The orbit, mass, size, albedo, and density
of (65489) Ceto/Phorcys:
A tidally-evolved binary Centaur
W.M. Grundy1, J.A. Stansberry2, K.S. Noll3, D.C. Stephens4, D.E. Trilling2,
S.D. Kern3, J.R. Spencer5, D.P. Cruikshank6, and H.F. Levison5.
1. Lowell Observatory, 1400 W. Mars Hill Rd., Flagstaff AZ 86001.
2. Steward Observatory, University of Arizona, 933 N. Cherry Ave., Tucson AZ 85721.
3. Space Telescope Science Institute, 3700 San Martin Dr., Baltimore MD 21218.
4. Formerly at Dept. of Physics and Astronomy, Johns Hopkins University, Baltimore MD 21218;
now at Dept. of Physics and Astronomy, Brigham Young University, N283 ESC Provo UT 84602.
5. Southwest Research Institute, 1050 Walnut St. #400, Boulder CO 80302.
6. NASA Ames Research Center,  MS 245-6, Moffett Field CA 94035.
In press in Icarus 2007
Primary contact: Will Grundy
E-mail: W.Grundy@lowell.edu
Voice: 928-233-3231
Fax: 928-774-6296
Running head: Binary Centaur (65489) Ceto/Phorcys
Manuscript pages: 25
Figures: 5
Tables: 5
ABSTRACT
Hubble Space Telescope observations of Uranus- and Neptune-crossing object (65489)
Ceto/Phorcys (provisionally designated 2003 FX128) reveal it to be a close binary system.  The
mutual orbit has a period of 9.554 ± 0.011 days and a semimajor axis of 1840 ± 48 km.  These
values enable computation of a system mass of (5.41 ± 0.42) × 1018 kg.  Spitzer Space Tele-
scope observations of thermal emission at 24 and 70 µm are combined with visible photometry to
constrain the system's effective radius (109
�11  km) and geometric albedo (0.084
�0.021
�0.014 ).  We esti-
mate the average bulk density to be 1.37
�0.66
�0.32  g cm
, consistent with ice plus rocky and/or car-
bonaceous materials.  This density contrasts with lower densities recently measured with the
same technique for three other comparably-sized outer Solar System binaries (617) Patroclus,
(26308) 1998 SM165, and (47171) 1999 TC36, and is closer to the density of the saturnian irregular
satellite Phoebe.  The mutual orbit of Ceto and Phorcys is nearly circular, with an eccentricity
� 0.015.  This observation is consistent with calculations suggesting that the system should
tidally evolve on a timescale shorter than the age of the solar system.
Keywords: Centaurs, Kuiper Belt, Transneptunian Objects, Satellites.
1. Introduction
Objects following unstable, giant-planet crossing orbits in the outer solar system have been
termed Centaurs
 (e.g., Kowal et al. 1979; Elliot et al. 2005).  They are thought to be bodies per-
turbed from the transneptunian region, evolving on timescales of the order of ~10
 years to either
being ejected from the solar system, suffering catastrophic impacts, roasting in the heat of the
Sun as comets, or getting parked in cold-storage in the Oort cloud (e.g., Duncan and Levison
1997; Holman 1997; Levison and Duncan 1997; Horner et al. 2004).  Centaurs offer a sample
from the transneptunian region that is closer and more accessible to Earth-bound observers.
They are less accessible than comets, but could have surfaces more pristine than those of comets
which have spent more time closer to the Sun.
A typical member of the Centaur population has experienced numerous close encounters
with one or more of the giant planets (e.g., Duncan et al. 1988; Levison and Duncan 1997).  Such
events might be expected to induce observable effects on the mutual orbits of binary Centaurs,
when compared statistically with the mutual orbits of binary transneptunian objects (TNOs) in
1 In this paper we use the Deep Ecliptic Survey (DES) definition of Centaurs as non-resonant objects with perihelia
between the orbits of Jupiter and Neptune (Elliot et al. 2005).  The Minor Planet Center defines transneptunian
dynamical classes somewhat differently, and would classify some DES Centaurs, including (65489) Ceto/Phorcys,
as members of the scattered disk (e.g., Gladman et al. 2007).  The Committee on Small Body Nomenclature of the
International Astronomical Union has recently adopted a naming convention for objects on unstable, non-resonant,
giant-planet-crossing orbits with semimajor axes greater than Neptune's.   Befitting their Centaur-like transitional
orbits between TNOs and comets, they are to be named for other hybrid and shape-shifting mythical creatures.
