Efforts on 1937 UB "Hermes", a long-lost Apollo Asteroid, rediscovered
in 2003, now numbered: (69230) Hermes
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
Remark. Unchanged text of Sept.2000 (sections 1, 2) or Dec.2001 (section 3)
1. The present situation
2. Some more recent measurements of trails
3. Orbits of variation and search lines
Note. Section 3 is maintained, since trails of Hermes happened to appear close
to both the search lines derived for 2001 and 2003, although the real orbit of
Hermes does not correspond to the orbits used in the derivation.
The present situation (text written in Sept.2000)
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.
The missing Sonneberg plates that correspond to the published positions of the
four nights Oct. 26.9 - 29.9 were exposed for about half an hour at a Tachar
camera. The plate centers, 2h;+10d in the first two and 1h;+10d in the last
two cases, were favorable for catching trails of Hermes. However, due to the
distances from the centers, large optical distortions have affected the trails
and the stellar images, in addition to the disadvantages mentioned above.
Fortunately, a photographic copy on paper is still available for the last of
these plates, T2499 of Oct.29.9. The paper copy is enlarged by a factor of 3.3
and covers the part of the plate with the trail. The enlargement is favorable,
but distortions in the paper are possible. The photo was copied on a film that
we have measured and reduced with modern positions of the comparison stars.
The four missing plates cover a part of the +10d zone of declination, but the
sky patrol at Sonneberg also used a -4d zone at that time. Three plates of this
zone taken on Oct.26.9, 27.9, and 29.9 are available in the collection and show
trails of Hermes as well. These trails appear in the northern part of the plates
and especially the last one is close to the border between very deformed stellar
images. The log book associated to the -4d zone reports "vereinzelt Wolken" for
the last two of these three plates, or "sometimes single clouds". This remark
does not refer to plate T2499 that was exposed later. Although nothing is
reported for that plate, perturbations by clouds appear as possible.
In spite of all difficulties, we have tried to derive positions from the
three plates of the -4d zone as well. Certainly the following positions from
the sky patrol at Sonneberg are less accurate than indicated, although we
have used only comparison stars from the PPM Catalogue that are close to the
trails. The formal accuracy of our measurements is misleading. Effects of
imperfect guiding are visible on two plates exposed for 60 minutes: At the
centers of these plates the stellar images are not round but clearly more
extended in one direction. In one of these cases the trail of Hermes appears
as curved and irregular. We have used a program by Siegfried Roeser in our
reductions.
1937 UB, positions from patrol plates taken at Sonneberg
Plate 1937, UT RA (2000.0) Decl Comp.Stars, Center Remarks
number of plate
h m s d m s
E3775 Oct.26.92188 2 08 15.7 +06 31 11 17 2 h 1
26.94549 2 08 05.9 +06 30 57 17 -4 d 1
E3779 27.91817 1 58 37.8 +07 08 33 30 2 h 2,3,4
27.95984 1 58 12.9 +07 11 22 30 -4 d 2,4
E3795 29.85266 0 43 15.0 +11 32 02 26 1 h 2,5
29.89433 0 38 26.4 +11 47 27 26 -4 d 2,5
T2499, Oct.29.91875 0 35 09.1 +11 55 50 10 1 h 3
copy 29.9 0 34 13.6 +11 58 27 10 +10 d 6
29.9 0 32 59.6 +12 01 51 10 6
29.93958 7
Remarks
1. Bad definition of ends of faint trail
2. Visible effects of imperfect guiding; Perturbations by clouds of unknown
duration
3. Bad definition of beginning of trail
4. Irregular form of trail
5. Long trail not far from edge of plate
6. Point within trail, that fades towards an apparent end in a stellar image
7. End of exposure, the visible trail has ended before
According to the circumstances mentioned above the geocentric distance of
Hermes at a given epoch in 1937 results with some uncertainty. A variation of
this distance in some range is possible. We have adopted a number of values
for this distance and derived for each of them a corresponding orbit of
variation. For the epoch JD 2428834.5 the values of the semi-major axis of
our set of orbits cover the range from 1.624 to 1.661 au . Marsden's result
corresponds to 1.639 au at this epoch. Forward integrations of our set of
orbits lead to further close approaches in many cases: approaches to the earth
are possible at both the nodes, close approaches to Venus are possible as well.
