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Icarus 257 (2015) 207–216
Contents lists available at ScienceDirect
journal homepage:
Vesta’s missing moons: Comprehensive search for natural satellites
of Vesta by the Dawn spacecraft
Lucy A. McFadden a,⇑, David R. Skillman a, Nargess Memarsadeghi a, Jian-Yang Li b, S.P. Joy c,
C.A. Polanskey d, Marc D. Rayman d, Mark V. Sykes b, Pasquale Tricarico b, Eric Palmer b,
David P. O’Brien b, Stefano Mottola e, Uri Carsenty e, Max Mutchler f, Brian McLean f, Stefan E. Schröder e,
Nicolas Mastrodemos d, Conrad Schiff a, H. Uwe Keller g, Andreas Nathues h, Pablo Gutiérrez-Marques h,
C.A. Raymond d, C.T. Russell c
NASA Goddard Space Flight Center, Greenbelt, MD 20771, United States
Planetary Science Institute, Tucson, AZ 85719, United States
IGPP, UCLA, Los Angeles, CA 90095, United States
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, United States
DLR – German Aerospace Center, Institute of Planetary Research, Berlin, Germany
Space Telescope Science Institute, Baltimore, MD 21218, United States
Institut für Geophysik und Extraterrestrische Physik (IGEP), University Braunschweig, Germany
Max-Planck Institute for Solar System Research, 37077 Göttingen, Germany
a r t i c l e
i n f o
Article history:
Received 11 August 2014
Revised 25 March 2015
Accepted 29 April 2015
Available online 5 May 2015
Asteroid Vesta
Asteroids, dynamics
Satellites of asteroids
a b s t r a c t
Earth-bound searches for natural satellites of 4 Vesta have been reported since 1987. With use of technological advances and observing capability has come a reduction in the detectable size of a possible
satellite. The Dawn mission brought a small camera close to Vesta itself. In our search, which was carried
out with a comprehensive data acquisition strategy and by experienced searchers, we find no satellites to
a detection limit as small as 3-m radius. Various observation and analysis strategies are discussed in
detail. It is now time to factor the null result of this search into the context of satellite formation among
other main belt asteroids and to conduct dynamical modeling to explore the suspected forces contributing to the absence of satellites at Vesta today.
Ó 2015 Published by Elsevier Inc.
1. Introduction
Within the Solar System many objects have natural satellites
that are bound to the primary body as it also orbits the Sun.
Earth’s moon, the Outer Planets’ satellite systems, some Kuiper
Belt Objects (KBOs) (Veillet et al., 2002; Noll et al., 2008) and
even small near-Earth objects (NEOs) (Margot et al., 2002) are
examples. The presence or absence of a satellite has implications
for the primary body’s collisional and dynamical history, and permits measurement of mass, size and bulk density. Within the
Main Asteroid Belt, almost 100 asteroids with co-orbiting, smaller
bodies within the gravitational sphere of influence (SOI, the
region around an asteroid where the primary gravitational
influence on an orbiting body is that body) (e.g. Bate et al.,
⇑ Corresponding author at: Planetary Systems Laboratory, Code 693, Goddard
Space Flight Center, 8800 Greenbelt Rd, Greenbelt, MD 20771, United States.
E-mail address: [email protected] (L.A. McFadden).
0019-1035/Ó 2015 Published by Elsevier Inc.
1971) of the larger asteroid are known (e.g. Johnston, 2014;
Merline et al., 1999, 2002). We compare Vesta’s gravitational
SOI with Earth, Jupiter, Ceres, a NEO and Pluto in Table 1. Ceres
contains approximately a third of the current asteroid belt by
mass (e.g. O’Brien and Sykes, 2011), with Vesta being the second
most massive. Vesta has a reasonably-sized SOI relative to other
bodies with natural satellites, and if the conditions exist for
capture or retention of ejecta from an impact on Vesta, one might
expect satellites to exist if not now, then in the past. 1999 KW4, a
small Earth-crossing binary system (Ostro et al., 2006), has a SOI
that is orders of magnitude smaller than Vesta’s. Further, its value
varies by almost a factor of 2 throughout its orbit, yet its satellite
remains. Dynamical models of the formation of the asteroid belt
require migration of bodies from the Kuiper Belt to populate
the asteroid belt (Levison et al., 2009; Walsh et al., 2012) and
many KBO’s are multiple systems. Satellite capture requires a
mechanism in which energy is lost to match the orbital velocity
of the primary.
L.A. McFadden et al. / Icarus 257 (2015) 207–216
Table 1
Comparison of the gravitational sphere of influence (SOI) for some planets, asteroids and dwarf planets.
Object name
Mass (kg)
1999 KW4
1999 KW4 (perihelion)
1999 KW4 (aphelion)
Sphere of influence r A ¼ dA
1.99 10
5.97 1024
1.90 1027
2.59 1020
9.34 1020
2.4 1012
2.4 1012
2.4 1012
1.31 1022
Distance from Sun (km)
Radius (km)
Sphere of influence (SOI)a (km)
Relative SOIb
1.50 108
7.79 108
3.54 108
4.14 108
9.61 107
1.62 108
2.99 107
5.87 109
9.245 105
4.822 107
3.937 104
7.684 104
3.13 106
, where dA is distance from Sun,
is mass relative to the Sun.
SOI scaled to body’s radius.
Binzel and Xu (1993) located asteroids with similar spectral signatures as Vesta’s lying in its orbital plane with semi-major axes
between the m6 secular resonance with Saturn at 2 AU and the
3:1 Kirkwood Gap at 2.5 AU. These asteroids comprise the dynamical Vesta family. Hubble Space Telescope images and subsequent
analysis of Vesta’s shape (Thomas et al., 1997) suggested a large
basin that was subsequently resolved into two very large basins,
Rheasilvia and Veneneia, imaged by Dawn’s Framing Camera (FC)
as the spacecraft approached and orbited Vesta in 2011–2012
(Jaumann et al., 2012; Schenk et al., 2012). Ejecta from these basins
likely produced the Vesta family (Marzari et al., 1996; Zappalà
et al., 1984). Dynamical modeling prior to the Dawn mission suggested an impact by a 42 km body, 1 billion years (byr) ago
(Asphaug, 1997). Remarkably, crater size frequency distributions
support this age (Schenk et al., 2012; Marchi et al., 2012). An alternate and older age determination of these basins (3.5 and 3.7 byr)
is presented by Schmedemann et al. (2014), assuming a lunar-like
crater production function. Chaotic dynamics and secular perturbations (Wisdom, 1985) have resulted in fragments from Vesta colliding with Earth, surviving passage through Earth’s atmosphere
and being found as meteorites; the Howardite–Eucrite–Diogenite
(HED) group (McSween et al., 2011). There are samples of Vesta
in the terrestrial meteorite collection, there are craters formed
from collisions and reaccumulation of ejecta fragments on Vesta’s
surface (e.g. Russell et al., 2012; Jaumann et al., 2012).
Given the large amount of ejecta from Vesta and the varied
dynamical outcomes that resulted, it is logical to ask if any fragments entered into orbit around Vesta, either directly or after a
re-encounter. The above considerations lead us to ask if there are
any satellites remaining in Vesta’s orbit today?
Direct imaging (Gehrels et al., 1987), coronographic imaging
(Gradie and Flynn, 1988), speckle interferometry (Roberts et al.,
1995) and imaging with Hubble Space Telescope (McFadden
et al., 2012) have been used to search for satellites orbiting Vesta
in the past. None have been found to a previously reported size
limit of 22 m radius. Until now, the region inside of 14 Vesta radii
(3500 km) had not been searched due to scattered light from
Vesta. Is it due to chance that neither satellites nor a debris field
are remnant in orbit around Vesta today? Were the instruments
that searched for satellites in the past inadequate to detect anything orbiting Vesta? Or has the past collisional history removed
any object or objects that once may have been in orbit around
The Dawn spacecraft spent more than a year at Vesta and we
searched again for natural satellites. We designed a search that
would improve upon past searches by looking closer to Vesta than
possible in previous efforts. In this paper we describe the two
observational sequences acquired for the satellite search using
Dawn’s FC and report processing and preparation for search by
the team of satellite searchers. Seven observers searched and
reported that no satellites were found. However, we did find moving objects including background asteroids, cosmic rays and something close to the camera and moving fast that is probably debris
from the spacecraft. Next, we determine the upper limits of detection by implanting simulated objects with randomly chosen orbits
and magnitude into a subset of the satellite search images. The
observers searched again and report their findings in Section 6.
Upper limits of detection in the meter-size range are then calculated assuming the same albedo and phase function as Vesta. We
discuss our approach and consider changes for future satellite
searches in the final section and consider the implications for the
absence of satellites in the context of the impact and ejecta history
of Vesta in the discussion.
The mission’s approach phase included searching for satellites
around Vesta for more than two months. During these sequences,
Vesta was targeted on a regular basis and if there were a satellite,
this was the time when it would most likely be observed and not
occulted by Vesta itself. Our upper limit of detection during
approach was an object 5.3 m radius assuming Vesta’s global geometric albedo of 0.38 (Li et al., 2013). During a dedicated satellite
search mosaic, carried out at three different times, the limiting
radius of detection was 3.1 m and 4.3 m for 20 s and 270 s exposures respectively. We discuss the reason for the reverse relation
between detection limits and exposure times in Section 6. If any
larger collisional ejecta were in orbit around Vesta in the past, they
are not there now.
2. Observations and search approaches
The satellite search was carried out with Dawn mission’s FC
(Sierks et al., 2011) an F/7.5 imager with a focal length of
150 mm, 5.5° 5.5° field of view and pixel size of 19.23 arcsec as
determined using Astrometrica software (Raab, 2011). The clear filter, designed for detecting stars, dust and the moon search, was
always used to maximize photon collection and signal. Two data
acquisition schemes were used; (1) direct pointing at Vesta beginning at 1.24 million km range, and (2) acquisition of a dedicated
satellite search mosaic. The data sets were processed and analyzed
using 5 different approaches, all of which complement each other
and result in an increased reliability of the search results. We discuss the data acquisitions followed by the data processing that produced searchable images.
2.1. Direct pointing
Direct pointing at Vesta served the project’s optical navigation
(OpNav) requirements and for the satellite search, included 14
acquisitions each consisting of 20 successive, 1.5 s exposures
pointed at Vesta. These were also used to design the ion propulsion
L.A. McFadden et al. / Icarus 257 (2015) 207–216
thrust sequences that put the spacecraft into orbit around Vesta
and to determine exposure times and data compression settings
for orbital science observations. There were two additional
sequences called Rotational Characterization 1 (RC1) and
Rotational Characterization 2 (RC2) to determine Vesta’s pole orientation. These sequences included ride along ‘‘OpNav’’ imaging consisting of alternating 0.008 s (for Vesta) and 1.5 s exposures (for
stars), 36 in RC1 and 52 in RC2, taken within 3–6 min in time, a
shorter interval than the 0.5–2.0 h of the ‘‘standard’’ OpNav
sequences. We used the 1.5 s exposures to search for satellites.
Images from each sequence were coadded and searched for the
presence of satellites. An example is shown in Fig. 1. Table 2 presents observing circumstances at each OpNav and RC along with
the size of Vesta in pixels and the limiting detectable radius
derived from the experiment with implanted objects described in
Section 5. The orbital period of satellites in circular orbit around
Vesta ranges from 1.77 to 159 h for orbits from 1 to 20 Vestan radii.
The variation in the duration of the OpNavs allows for detection of
motion of potential satellites across more than one pixel.
2.2. Satellite search mosaic
The satellite search mosaic images extended 5000 km (20
Vestan radii) from Vesta’s surface. This region is designated the
operational sphere in which the spacecraft orbited (Polanskey
et al., 2011). The goal was to search for objects smaller than
Hubble Space Telescope’s limit of 22 m in radius (McFadden
et al., 2012) and closer to Vesta than previously searched (14
Vestan radii). The first mosaic sequence was carried out before
RC2, on 2011 July 9. At each image mosaic station, 4 sets of 3
images with 1.5 s, 20 s and 270 s exposures respectively, commanded at 5 s intervals were acquired (Fig. 2A). There are six
mosaic stations (Fig. 2B) with data collection at intervals of
21 min each, with 10 min turn and settle periods between stations.
A single mosaic took 2:45 h. This mosaic pointing and data acquisition was carried out twice before RC2 observations. Mosaic 3
began after a complete Vesta rotation of 5.4 h and was completed
on 2011, July 10, 8:17. The goal was to have order of magnitude
scaling in the image exposure durations and image time separations (Fig. 2C) because we are searching for objects with no known
constraints in orbital characteristics other than being gravitationally bound to Vesta. As implemented, the time between the first
and second mosaic was 186 min and 785 min between the first
and third mosaic. A total of 216 images were commanded, two
were corrupt resulting in 214 usable images. The station pointing
is listed in Table 3. For reference, a body orbiting close to Vesta
has an orbital period of 1.77565 h, while an orbit at 20 Vestan radii
has a period of 452.12235 h (18.83843 days).
3. Data processing and search approaches
Fig. 1. Eighteen RC2 images scaled and coadded to enhance stars and possible
satellites. A satellite, if detected, would have a trail in a different direction relative
to background stars and with the same number of detections as background stars,
yet spaced according to its relative motion with respect to Vesta.
The satellite search team used multiple methods of processing
and searching and the data were scanned by many sets of eyes,
an important point given that we found no satellite to the detection limits of the FC. Using different and independent approaches
and searching with multiple and experienced eyes added certainty
to our results. We designed our processing schemes from previous
successful searches for satellites of Pluto (e.g. Steffl et al., 2006) and
considered the capabilities of the FC and the spacecraft’s motion.