Some 30 objects are currently known to fall into this category, although only Ceto/Phorcys and (42355) Typhon/
Echidna have been named according to the new policy, so far.  The names (announced without explanation in
IAUC 8778) come from classical Greek mythology.  The primary body is named for Ceto (K����), an enormous
sea monster, born of Gaia.  English words like “cetacean” derive from her name.  The secondary is named for
Phorcys (�ó	
��), her brother and husband, depicted as part man, part crab, and part fish.  Together, they begot
numerous terrible monsters, including the Gorgons.
stable heliocentric orbits.  For several years, Noll et al. (2004a, 2004b, 2006, 2007) have been
carrying out a deep search for binaries among various dynamical classes of TNOs, most recently
using the Advanced Camera for Surveys High Resolution Camera (ACS/HRC, Ford et al. 1996)
aboard the Hubble Space Telescope (HST).  An important result from this work is the finding
that the dynamically cold “Classical” sub-population has relatively high binary rates compared
with other transneptunian sub-populations (Stephens and Noll 2006).  Recently, we (KSN,
WMG, DCS, and HFL) have put greater emphasis on searching for binaries among the more dy-
namically excited sub-populations, including the Centaurs.  Prior to its untimely demise, we used
ACS/HRC to search for satellites around 22 Centaurs (as per the DES definition), finding com-
panions for two of them.  The first, (42355) Ty-
phon/Echidna (provisionally designated 2002 CR46),
was discovered in 2006 January and a second,
(65489) Ceto/Phorcys (provisionally designated
2003 FX128), was discovered in 2006 April (Noll et
al. 2006).  The latter system is the subject of this pa-
The initial discovery of (65489) Ceto/Phorcys
was 2003 March 22 at the Palomar 1.2 m Schmidt
camera by C. Trujillo and the Near-Earth Asteroid
Tracking (NEAT) team (MPEC 2003-H33).  It was
soon identified in a series of pre-discovery images
dating back to 1987, enabling its elongated helio-
centric orbit (shown in Fig. 1) to be determined,
with osculating heliocentric elements: semimajor
axis a� = 102 AU, inclination i� = 22
, and eccen-
tricity e� = 0.82.  The orbit crosses the orbits of
both Uranus and Neptune and also extends far be-
yond the solar wind radiation environment to an
aphelion of about 186 AU, well beyond the 94 AU
distance where Voyager 1 crossed (or was crossed
by) the heliosphere termination shock (e.g., Decker
et al. 2005) with important implications for radi-
olytic processing of its surface (Cooper et al. 2003).
2. Hubble Space Telescope Observations and Analysis
The binary nature of (65489) Ceto/Phorcys was discovered in HST ACS/HRC images ob-
tained 2006 April 11 UT (see Fig. 2), as part of Cycle 14 program 10514 (led by KSN).  Details
of the clear filter combination and dithering techniques used in program 10514 are described by
Noll et al. (2006).
Follow up ACS/HRC images were obtained on May 6, 10, 30, and 31 UT as part of Cy-
cle 14 program 10508 (led by WMG).  The scheduling of these observations benefited from a
statistical ranging Monte Carlo type of analysis inspired by the work of J. Virtanen and col-
leagues (e.g., Virtanen et al. 2001, 2003).  This approach enabled us to optimize the timing of
Fig. 1: Plan view of the Solar System, showing the
heliocentric orbit of (65489) Ceto/Phorcys (dotted
curve) compared with orbits of the four gas giants
(solid curves), with points indicating positions as of
2007 July.  The orbit crosses the orbits of both
Uranus and Neptune, but considerable time is also
spent well beyond 94 AU from the Sun, the dis-
tance at which Voyager 1 crossed the heliosphere
termination shock (e.g., Decker et al. 2005)..
-50 0 50 100 150
Distance from Sun (AU)
subsequent observations for satellite orbit determination, within the limitations of HST schedul-
ing and the restricted visibility windows imposed by the two-gyro mode in which HST is cur-
rently operating.  Our implementation of the technique is described in a forthcoming paper
(Grundy et al. in preparation).  The follow up observations used the F606W and F814W filters of
the ACS/HRC camera.  For each visit, eight 223 second exposures (four in each filter) were ob-
tained, dithered over a four-point box pattern so that images with defects such as hot pixels or
cosmic rays contaminating the flux of the binary system could be easily identified and excluded
from further analysis.
2.1. Photometry and astrometry
Data were processed through the standard CAL ACS pipeline at Space Telescope Science
Institute (STScI), producing dark-subtracted, flat-fielded images (for details, refer to http://
www.stsci.edu/hst/acs/documents/handbooks/cycle16).  Astrometry and pho-
tometry were calculated from these images by fitting model point spread functions (PSFs) gener-
ated by Tiny Tim (Krist and Hook 2004) and correcting the results for the geometric distortion
arising from the separation between the ACS camera and the optical axis of the telescope.  De-
tails of the binary-PSF fitting procedure are described in Stephens and Noll (2006).  The PyRAF
program xytosky in the STSDAS package (http://www.stsci.edu/resources/soft-
ware_hardware) was used to translate the pixel coordinates found for Ceto and Phorcys to
their true right ascension and declination values.  Accurate separations and position angles for
the binary pair could then be calculated, and measurements from the multiple images combined
to get the average relative sky plane astrometry for each visit in Table 1.