We have searched files of observations for later observations of Hermes, but
in vain. If another close approach to earth has occurred at all, a missing
movement towards opposition or bright moonlight can have prevented observations.
Furthermore, both the incoming and the outgoing branches of the orbit of Hermes
are turned to the south of the ecliptic.
There is a subset of orbits that has avoided very close approaches to the
inner planets until now and will lead to the vicinity of earth not before
Oct. 2003. In this subset the range covered by the mean longitudes increases
at first, due to the different mean motions, but later on special perturbations
stop and reverse this process. Therefore, a comparatively large set of orbits
corresponds to an approach in Oct. 2003. This seems to indicate a larger
probability for a return of Hermes in that year, if compared with other years.
Anyway, an orbit of this subset is useful to represent the quality of the orbit
of Hermes at the present time, or to allow the derivation of search lines. An
example for this is given below.
Actually, according to a search along lines computed for August 2001, Hermes
does probably not move on an orbit of this subset. At Siding Spring Observatory,
NSW, Australia, Dr.Robert H. McNaught tried to find Hermes in the vicinity of
these search lines, but did not find the object. More details on this are given
in a special section.
1937 UB, incoming branch of the orbit, search lines
according to a special orbit of variation integrated to Sept. 2003.
Elements of this orbit for the epoch JDATE= 2452900.5 = 2003 Sept.18.0,
angles are given in degrees :
a= 1.654884 e= 0.626246 M= 317.0
omega,node,incl.: 92.0503 , 34.6105 , 6.1673 (2000.0)
V magnitude from H = 16.8 G = 0.15 , H depends on 3 trails of 1937
and B-V = 0.8 .
The round value given for the mean anomaly, M, of this orbit is varied from
315.0 to 319.0 at 1.0 deg intervals to generate 5 subsequent ephemeris places
for some dates in Sept./Oct. 2003. The first four places derived for a date
correspond to the subset of our orbits of variation mentioned above. It is
meaningful to derive more places by use of smaller values of M.
However, the resulting search lines are approximately valid for Sept./Oct.
of other years as well. To be more accurate in 2001, for instance, subtract
12 hours from the time given for an ephemeris place of 2003. This fits the
position of the earth, but the elements of the orbit of Hermes will differ
in other years, especially in case of strong perturbations by Earth or Venus,
see the Note given at the end of the search lines.
1937UB Hermes, search lines generated by variation of mean anomaly,
they are approximately valid for the same dates of
years preceding or following 2003.
0 h TT R.A. (2000) Decl. Delta r Mag.(V) Phase
03 9 18 1 54.7 3 0 .538 1.482 17.4 22.3
03 9 18 2 6.9 4 22 .529 1.462 24.6
03 9 18 2 19.6 5 47 .521 1.441 27.0
03 9 18 2 32.9 7 13 .515 1.421 29.5
03 9 18 2 46.7 8 40 .510 1.400 17.4 32.0
03 9 22 1 53.9 2 47 .485 1.444 17.0 20.3
03 9 22 2 7.7 4 19 .475 1.424 23.0
03 9 22 2 22.2 5 54 .466 1.403 25.7
03 9 22 2 37.4 7 31 .460 1.383 28.7
03 9 22 2 53.3 9 8 .455 1.362 17.1 31.7
03 9 26 1 52.2 2 29 .434 1.406 16.7 18.1
03 9 26 2 7.8 4 12 .423 1.386 21.1
03 9 26 2 24.4 5 59 .413 1.365 24.4
03 9 26 2 42.0 7 50 .406 1.344 27.8
03 9 26 3 .6 9 41 .400 1.322 16.8 31.5
03 9 30 1 49.2 2 6 .386 1.368 16.3 15.5
03 9 30 2 7.0 4 3 .373 1.347 19.0
03 9 30 2 26.3 6 5 .362 1.325 22.8
03 9 30 2 46.9 8 12 .354 1.304 26.9
03 9 30 3 8.9 10 19 .348 1.282 16.4 31.4
03 10 4 1 44.6 1 37 .339 1.329 15.8 12.6
03 10 4 2 5.1 3 49 .324 1.307 16.5
03 10 4 2 27.7 6 11 .312 1.285 21.0
03 10 4 2 52.4 8 39 .303 1.264 26.1
03 10 4 3 18.9 11 8 .297 1.242 16.0 31.5
03 10 8 1 38.1 1 1 .295 1.289 15.3 9.5
03 10 8 2 1.9 3 32 .278 1.267 13.7
03 10 8 2 28.8 6 19 .264 1.245 19.0
03 10 8 2 58.9 9 15 .254 1.223 25.3
03 10 8 3 31.7 12 12 .248 1.200 15.5 32.2
03 10 12 1 28.9 0 15 .252 1.248 14.8 7.0
03 10 12 1 56.6 3 10 .233 1.226 14.7 10.5
03 10 12 2 29.3 6 30 .217 1.204 14.8 16.8
03 10 12 3 7.1 10 6 .206 1.181 14.9 24.8
03 10 12 3 49.4 13 40 .201 1.159 15.0 33.9
03 10 16 1 15.9 - 0 45 .212 1.207 14.4 7.8
03 10 16 1 48.3 2 39 .189 1.185 14.1 7.5
03 10 16 2 29.1 6 47 .171 1.162 14.1 14.3
03 10 16 3 19.0 11 24 .159 1.139 14.3 25.1
03 10 16 4 16.2 15 49 .156 1.116 14.5 37.6
Note
In years different from 2003 the above search lines approximately describe
a possible approach of Hermes near the ascending node of its orbit, but then
the original elements of 1937 and the perturbations do not correspond to the
orbits used above. We have used other orbits of variation of our set to model
approaches of Hermes near the ascending or descending node in some years. We
can try to do this for other years. September and October of a year offer the
best chance to rediscover this long-lost asteroid, but observers south of the
equator have a second chance in May and June.
Ask for more information by use of one of the e-mail addresses given above.
To get an early decision about the presence of Hermes within the subset of
orbits mentioned above, an extended subset of about 14 percent of our most
probable orbits of variation was integrated to a suitable epoch in 2001, and
search lines, as shown below for two dates in Aug. 2001, were derived. The
range of elongation at 80 deg. is limited, but the predicted brightness is low
and subject to uncertainty.
Nevertheless, Dr. Robert H. McNaught has kindly agreed to cooperate with us in
an attempt to look for Hermes according to search lines prepared for Aug. 2001.
Although he lost several nights by unfavourable weather conditions, he could
use the 1.0-m telescope with CCD at Siding Spring Observatory to look along the
computed lines. Unfortunately, Hermes did not appear in this search. Probably
its orbit differs from those considered here.
Here we give some of the numerical details used in this project:
The following five orbits represent the subset at the epoch JD 2452100.5 and
demonstrate the range covered by the elements. The second orbit corresponds to
a minimum of the mean anomaly, M, at this epoch. The minimum results from the
action of the perturbing planets. The angles are given in degrees.
M a e Peri. Node Incl. (2000.0)
303.76713 1.6551120 0.6260578 92.05172 34.61524 6.15859
302.73818 1.6564481 0.6263287 92.04297 34.62198 6.15908
304.73875 1.6558763 0.6262860 92.02089 34.63375 6.16246
306.73529 1.6547045 0.6262063 92.00276 34.63727 6.16741
307.56633 1.6545808 0.6262315 92.01415 34.62452 6.16721
V magnitude from H = 16.8 G = 0.15 , H depends on 3 trails of 1937
and B-V = 0.8 .
Four positions derived from the four last orbits, respectively, represent
search lines given below for two subsequent dates in August 2001. Places from
the first orbit are close to these lines.
TT R.A.(J2000) Decl. Delta R El. Ph. V
01 8 25.0 4 22.5 18 40 .905 1.295 84.9 51.0 19.0
01 8 25.0 4 40.8 19 51 .924 1.251 80.5 52.8
01 8 25.0 4 59.5 20 54 .945 1.205 76.0 54.5
01 8 25.0 5 7.1 21 17 .955 1.186 74.2 55.0 19.1
01 8 26.0 4 27.1 18 55 .892 1.285 84.8 51.5 19.0
01 8 26.0 4 45.8 20 5 .912 1.241 80.2 53.4
01 8 26.0 5 4.8 21 6 .934 1.195 75.7 55.0
01 8 26.0 5 12.6 21 29 .945 1.176 73.8 55.6 19.1
Text of sections last modified: 2001 Dec. 6
Changes in main title and index: 2003 Nov.