3782 Celle: Discovery of a Binary System within the Vesta Family of Asteroids
W. H. Ryan1, E. V. Ryan1, and C. T. Martinez2
1
New Mexico Institute of Mining and Technology (NMIMT), 801 Leroy Place, Socorro,
NM, 87801
2
University of New Mexico, Department of Physics and Astronomy, Albuquerque, NM,
87131
Corresponding author:
William H. Ryan
MRO/R& ED
New Mexico Institute of Mining and Technology
801 Leroy Place
Socorro, NM, 87801
bryan@nmt.edu
Phone: 505-835-6646
Fax: 505-835-6807
Keywords: asteroids, photometry, binaries, lightcurves.
1
Abstract
Photometric observations of the minor planet (3782) Celle, which has been associated
both dynamically and spectroscopically with the Vesta asteroid family, were obtained
using the 1.8-meter Vatican Advanced Technology Telescope during September 2001
and December 2002 - January 2003. Analysis of these data reveals a normal rotational
lightcurve (P=3.84 hr, amplitude = 0.10-0.15 mag). During the 2002 - 2003 run,
anomalous attenuation events were observed lasting for about 2.6 - 3.5 hrs that varied in
amplitude from 0.15 - 0.3 mag. The attenuations were of two distinct types that can
clearly be identified as primary and secondary occultation/eclipses similar to those that
have been previously observed in known minor planet binary systems (Pravec et al.
2000). We therefore interpret our data as clear evidence that (3782) Celle is actually an
asynchronous binary system with an orbital period of 36.57 +/- 0.03 hrs (Ryan et al.
2003). A preliminary model, based on spherical components, yields a primary-tosecondary diameter ratio of 0.43 +/- 0.01 and a combined bulk density of 2.2 +/- 0.4
gm/cm3 for the two components. Because these objects are likely to be composed of
basaltic fragments, this density is indicative of a moderate to highly fractured internal
structure for at least one, if not both, of the binary components. Since the Vesta family is
believed to have been created via a cratering event, this finding has important
implications for understanding possible ejecta reaccumulation and satellite formation in
subcatastrophic collisions.
2
I. Introduction
Although a large database of lightcurves exists for main-belt and other asteroid
populations (e.g., Near-Earth asteroids), few researchers have focussed on deriving the
photometric properties of asteroids in a particular family. One notable exception is the
study of the Koronis family initiated by Binzel (1987), and continued by Slivan et. al.
(2003), which analyzed the uniform alignment of the family members’ spin orientations.
This study has demonstrated that interesting new phenomena can be discovered when the
aggregate photometric and spin properties of the components of a single family are
examined. In an effort to better understand large-scale collisions and their outcomes, an
observational study of the Vesta family of asteroids was undertaken starting in 1999
(Ryan et al. 2000). The objective is to determine spin rates, orientations, and shapes for
as many family members as possible. It was anticipated that this will provide tighter
constraints in the modeling of collisional processes, and could possibly elucidate impact
conditions required to create asteroid families.
Statistical analysis, spectroscopic studies, and imaging data, all uniquely point to an
impact origin for the Vesta asteroids, making it an ideal family for study. Zappala et al.
(1994) have statistically classified 64 asteroids as comprising the Vesta family, and
Bendjoya and Zappala (2002) have updated this to include 231 to 242 members. Further,
Vesta has a spectrally distinct crustal composition (basaltic) which permits any fragments
excavated from it to be easily traceable. Binzel and Xu (1993) observed 520 km diameter
Vesta and smaller asteroids (4 - 7 km) in its vicinity, and concluded that eight of the
asteroids for which they obtained spectra in the region of Vesta had been chipped from
Vesta's crust. Bus and Binzel (2002) and Burbine et al. (2001) have also obtained spectra
of some of these bodies and link them compositionally to Vesta. Images taken by the
Hubble Space Telescope of asteroid Vesta (Zellner et al. 1997) confirm that there is a
large (~450 km) impact basin (Thomas et al. 1997) across Vesta's southern hemisphere.
This hints at the possibility that this family formed as a result of a cratering collision with
the observed impact basin as the source region for the so-called Vesta “chips”. Since a
compositional database exists for a subset of the family members, this photometric
investigation is intended to provide the lightcurve data necessary to complete the picture.
The ultimate goal of this observational study, and subsequent spin vector and shape
analysis, is to address a very important issue highlighted by Binzel and Xu and raised as a
consequence of numerical modeling results. What is the mechanism for excavating these
cratering fragments off of Vesta’s surface? Were the Vesta chips ejected as large, intact
spall fragments (having a thin, elongated shape) or are they smaller pieces of material
that have re-accumulated into larger rubble piles (having roughly spherical, ellipsoidal, or
lumpy shapes)? Being able to answer these questions will help to constrain and test
numerical models of family formation (Melosh and Ryan 1997; Asphaug 1997; Michel et
al. 2001).
During the first phase of this survey, a binary asteroid system was fortuitously discovered
amongst the Vesta chips. An anomalous attenuation was observed in what was an
otherwise "normal" lightcurve for the Vesta asteroid family member 3782 Celle (Ryan et
3
al. 2003). The discovery of a binary system for this cratering impact-generated asteroid
family is a key piece of information to be incorporated into physical models of collisional
origin, and will certainly help address the questions raised above. A preliminary model of
the data allowed the calculation of a mean density for the components of this binary
system of 2.2.4 g/cm3. Assuming that the material comprising these bodies is basaltic,
this lower-than-expected bulk density hints at a moderate to highly fractured internal
structure for the Celle system. This paper concentrates on the details of these
observations and their implications, which are discussed in the following sections. Future
papers will address the other observational data collected for this very interesting asteroid
family.
II. Observations and Data Reduction
3782 Celle was observed for a total of 15 nights using the 1.8-meter Vatican Advanced
Technology Telescope (VATT) during September 2001 and December 2002 - February
2003 (all dates in this paper are UT dates). The observational circumstances are given in
Table 1. This table includes the UT date of mid-observation, heliocentric, (r), and
geocentric () distances, solar phase angle (), geocentric ecliptic longitudes and
latitudes, and the mean R magnitude, reduced to unit heliocentric and geocentric
distances.
Observations were made tracking at sidereal rate with typical exposures in the Harris R
band of 60-120 seconds. The resulting images were bias subtracted and flat field
corrected. Aperture photometry was then performed on the asteroid and an ensemble of
5-8 comparison stars in each image using the IRAF (Tody 1993) apphot routine.
Differential magnitudes between the program object and the ensemble were calculated,
yielding typical errors on the order of 0.005 mag or less. Due to the large aperture of the
VATT and the relatively bright target, non-photometric nights containing thin clouds
were routinely utilized. However, the limits of this technique were tested through thicker
clouds during the December 2002 run, resulting in somewhat noisier data.
On nights with photometric conditions during the 2002-2003 apparition, BVRI exposure
sequences were taken for Celle and VR sequences for the comparison stars used for
differential photometry on previous non-photometric nights. This, along with the
measured V-R for Celle, permitted the absolute calibration of the R magnitudes to ~0.01
mag or better using Landolt (1992) standards and also allowed the determination of the
following mean observed color indices (not corrected for solar colors) for Celle: B-V =
0.883  0.014, V-R = 0.491  0.009, and V-I = 0.802  0.032. The errors quoted are the
standard deviations of 21 measurements taken over four nights. The mean V-R (the color
used in the transformation of the differential R magnitudes to the standard system) of
each night’s comparison ensemble was typically within 0.15 magnitudes of the program
object, thus minimizing any systematic errors in the reported R magnitudes.