Table 1. HST ACS/HRC observational circumstances and 1-� relative astrometry
Average UT date and
a ��b ��b
(AU) (degrees) (arcsec)
2006/04/11 21.691 27.753 26.785 0.542 +0.0172 ± 0.002 +0.0833 ± 0.003
2006/05/06   7.447 27.813 26.881 0.812 �0.0475 ± 0.002 �0.0687 ± 0.001
2006/05/10   4.510 27.822 26.912 0.916 �0.0032 ± 0.001 +0.0860 ± 0.002
2006/05/30   0.217 27.870 27.129 1.440 +0.0362 ± 0.001 +0.0747 ± 0.001
2006/05/31   1.692 27.873 27.143 1.466 +0.0829 ± 0.002 +0.0295 ± 0.002
Fig. 2: Example Hubble Space Telescope ACS/HRC single frames of Ceto and Phorcys (centered on Ceto), tak-
en 2006 April 11, May 5, May 10, May 30, and May 31 UT, from left to right.  The HRC pixels are projected to
sky-plane geometry with North up and East to the left, revealing the geometric distortion at the HRC focal
plane.  For scale, the mosaic of images is 2.0 × 0.4 arcsec.  The left-most image was one of the binary discov-
ery sequence of images, obtained through the CLEAR filter as part of program 10514.  The other four images
were obtained through the F814W filter as part of program 10508.                                                      
                      
The distance from the Sun to the target is r and from the observer to the target is �.  The phase angle, the an-
gular separation between the observer and Sun as seen from the target, is g.
Relative right ascension �� and relative declination �� are computed as �� = (�2 − �1)cos(�) and �� = �
2 − �1, where subscripts 1 and 2 refer to Ceto and Phorcys, respectively.
The PSF model binary solutions were also used to calculate individual magnitudes for Ceto
and Phorcys.  To get the magnitude of one object, we subtracted the model PSF of the other from
each image and then used the PyRAF multidrizzle task in the STSDAS package to remove the  ge-
ometric distortion.  For each resulting undistorted image, the total flux within a 3 pixel radius
was measured and corrected to an aperture of 20 pixels (0.5 arcsec) computed for an undistorted
model PSF.  We then applied the Sirianni et al. (2005) AC05 (0.5 arcsec to ∞) aperture correc-
tion coefficients, the photometric zero point for each filter, and the charge transfer efficiency cor-
rection to get the final HST magnitude in each image.
To compare the HST magnitudes with ground based results and to help constrain the size
and albedo of (65489) Ceto/Phorcys, transformation coefficients were derived to convert the
F606W and F814W magnitudes to Johnson-Cousins V and I magnitudes.  The ACS and Johnson-
Cousins filters are not exact counterparts, so assumptions had to be made about the spectral ener-
gy distribution of Ceto/Phorcys.  We applied a reddening coefficient to a solar spectrum until it
had the same F606W�F814W color as (65489) Ceto/Phorcys.  We then convolved this spectrum
with the HST and Johnson-Cousins filters using the synphot task under STSDAS to get transfor-
mation coefficients specific to Ceto/Phorcys.  These coefficients were used to transform the HST
magnitudes of Ceto and Phorcys in each image to the Johnson-Cousins system.  For each visit
the F606W, F814W, V, and I magnitudes were averaged to produce Table 2.
Table 2. Photometry from Hubble Space Telescope ACS/HRC observations
Observation                       Ceto                                          Phorcys                    
Date (UT) F606W F814W V I F606W F814W V I
2006/05/06 21.43 20.54 21.68 20.56 21.94 21.12 22.15 21.14
2006/05/10 21.35 20.53 21.57 20.55 21.94 21.10 22.18 21.13
2006/05/30 21.49 20.61 21.74 20.63 22.10 21.24 22.35 21.26
2006/05/31 21.49 20.63 21.72 20.65 22.07 21.24 22.29 21.26
Table note: Photometric 1-� uncertainties in F606W and F814W filters are about ±0.04 mag.  Color transfor-
mation uncertainties inflate the V and I uncertainties to about ±0.06 mag.
Two filters were used in the follow-up observations to search for color differences between
Ceto and Phorcys.  The average F606W�F814W colors were 0.867 ± 0.028 and
0.836 ± 0.028 mag for Ceto and Phorcys, respectively.  Ceto's measured color is slightly redder
than that of Phorcys, but the difference is statistically insignificant.  Our average V�I color for
the system is 1.07 ± 0.04, corresponding to a spectral slope of 15.3 ± 1.5 (% rise per 100 nm
relative to V), putting Ceto/Phorcys among the gray color clump of Centaurs, albeit at the red
edge of that clump (e.g., