5 14.1
2003 10 20 01 29.64 +01
54.2 0.159 1.153
171.6 7.2 13.9
2003 10 21 01 24.96 +01
39.8 0.149 1.143
170.4 8.4 13.8
2003 10 22 01 19.63 +01
23.7 0.139 1.132
168.7 9.9 13.7
2003 10 23 01 13.53 +01
05.6 0.130 1.122
166.7 11.7 13.6
2003 10 24 01 06.49 +00
45.0 0.120 1.111
164.4 13.9 13.5
2003 10 25 00 58.31 +00
21.4 0.111 1.101
161.7 16.5 13.4
2003 10 26 00 48.72 -00
05.8 0.102 1.090
158.5 19.5 13.3
2003 10 27 00 37.38 -00
37.7 0.094 1.079
154.9 23.0 13.2
2003 10 28 00 23.82 -01
15.1 0.085 1.069
150.7 27.1 13.1
2003 10 29 00 07.46 -01
59.5 0.077 1.058
145.7 31.9 13.0
2003 10 30 23 47.55 -02
52.2 0.070 1.048
139.9 37.7 12.9
2003 10 31 23 23.17 -03
54.3 0.063 1.037
132.9 44.5 12.9
2003 11 01 22 53.40 -05
06.0 0.057 1.026
124.6 52.8 12.9
2003 11 02 22 17.54 -06
24.6 0.052 1.015
114.8 62.6 13.0
2003 11 03 21 35.78 -07
43.7 0.049 1.005
103.5 73.8 13.2
2003 11 04 20 49.79 -08
52.5 0.048
0.994 91.3
86.0 13.5
2003 11 05 20 02.81 -09
40.6 0.048
0.983 78.9
98.3 14.0
2003 11 06 19 18.50 -10
04.2 0.051
0.973 67.2 110.0
14.7
2003 11 07 18 39.44 -10
06.9 0.055
0.962 56.8 120.4
15.6
2003 11 08 18 06.51 -09
56.1 0.061
0.951 48.0 129.3
16.5
2003 11 09 17 39.39 -09
38.5 0.067
0.941 40.7 136.7
17.5
2003 11 10 17 17.22 -09
18.6 0.074
0.930 34.5 142.9
18.5
2003 11 11 16 59.06 -08
59.1 0.082
0.920 29.5 148.0
19.6
2003 11 12 16 44.08 -08
40.9 0.090
0.909 25.3 152.3
20.6
A bright near-earth-object candidate,
reported this morning by
B. A. Skiff, was placed on The NEO Confirmation Page by T. B.
Spahr quickly
enough that follow-up observations could be made by J. Young
within four hours.
Spahr then located the Oct. 5 observations (which had been
reported as a
likely main-belt object) and recognized the object as 1937 UB
(Hermes).
With the help of the LINEAR Team, single-night observations (also
reported
as likely main-belt objects) could then be identified back to
Aug. 26. The
orbital elements provided here have not been linked to the 1937
observations,
since when the object has made almost exactly 31
revolutions. Radar
observations at the present apparition would be very useful.
Brian G.
Marsden
(C) Copyright 2003
MPC
M.P.E.C. 2003-T74
==========
(8) BACKGROUND INFO: EFFORTS ON 1937 UB "HERMES", A
LOST ASTEROID
Rechenzentrum Heidelberg
http://www.rzuser.uni-heidelberg.de/~s24/hermes.htm
by Lutz D. Schmadel, Astron.Rechen-Institut, Heidelberg,
Germany,
s21@ix.urz.uni-heidelberg.de
and Joachim Schubart, Astron.Rechen-Institut, Heidelberg,
Germany,
s24@ix.urz.uni-heidelberg.de
--------------------------------------------------------------------------------
Index
1. The present situation
2. Some more recent measurements of trails
3. Orbits of variation and search lines
The present situation
Reinmuth discovered 1937 UB Hermes on 1937 Oct. 28.9 UT. The
object had left long trails on two simultaneous exposures by the
Bruce Astrograph at Heidelberg. Direct attempts to get further
positions failed, but trails of Hermes were found on plates
exposed at Oak Ridge (Oct.25.2), Johannesburg (Oct.27.9), and
Sonneberg (sky patrol plates Oct.26.9 - 29.9). MPC 5971 of May
1981 gives a list of the positions. Due to the short arc and the
proximity to the earth a reliable determination of the orbit is
impossible, but the effects of daily parallax allow a qualitative
derivation: Brian G. Marsden published a best fit to the
observations in MPC 3014 of Oct. 1969. Since the resulting
orbital period is too uncertain, a prediction of the position of
Hermes in its orbit is not possible. There are no known
observations of Hermes from the years after 1937.
Nevertheless, we have found it interesting to do some work on the
observations and on possible variations of the orbit of Hermes.
Unfortunately, most of the basic plates with trails of Hermes are
missing in the respective collections of plates. This is true for
the better one of the pair of the discovery plates, for the
Johannesburg plates, and for the four Sonneberg patrol plates
with published positions. The Oak Ridge plate of 1937 Okt. 25.2
is available in the plate collection of Harvard Observatory. Only
a provisional position of moderate accuracy was derived from this
plate in 1937 by L.E.Cunningham. In 1994 Gareth Williams looked
at this plate and found the trail of Hermes, but it is very faint
and the ends of the trail are very ill-defined, the trail seems
to be involved with a star near one end (personal communication
by Brian G. Marsden). Apparently it is not possible to improve
Cunningham's position. The published positions from Sonneberg
refer to four subsequent nights, but due to the very short focal
length of the patrol cameras, and to the imperfect way of guiding
during the exposure, these positions are inaccurate. Marsden
omitted them in his best fit mentioned above.
FULL PAPER at
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