The observation times for the R data have been corrected by subtracting the light travel
time from Celle and the magnitudes have been reduced to unit geocentric and heliocentric
4
distances. For phase angles greater 8, the nightly mean R magnitudes from Table 1 for
the 2002-2003 opposition imply a linear trend of 0.029 mag/. Since this yields a
variation during a single night that is smaller than the typical noise in the data, and given
that it is not completely clear that this trend is applicable to data taken during the
anomalous attenuations, no phase correction was applied to the data within each night.
During the September 2001 run, two nights of differential photometric data were
obtained for 3782 Celle. No attenuation events were observed, and it displayed what
appeared to be a normal doubly periodic lightcurve associated with the asteroid’s
rotation. Using the standard Fourier technique described by Harris and Lupishko (1989),
a period of 3.840 hours was derived and the composite lightcurve shown in in Figure 1
was generated. In the composite curves, differential magnitudes with respect to a best fit
nightly zero point are folded with the derived period and plotted versus rotational phase.
The order of the fit, n, is chosen by increasing the number of Fourier terms in trial fits
until the 2, normalized to the number of data points, is the same order of magnitude as
the variance of the observed differential magnitudes. For data calibrated to the standard
system and distance corrected, these nightly zero points represent the mean R magnitudes
quoted in Table 1. However, for uncalibrated data, as was obtained during this particular
opposition, these zero points are simply free parameters in the fit. For the September
2001 run, this technique for combining data from multiple nights yielded approximately
80 coverage of Celle’s rotational phase.
Since shape determination of main belt asteroids requires observations from multiple
oppositions, Celle was again observed for three nights using the VATT in December
2002, before it moved too far into the Milky Way. In the lightcurve for December 10,
2002 shown to the left in Figure 2, differential magnitudes up to twice the anticipated
lightcurve amplitude were observed during one of the sporadic clearings on an otherwise
cloudy night. The initial assumption was that the points near the end of the night were
spurious due to cloud cover. Therefore, even though the data from earlier in the night
displayed a higher than expected amplitude, an attempt was made to incorporate them
into a composite curve. However, this failed, and, supported by familiarity with the
attenuations observed during later runs, it was determined that the points at the end of the
night most likely occurred after the attenuation ended. Therefore, only these noisier
points are included in the composite curve shown to the right in Figure 2 for all three
nights of the run, allowing an estimation of the mean R magnitude for the night.
Although the data from December 10 were of marginal quality and provided very little
coverage of either the rotational curve or the attenuation event, it was these spurious
observations that prompted further analysis of Celle in 2003.
Complete coverage of an anomalous attenuation on the night of January 5, 2003 with a
duration of ~3 hours was observed under photometric conditions, confirming suspicions
regarding the December 10 data from the previous run. The lightcurve showing this event
is presented in the left hand plot of Figure 3. Data from two other nights during this run
displayed the previously observed 3.84 hour period, reinforcing the notion that the
January 5 event was truly anomalous. Therefore, these data, along with the data from
January 5 excluding that taken during the attenuation event, were combined to generate
5
the composite lighcurve shown in the right hand plot of Figure 3. Anomalous events were
also observed on January 27, 28, 30, and 31. The lightcurves displaying these events
against the background of the 3.84 hour are presented in Figure 4. The multitude of gaps
in these curves is due to interference by field stars since, by this time, Celle had moved
fully into the Milky Way. During the three other nights of the run, Celle again displayed
only the 3.84 hour variation. Therefore, a similar analysis was performed that excludes
the anomalous attenuations to generate the composite lightcurve for January 26 February 1, 2003 that is shown in Figure 5.