Image processing and algorithms used for data processing are
Table 2
Observational circumstances during direct pointing satellite search with limiting magnitude 10.7 as determined from implanted objects into OpNav 16.
Heliocentric distance (AU)
Range to Vesta (km)
Phase angle (°)
Vesta apparent
size (FC pixels)
Limiting detectable
radius (m)
Note that numbering of the OpNavs has gaps for the following reasons: OpNav11 was lost due to spacecraft going into safe mode. OpNav14 was cancelled to make up
thrust time lost during safe mode status. There were OpNav sequences added to RC1 and RC2 yet the naming is as listed in the table.
L.A. McFadden et al. / Icarus 257 (2015) 207–216
Table 3
Station pointing for satellite search mosaics.
Mosaic #1
2011 July 09
Mosaic #2
2011 July 09
Mosaic #3
2011 July 10
Group 1 conducted three major tests that were used and refined
as Dawn approached Vesta:
Visual motion detection with Vesta at the center
Visual motion detection with the star field co-registered
Stacked images showing star and satellite trails [Stacked].
Fig. 2. (A) Schematic representing the timing of exposures within a single mosaic
station of the dedicated satellite search sequence. (B) Schematic representing the
positions of the FC’s footprint (squares) relative to Vesta (center disk) and the
planned orbits for the Dawn spacecraft (ellipses). (C) The cadence in time of the
three satellite search mosaics designed to reduce the chance of the search aliasing
with a satellite’s revolution.
described in Memarsadeghi et al. (2012) and are summarized in
Fig. 3. All procedures include image processing to subtract dark
and bias frames and remove the instrument’s flat field.
When calibrated data (level 1B) (Schröder et al., 2013) were
released, we repeated the searches to see if satellites could be
detected with the improved calibration. During the early OpNav
sequences, the images were processed to generate Integrated
Software for Imagers and Spectrometers (ISIS) cubes (Edwards,
1987; Anderson et al., 2011) with dark field correction, a correction
to eliminate shutter-induced smearing, and image stretch to compensate for scattered light. Then using the blink routine in ISIS, we
searched through the stack of images looking for motion. The
Motion-Vesta technique required the least amount of
processing. The star field moved only a few pixels within the image
and between images for the early OpNav sequences. As Dawn got
nearer, every star in the field moved on the order of 10 or more
pixels. A satellite orbiting Vesta would either be a point of light
moving in a different direction than the stars, or if its orbital velocity were low, it would remain fixed in the frame with the same relative position as Vesta.
The Motion-Star search required co-registering stars to remove
their motion. This was done using the coregistration (‘‘coreg’’)
function in ISIS. Again, we used the blink routine to search for
motion. For these image sets, the stars are fixed in the frame while
Vesta moves. If a satellite were present it would be noticed by its
motion relative to stationary stars. This search technique was more
useful than the Motion-Vesta technique until Dawn was nearer
Vesta. At close range, the star field changed too much between
the first and last image so co-registration, designed for small offsets, was not possible.
The stacked technique was found to be an easier way to search
for satellites, although it was not as robust. For this test, we
stacked the OpNav images into a cube and read the 3D cube into
IDL. For each sample and line of the 3D cube, we took the highest
data number (DN) value to generate an image of the maximum values. Because the image is mostly black except for stars, the resulting maximum value images showed the star as trails while
suppressing scattered light and noise (Fig. 3A). Vesta remained
dominantly in the center of the frame while the background stars
produced dotted trails in parallel lines. A satellite would be noticed
as a trail of light that had a different direction and point spacing,
assuming there was not an exact match with the star motion.
Additionally, once Vesta became large in the field of view
(OpNav 6), we began to use a high pass filter to remove the scattered light. We used the ISIS routine, highpass with both samples
and lines set to 11. This technique allowed us to see closer to
L.A. McFadden et al. / Icarus 257 (2015) 207–216
Fig. 3. (A) OpNav images stacked into a cube and filtered selecting the highest data number (DN) value. This image shows Vesta dominating with background stars as trails.
(B) A high-pass filter removes background stars, leaving only bodies moving less than a pixel during the sequence and/or persistent and known image artifacts. (C) Output
from automated processing pipeline. Circles denote known catalog stars and squares are ‘unidentified objects’ needing follow-up examination. (D) Difference of two images,
one created by coadding the first three images in the sequence, the other coadding the last three images in the sequence.
Vesta even when the scattered light was significant. To search for
satellites with low orbital velocity in a sequence, after the
high-pass filter, images were combined taking the median value
of each pixel (median filter). This removes both cosmic rays and
background stars, leaving only image artifacts (Fig. 3B) and satellites that moved less than a pixel during the sequence. This was
done with data from OpNav 10, 13, 16, 17 and 18. No satellites
were found.