III. Analysis of the Anomalous Attenuations
In the initial analysis of the longer period attenuations, the Fourier fit of the 3.84 hour
period was simply subtracted from the nightly lightcurves. However, the resulting
residuals plot displayed a signature of an eclipsing binary system similar to those
observed previously (Pravec, et. al. 2000, Mottola and Lahulla 2000, Pravec, et. al. 1998,
Pravec and Hahn 1997). With the premise that the measured magnitudes were due to the
integrated sum of the light from two bodies, it was determined that the observed
lightcurve would be more correctly interpreted as the linear sum of fluxes, not
magnitudes. Therefore, to analyze the nature of the attenuations, the nightly lightcurves
and fitted curve for the 3.84 hour variation were first converted to fluxes, the 3.84 hour
varying component was subtracted, and then converted back to magnitudes. The result for
the January 5, 2003 event is shown in Figure 6.
To determine the periodicity of anomalous attenuation events, the residuals from the
January 26 - February 1 run were simply folded with trial periods. Identifying two
distinct types of attenuation features and assuming that each occurs once per period, the
best fit was obtained with a period of 36.57 0.03 hours and the result is shown in Figure
7. Although there are gaps in the phase plot, coverage is complete enough to rule out any
shorter periodicites for which 36.57 would be an integer multiple, indicating that the
period is uniquely determined. For completeness, the residuals for January 4 - 6 are
folded with the same period and plotted in Figure 8. The fact that only one feature was
observed during this three day span is consistent with the ~18.3 hour periodicity of the
events. The second feature in this plot would have occurred at ~13 hours phase, just in
the gap between the data from the nights of January 4 and January 6.
IV. Interpretation and Model
The features observed in Figures 7 and 8 display the characteristics identified in
previously studied asynchronous binary minor planet systems. Such systems, where the
orbital features occur at regular intervals, but at different place in the primary's rotational
lightcurve on each occurrence, have been proposed as the one type of binary system that
can unambiguously be identified through lightcurve analysis (Weidenschilling et al.
1989, Merline et al. 2002). Therefore, in the following discussion, 3782 Celle will be
6
interpreted as such a binary system and the techniques employed in the analysis of 1996
FG3 (Pravec et al. 2000) will be used to model its characteristics.
Examining the residual plots in Figure 7, two distinct types of events are observed: a
feature with a flat-bottomed plateau similar to the one observed on January 5 and a much
deeper V-shaped feature. The flat feature can be interpreted as an event in which the
smaller, or secondary component of a binary system is completely obscured by the
primary (occultation) or the primary's shadow (eclipse). This will be referred to as a
secondary occultation or eclipse event. The deeper, V-shaped minimum can be
interpreted as one in which the smaller secondary passes in front of the primary. For
binary components of equal albedos, the depths of the two types of events should be
approximately equal at zero solar phase angle. However, the primary events in Figure 7
occurred at phase angles between 9.5-10.7. In this case, the shadow of the secondary is
displaced with respect to the observer’s line of sight and allows for the possibility of
detecting both the secondary's shadow projected onto the primary's surface (eclipse) as
well as an obscuration by the secondary itself (occultation). The small inflection in the
leading slope of the primary event at approximately the same depth as the secondary
event hints at a slight gap in time between the occurrence of totality of an
eclipse/occultation event and the onset of an occultation/eclipse (i.e., the other type
event). This is consistent with the fact that the depth of the primary event is
approximately twice that of the secondary. Presumably, this is due to the total depth of
the primary minimum being the combined effect of an occultation and an eclipse by the
secondary on the larger primary. In contrast, when the larger primary or its shadow
totally obscures the secondary, no further attenuation would be detected due to the onset
of the other type of event.
A first order model of the binary system can be generated by examining the intensitysubtracted January 5 event in Figure 6 in detail and by making the following postulates:
1) The primary and secondary components have similar albedos and are approximately
spherical.
2) The mutual orbit is nearly circular and has the 36.57 hour period identified in
Figure 7.
3) The bottom plateau of the January 5 event represents a total occultation/eclipse of
the secondary component and is due to the passage of the secondary behind the
primary along its full diameter.
Estimating the depth of the January 5 event to be 0.18  0.01 mag, Postulates 1 and 3
imply that the ratio of the secondary to primary diameters is ds/dp = 0.43  0.01. To
estimate the radius of the orbit, a, it is recognized that the angle that the secondary travels
through during the duration of the event, t, is   2 t/P, where P is the orbital period
and zero phase angle has been assumed. For non-zero phase angle, this would be
modified as    + , where  is the solar phase angle expressed in radians. For the
7
total duration of the event, the angle may also be expressed in terms of sizes associated
with the system as   (dp + ds)/a. Therefore,
 ds 
1  d 
p
a
.
 
dp
2 t  
P


(1)
Estimating the total duration (from beginning of decline to end of rise) of the January 5
event to be 2.7  0.1 hours implies a/dp = 3.3  0.2. Similar analysis of the duration of the
bottom plateau of the event leads to the same formula as Eq. 1, but with (1+ds/dp)
replaced with (1-ds/dp) in the right hand side numerator. Estimating the duration of this
plateau to be 1.1 0.1 hours then implies a/dp = 3.6  0.5. The fact that these agree to
within observational errors lends support to the postulate that the secondary did travel
behind the primary nearly along its full diameter since the relative duration of totality to
the total event length depends in part on where in the primary's cross section that the
passage takes place. This leads to a further consistency check by noting that for passage
exactly along the primary’s widest part, the difference between the time of totality and
the total duration of the event should be (ds/a)P/  1.5 hours, which agrees, within
observational errors, with the measured time difference of 1.6 hours. The mean a/dp,
weighted by the inverse of the variances resulting from the two calculation methods,
yields 3.3  0.2. The fact that this is equivalent, to two significant figures, to the result
calculated from the total duration is not surprising since it is much less sensitive to errors
in timing than the calculation from the length of the bottom plateau.
With this simple model of the system, the density of the primary can then be calculated
using Kepler's Laws as
24
p 
GP 2
 a

d
 p
3

1

.
3
 




 ds  
1    s


p  d p  
 
  

(2)
For the case where s/p  1 and adopting a/dp = 3.3  0.2, this yields
 = 2.2  0.4 g/cm3. The formal errors quoted for diameter ratio (ds/dp), the orbital radius
to primary diameter ratio (a/dp), and the density () are obtained by direct propagation of
the uncertainties associated with the estimates of the depth and the duration of the
January 5 event. However, there are additional uncertainties due to the simplistic
assumption of the model. In particular, this result assumes a spherical primary. Modeling
the primary more generally as an ellipsoid, the approximation that at least two of the axes
are equal is supported by the relatively small lightcurve amplitude. However, the third
axis is unconstrained since calibrated magnitudes exist for only one opposition.
Therefore, the actual errors in the calculated dimensions and density of the Celle system
might be considerably larger than those derived from observational uncertainties alone.
8
Further, the value  = 2.2  0.4 g/cm3 is derived assuming that the primary and
secondary have the same density (s/p  1). It is also possible that the primary is more
fractured than the secondary, or that the secondary is even largely intact. For this case,
s/p > 1, which would imply a bulk density for the primary even lower than 2.2 g/cm3. In
any event, this value for the density, when compared to the densities measured for the
Howardite, Eucrite, and Diogenite (HED) meteorites believed to have come from Vesta
(Kelley et al. 2003), falls in the fractured to rubble pile porosity range as noted in Britt et
al. (2002). The HED’s have densities that range from 2.9 – 3.3 g/cm3 (Kitts and Lodders
1998), which (using a mean of these values) would give approximately 30% macroscopic
porosity for the bodies in the Celle system.
V. Discussion and Conclusions
As mentioned previously, this observational study of the Vesta family is designed to
reveal whether the asteroids have dimensions similar to spalls (indicating intact
fragments from the impact) or whether they more closely resemble ellipsoidal, reaccumulated rubble-piles. If the Vesta asteroid shapes are diagnostic, we can make a
clear conclusion about the manner in which fragments are ejected in a potentially familyforming impact event (intact or re-accumulated), either confirming or refuting current
numerical results. The shape analysis will be the subject of a future paper, however the
density for the Celle system reported in this paper (placing the bodies in the fractured
regime) gives an indication independent of shape studies that some of the family
members may have fragmented interiors. This would be in line (within the error bars and
assumptions above) with the results from Michel et al. (2001) whose numerical outcomes
imply that large asteroid family members are formed via re-accumulation of smaller
ejecta fragments post impact.
A summary of the derived parameters for the 3782 Celle binary system based on the
postulates stated in Section IV is presented in Table 2. The absolute size scales of the
system are based on a primary diameter of 6.1 km. This is calculated using an absolute
magnitude of H=12.5 (Giorgini et al. 1996), a Vesta-like albedo of 0.4, and ds/dp = 0.43.
Additional observations at varying geometries are planned at Celle’s next opposition in
mid-2004 in order to construct a more complete model of the binary system and to refine
this density estimate. This will allow more definitive conclusions to be made as to the
competency of Celle’s internal structure.
Several plausible mechanisms to explain the formation of asteroid binaries have been
discussed in Weidenschilling et al. (1989), Merline et al. (2002), and the references cited
therein. Most likely, there is no single explanation that would apply to binaries observed
within the main belt and in the Near-Earth region. Celle and its satellite are similar sized
bodies, having a primary-to-secondary diameter ratio of ~2.3. It is also a very tightly
bound system with the semi-major axis of the satellite’s orbit equal to 3.3 primary-body
diameters. Therefore, the component and orbital characteristics of the Celle system are
more similar to those for NEA systems (Merline et al. 2002) than other main belt binaries
discovered, although this might be a selection effect of the detection techniques utilized.
9
The mechanism most quoted for NEA binary formation is the tidal splitting theory of
Bottke and Melosh (1996). However this would not apply to the Celle system, or any
other main belt asteroid binary. Hartmann (1979) suggested the possibility that fragments
from collisional events could result in binary systems. Durda et. al. (2004) have
demonstrated numerically that bound systems of fragments from catastrophic and
subcatastrophic collisions are indeed possible and could be a mechanism for the creation
of binaries in the main belt, although they do not specifically examine the outcomes of a
cratering event. Rotational fission, where a single spinning fragment splits into two
smaller ones is also a possibility. The phenomenon of rotational splitting has been
observed in laboratory impact experiments by Fujiwara and Tsukamoto (1980) and by
Giblin et al. (1998). Moreover, based on the nominal dimensions presented in the
previous section, the total angular momentum of the Celle system is consistent with a
spherical parent body rotating with a period of 2.3 hours, which is within the uncertainty
range of critical spin rates for fission of a strengthless body with the the derived density.
Another possibility for the creation of this binary system is that Celle and its secondary
formed as a consequence of a fragment jet. Martelli et al. (1993) noted that laboratory
experiments performed in an open environment allowed them to observe that some of the
ejecta had “clumped” trajectories, which if applied to asteroidal collisions, could result in
gravitationally bound small fragments.
Finally, a preliminary analysis of the other data obtained for the Vesta family members
observed thus far as part of this photometric survey suggest the possibility that the Celle
binary system is not a unique occurrence. At least one other dynamical family member,
3703 Volkonskaya, has displayed lightcurve features similar to the signatures associated
with occultation/eclipse events (W. Ryan, E. Ryan, and C. Martinez, unpublished data,
2003). Therefore, further analysis of Volkonskaya and the determination of whether there
are a statistically significant number of binaries within the Vesta family has now become
another goal of the continuing observational study being undertaken by the authors.
Acknowledgements
This work is supported by NASA Planetary Astronomy Grant NAG5-8734 and is based
on observations with the VATT: the Alice P. Lennon Telescope and the Thomas J.