Another searcher, (named group 2), blinked images using a commercial software package Maxim-DL (2008) and Astrometrica
(Raab, 2011) after calibration and solving to determine world coordinates using (Lang et al., 2010). Animated gif files
were produced providing another method of visual scanning. In
these data products, a moving target would reveal itself in long
exposures pointing at Vesta by motion in a different direction than
the background stars when images in a time sequence were stacked
and registered. Images with suspected moving targets were examined frame by frame for the following conditions that are required
of a true detection of an object: (1) deviates from the system point
spread function (PSF) because of motion of the putative satellite, (2)
the appearance of the object in each frame in the time sequence and
(3) absence of image artifacts or hot pixels at the position of the suspected satellite. When blinking many images, the eye can note and
ignore cosmic rays as they are short lived and do not have a system
PSF. An unsharp mask filter was used to enhance high frequency
signal by one of the co-authors (group 3). This approach, coupled
with visual searching, with no detection software, has yielded
positive results in the past (Weaver et al., 2006; Stern et al., 2007;
Showalter et al., 2012).
Two independent groups used algorithms for automated object
detection and compared the identified objects to those in star catalogs (group 4a, b). The process used by group 4a, began with
astrometric calibration followed by alignment of both raw and
median filtered data sets by reading into SAOImage DS9 (2014).
They were then overlain with the Tycho-2 star catalog. All bright
sources were identified with stars or hot pixels. Upon detecting
object motion, the star-aligned and stacked image was compared
with a ground-based archive image of the same sky region showing
that no bright star is present at the position of the asteroid, and
confirming that other bright sources on the FC image correspond
to stars.
The second of group 4, 4b, used an automated star matching
process. The raw data in Flexible Image Transport System (FITS)
files from the Dawn Science Center were processed through (Lang et al., 2010) to obtain an approximate
World Coordinate System (WCS) transformation. Each image was
then processed through a series of common pipeline steps including dark removal, bias subtraction, flat-field removal, and
unsharp-masking. Following this, an image detection algorithm
based on DAOPHOT (Stetson, 1987) was applied to find objects
with a Gaussian PSF and reject any objects found within a couple
pixels of known hot/bad pixels. The approximate WCS solution
was used to automatically identify stars from the Guide Star
Catalog (Lasker et al., 2008) and UCAC3 (Zacharias et al., 2010)
L.A. McFadden et al. / Icarus 257 (2015) 207–216
catalogs. A new astrometric calibration based on a cubic polynomial fit to the detector plane was computed with a typical rms
(root mean square) of 15–20 arcsec. An approximate photometric
calibration was also computed fitting a polynomial between the
fluxes and catalog magnitudes that have typical rms of 0.3 magnitudes. The calibrations were put back into the FITS headers as new
keywords. Objects from this series of image catalogs that did not
match a known catalogue star became candidates for further processing. An example is shown in Fig. 3C. Candidates that appeared
to move with respect to the background objects were visually
examined for confirmation or rejection.
In a fifth approach, the first three images and the last three
images in a sequence or OpNav were summed, and subtracted
one from the other (Fig. 3D). If there were a moving object, the differenced image would show a dark–bright signature of different
orientation and spacing between dark and bright signatures of
the stationary background stars. The technique worked until the
spacecraft was closer to and pointed at Vesta. At this point, the
background stars were not stationary and image registration was
4. Results
4.1. OpNav and RC1, RC2 searches
No satellites were found in the OpNav nor RC1 and RC2
sequences. Background asteroids and some fast moving things
were detected and are described below. In advance of data acquisition, known background asteroids were identified in the camera’s
field of view using 553,917 objects in the Minor Planet Catalog. In
order to be visible by Dawn, an asteroid has to be within 2.74° of
the center of Vesta when it is in the center of the field, as is the case
for OpNav images and RC1 and RC2 sequences. 511 Davida was
found during OpNav 3 on May 17, 2011 at V magnitude of 11.5.
We knew ahead of time that Davida was in the field of view, and
because we did not know where, it is considered a found object.
We thus consider 11.5 magnitudes an upper limit to detection
because the images had to be stacked in order to satisfy the
requirement noted in Section 3 that the PSF deviate from the system PSF. The brightest anticipated asteroid was 487 Venetia, which
was observed in OpNav 4 on May 24, 2011 at V magnitude of 10.9
found by blinking images in the sequence. Both 487 Venetia and
511 Davida were detected by comparing the images to a
ground-based field of background stars (Fig. 4). If there is no background star and the image has the characteristics of the system
PSF, the asteroid is considered detected. Through the course of
the sequence, neither of these asteroid’s relative motion extended
beyond a single pixel.
Another asteroid of interest was 206,978 (2004 TP110), at magnitude 12.8 and 7 million km from Vesta. It was not detected, further bounding the detection limits of the camera and a check to the
experimental simulation described in the next section. With this
asteroid’s large motion of 8 arcsec/min it would have moved
across multiple pixels were it detected.
Fig. 5 shows a fast moving object that was seen in four frames.
The most probable explanation is that small debris from the spacecraft is moving through the field of view of the FC. It is so close that
it is out of focus, as the PSF is large as is its motion relative to the
spacecraft. These out-of-focus streaks have been seen regularly
since launch in 2007 and have been determined to be unimportant
for science or engineering.
4.2. Mosaic search
Considering the orbital dynamics of expected objects in orbit
around Vesta, combined with the motion of the spacecraft with
Fig. 4. (A) Circle marks asteroid 511 Davida found in OpNav 3 on May 17, 2011.
Because it is a distant asteroid, its motion is less than a pixel during the OpNav
sequence (68.5 min). (B) Asteroid 487 Venetia is in the field of view during OpNav 4
on 5/24/11 also with no detectable motion.
respect to Vesta, almost all possible satellites will stay in a single
pixel during a 20 s exposure, and almost all satellites will trail
across multiple pixels during the 270 s exposures. In any search
for reasonably fast moving objects using the 270 s exposures, the
sought-after signature will be a trail of several, up to 20 pixels.
We found no objects in orbit around Vesta after processing, blinking and scanning the mosaic search images.
Minor planet 972 Cohnia was found at magnitude V = 11 in
Mosaic 1 station 1 at RA = 20 10 57.0, DEC = +09 21 21. Its
expected motion of 1.08 arcsec/min would have barely carried it
to the next pixel during station 1’s data acquisition duration of
20 min. Due to some overlap in the stations, this asteroid also
appears in station 6 taken almost 3 h later and the asteroid moved
almost 10 pixels to RA = 20 10 51.82, DEC = +09 24 00.1 with
S/N 9. Other asteroids are predicted to be in the field of view
and were not found because they were too faint.
5. Generating and implanting synthetic satellites to determine
upper limits
To implant synthetic satellites on the FC images, we used a software image simulator developed for the proposed German
‘‘AsteroidFinder’’ space mission (Mottola et al., 2008). The simulator realistically reproduces the basic steps of the image formation
process: optical transfer through the optics, image projection onto
the detector, charge accumulation in the CCD, charge transfer and
the readout process. In order to represent moving objects, the
exposure is divided into discrete time steps, the number of which
is algorithmically determined based on the apparent speed of the
object. For each time step, the input point source, a Dirac Delta
L.A. McFadden et al. / Icarus 257 (2015) 207–216
Fig. 5. A sequence of 4 exposures acquired during Mosaic 1. (A) (Far right) 270 s exposure shows a streak moving from right to left. The second through fourth frames are (B)
1.5, (C) 20 and (D) 270 s exposures respectively and show trails proportional to the exposures. The object was in the field of view for almost 2 min. Its large PSF indicates that
it is out of focus and close to the spacecraft.
function, is convolved with the PSF of the FC optics (Sierks et al.,
2011), which is approximated with a Gauss function with a Full
Width at Half Maximum (FWHM) of 1.5 pixels. In order to provide
a realistic image simulation, the CCD pixels are oversampled by a
factor of 24 in each spatial dimension. The projected position of
the light source onto the CCD at each time step is computed based
on the apparent position of the object, which in turn depends on
the object’s motion and on the spacecraft’s pointing instability.
The latter is modeled in two parts: a random jitter and a systematic
drift, the motion vector of which is assumed to be constant during
an individual exposure, but its direction is changed in a random
way between exposures.
The input photon flux for each sub-pixel and time step is then
integrated and converted into electrons by multiplication by the
sub-pixel Quantum Efficiency (QE). The FC CCD features a lateral
anti-blooming gate to reduce charge spilling as under circumstances of extreme overexposure. However, because of this, the
portion of the pixel beneath the anti-blooming gate (about 30%
of the pixel surface) is insensitive to light. This effect is modeled
in the simulator by introducing an intra-pixel QE map.
After all sources have been integrated, photon noise is added for
each pixel, following Poisson statistics. At this point, the parallel
charge transfer process is simulated, in the course of which the
effects of the electronic shutter smearing and charge transfer inefficiency are computed. Finally, the readout process is simulated,
during which the conversion to digital units takes place, according
to the camera system gain, and readout noise is optionally added.
In this particular case, however, as the simulated image was added
to a real FC image, no additional readout noise was added, as it is
already present in the original image.
The magnitude zero point is based on the optics’ theoretical
performance and on the CCD data sheet provided by the manufacturer. A subsequent analysis of photometry calibrated to the V
magnitude of stars in the UCAC3 star catalog yielded a photometric
equation with a zero-point shift of 0.165 magnitudes, only a few
percent different from that used to generate the satellites in this
experiment. We therefore consider the upper limits to have an
uncertainty of 0.2 magnitudes. We selected OpNav 16 (Fig. 6)
and the three exposures at mosaic station 5 to insert simulated
satellites using the method described above. OpNav 16 was
selected as an optimum sequence because the spacecraft was close
to Vesta and scattered light did not dominate the signal from stars.
Station 5 images were selected because of the absence of abundant
and inhomogeneous scattered light from Vesta. In other words,
these data sets were selected to test the faintest detections that
our searchers would make. We define this as the limiting magnitude. It was not practical to search all images again. The satellites
are in randomly oriented circular orbits with radii 1.1–100 Vesta
radii, starting position angle, inclination (between cos i = 1 to
cos i = 0), and l, the ascending node, are also randomized as is their
magnitudes, though limited to a range of 7–13.
6. Search for implanted objects: results
The team searched the selected images containing randomly
implanted satellites with randomly generated magnitudes, and
reported the positions of each satellite found. We present the compiled detection efficiency achieved by each searcher in each image
set in Fig. 7A–C. All false detections were reexamined to be sure
they were not real objects. None were.
In OpNav 16, at a magnitude range of 8.5–9.0 (see
Supplementary material Table S1), corresponding to radii of
15.6–12.4 m, 50% of the searchers found 50% of the objects and
50% did not. This is roughly equivalent to a search completeness.
The faintest object found was 10.7 magnitude corresponding to a
radius of 5.7 m. The size of an object detected at each OpNav is calculated by scaling the limiting magnitude at OpNav 16 assuming
Vesta’s phase law and V-band geometric albedo of 0.38 (Li et al.,
2013) until Vesta filled the field of view (Table 2). The smallest
detectable radius was 5.3 m at OpNav 17. The mission’s OpNav
observations span 3 months, a factor contributing to the robust
nature of the search. The earlier detection size (at 50% efficiency)
of 22 m radius, determined with Hubble Space Telescope
(McFadden et al., 2012), was reduced between OpNav 10 and the
RC1 sequences to radius 18.1 m. Nothing was found larger than
5.3 m radius.
In Fig. 7B the fraction of objects found by 4 searchers at
half-magnitude intervals, referred to as search or detection efficiency, are shown for station 5, 20 s exposures (see
Supplementary material Table S2 for details of each searcher).
The 50% detection efficiency magnitude is between 10.5 and
11.0, corresponding to radii of 8.0 and 6.3 m, respectively. The
faintest object found in the 20-s exposures was 12.57 magnitude
or 3.1 m in radius for the observing circumstances (rh = 2.219 AU,
D = 37,929 km, phase = 28.7°) of the mosaic acquisition. For the
270-s exposures (Fig. 7C and Supplementary material Table S3),
the 50% efficiency occurred at 11.0–11.5 magnitudes or 6.3–
5.0 m radii, respectively. One searcher found an object at 11.82
magnitude or 4.3 m radius. We expected fainter objects to be
detected in 270-s exposures, while in fact the opposite is true.
Most likely, this results from higher background noise from scattered light from Vesta in the longer exposure, as well as the fact
that any fainter and fast-moving objects would spread across more
pixels, resulting in a brighter limiting magnitude of detection.
Thus, the 20 s exposures when co-added provide fainter detection
limits than the 270 s exposures. But the completeness level is
fainter in the 270 s exposures.
Examining both Fig. 7 and Tables S1–S3 show that different
observers had different search efficiencies. Some searchers missed
some brighter objects, yet found very faint ones. Visual acuity is
one criterion for effective searching, experience another, and
method of searching, yet another variable. The figures, as well as
results from previous satellite discoveries (Pluto’s moons for
L.A. McFadden et al. / Icarus 257 (2015) 207–216
possible that this repeated encounter has a pumping action that
clears Vesta of any satellites? As far as we know, this line of inquiry
has not previously been proposed and it may be worthy of further
Another candidate explanation is the idea that stable orbits
around Vesta are precluded by the particular structure of its gravitational field. Vesta’s gravity field is lumpy and contains spin–orbit resonances that make some orbital regimes dynamically
unstable as discussed by Tricarico and Sykes (2010). They also
point out regimes in which spin–orbit resonances are stable.
While their results were computed based on relatively
short-term numerical integrations prior to Dawn’s arrival at
Fig. 6. Synthetic satellites were inserted into OpNav 16 images. Satellites with
random orbits are seen with a trajectory that is markedly different from the
background stars that trail in the direction of spacecraft motion when the
spacecraft is pointed at Vesta.
example Weaver et al., 2006), indicate that the discovery of any
small body bears a component of chance. The faintest object
detected, of magnitude 12.57, was found by blinking and visual
detection by an experienced observer who has found asteroids previously. There were detections by the semi-automatic approach
that were missed by the visual searchers and vice versa. In the
OpNav 16 sequence with 1.5 s exposures, two visual observers
detected objects fainter than 9th magnitude, yet missed objects
of 6th magnitude. It is clear that to increase the detection limit
of a search, multiple, experienced observers are needed and that
multiple approaches improve the chances of detection.
7. Discussion
Why might we expect to find natural satellites gravitationally
bound to Vesta? First it is a fairly common state for minor planets
with a number of cases found among the Main Asteroid Belt, the
Kuiper Belt and Near Earth populations. Second, bound systems
persist, seeming to be robust to perturbations. 1999 KW4, a small
Earth-crossing binary system (Ostro et al., 2006), follows a highly
elliptical orbit with aphelion and perihelion distances of 1.08 and
0.20 AU respectively. Its motion exposes the binary to large variations in tidal forces, especially as it passes near to the Sun, yet it
currently has a satellite. Is there something peculiar to Vesta that
prevents it having a companion? We offer three possible explanations to account for its ‘‘missing moons.’’
First is that there is no mechanism preventing Vesta from having moons except for the ‘‘luck of the draw.’’ Vesta has a reasonably
large SOI. Yet there must be a mechanism that allows a body to
lose energy in order to be captured. The conditions of capture
may never have existed for Vesta.
Secondly, there may be a mechanism that strips Vesta of any
orbiting satellites. In this context, any object that avoids the fates
of either colliding with Vesta or failing to capture, could only persist in bound motion for a short period of time. One possible mechanism is the periodic encounter between Vesta and Asteroid 197
Arete. Every 18 years, Arete passes within 0.04 AU of Vesta from
which an early mass of Vesta was derived (Hertz, 1968). Is it
Fig. 7. (A) Detection efficiency (fraction found) for satellites inserted in OpNav 16
sequence binned at 0.5 magnitude intervals from 4 searchers’ efforts. (B) Same for
station 5 of the satellite search mosaic, 20 s exposure images from 4 searchers. (C)
Same for station 5, 270 s exposures conducted by 7 searchers.
L.A. McFadden et al. / Icarus 257 (2015) 207–216
Vesta, they strongly suggest that the lack of orbiting satellites cannot be caused by irregularities in Vesta’s gravitational field.
Numerical simulations of impacts (e.g. Durda et al., 2004) constrain the amount of material that could be launched into orbit,
and long-term integrations might be used to constrain the lifetime
of such satellites. If the formation and lifetime of orbiting bodies
around Vesta were examined one result might provide insight into
the question of whether Rheasilvia, if it were the primary source of
ejected material, is on the order of 1 byr old (Marchi et al., 2012) or
much older (>3 byr) as determined by Schmedemann et al. (2014).
The formation of the more recent and smaller Marcia crater
(Williams et al., 2014) should also be considered while modeling
the lifetime of material in orbit around Vesta. In any event, the
absence of a natural satellite in orbit around Vesta today is a fact
to be considered in any modeling scenario of Vesta’s impact history.
8. Conclusion
The satellite search carried out with the Framing Camera on
Dawn is comprehensive in terms of the proximity of the spacecraft
to Vesta, the time spent searching and the number of searchers and
diversity of analysis approaches used. We have reduced the limiting radius of any possible satellite by a factor of four over previous
studies. At this point, we take the lack of moons around Vesta as a
supported fact with little probability of being overturned. Rather
than regarding it as a simple null result, we believe it offers clues
to Vesta’s collisional history and dynamical environment.
We thank Herbert Raab for working with us to modify
Astrometrica so that asteroids could be projected into the Dawn
spacecraft’s frame of reference. The Dawn Flight Team made the
observations possible and we thank them for their superior driving
and operations implementation. This work was supported by the
Dawn mission through NASA’s Discovery Program, NASA’s Dawn
at Vesta Participating Scientist Program through Grants
NNX10AR56G to University of Maryland at College Park and
NNX13AB82G to Planetary Science Institute. Part of this work
was carried out at the Jet Propulsion Laboratory, California
Institute of Technology, under a contract with NASA to UCLA
NASA contract number, NNM05AA86C. The Framing Camera project is financially supported by the Max Planck Society –
Germany and the German Space Agency, DLR.
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