Bannan Astrophysics Facility. We are very grateful for the generous observing time made
available by the Vatican Observatory Research Group and the telescope operations
support provided by Matthew Nelson and Randall Swift. The authors would like to thank
reviewers R. Binzel and B. Merline for their thoughtful and careful reviews, and S.
Weidenschilling for his perceptive comments. We also wish to thank Lacey Stewart for
observing assistance during the December 2002 run.
10
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Figure Captions
Figure 1.
Composite lightcurve for 3782 Celle from observations taken in September 2001. The
parameter, n, displayed in this and subsequent composite lightcurve plots, is the order of
the Fourier fit that is required to achieve a 2, normalized to the number of data points,
that is the same order of magnitude as the variance of the observed differential
magnitudes.
Figure 2.
Lightcurve data (left) obtained on December 10, 2002 displaying anomalous differential
magnitudes and composite lightcurve (right), excluding anomalous data, for the three
nights of the December 2002 run.
Figure 3.
Lightcurve for January 5, 2003 (left), displaying a three hour anomalous event at
approximately mid-observation and composite lightcurve (right), that excludes data
during the anomalous event, for three days of the January 2003 run.
Figure 4.
Lightcurves from January 27, 28, 30, and 31, 2003 showing anomalous attenuation
events.
Figure 5.
Composite lightcurve for January 26 - February 1, 2003 (excluding anomalous events).
Figure 6.
Figure 6: Lightcurve for January 5, 2003 with the 3.84 hour variation removed.
Figure 7.
Residuals for January 26 - February 1, 2003 after 3.84 hour variation has been subtracted.
Figure 8.
Residuals for January 4 - 6, 2003 after 3.84 hour variation has been subtracted.
14
Tables
Date (UT)
2001 Sept
2002 Dec
2003 Jan
2003 Feb
r(AU)
18.4
19.3
9.4
10.4
11.4
4.3
5.3
6.2
26.3
27.3
28.3
29.2
30.3
31.2
1.2
2.492
2.493
2.595
2.594
2.593
2.578
2.577
2.576
2.562
2.561
2.560
2.559
2.558
2.558
2.557
(AU)
1.500
1.500
1.739
1.730
1.722
1.597
1.595
1.594
1.626
1.630
1.635
1.640
1.645
1.651
1.656
Phase
Angle
()
4.8
4.5
13.2
12.8
12.5
2.1
1.7
1.3
8.6
9.0
9.5
9.9
10.3
10.7
11.2
Ecliptic
Longitude
()
3.6
3.3
113.9
113.8
113.7
108.6
108.4
108.1
103.2
103.0
102.8
102.6
102.4
102.2
102.0
Ecliptic
Latitude
()
8.8
8.8
-1.3
-1.3
-1.3
-2.2
-2.3
-2.3
-2.9
-2.9
-2.9
-2.9
-3.0
-3.0
-3.0
Rmean
(mag)
-*
-*
13.10
13.09
13.09
12.68
12.66
12.62
12.96
12.99
13.02
13.01
13.00
13.04
13.06
Table 1. Geometric Circumstances and Mean R magnitudes, corrected for heliocentric (r)
and geocentric () distances, for 3782 Celle observations.
*
Note: For the September 2001 run, only differential photometry was obtained, and
hence, no mean R magnitudes are given.
15
Primary Rotational period
Orbital Period
Secondary to Primary diameter ratio (ds/dp)
Orbital radius to primary diameter ratio (a/dp)
Primary diameter
Secondary diameter
Orbital Radius
Density of components
3.839  0.002 hours
36.57  0.03 hours
0.43  0.01
3.3  0.2
6.1 km
2.6  0.1 km
20.0  1 km
2.2  0.4 g/cm3
Table 2. Parameter summary for the binary model 3782 Celle based on the postulates of
Section IV. Distances in km are scaled from the primary diameter, which is calculated
assuming H=12.5, an albedo of 0.4, and ds/dp =0.43, and quoted without error.
16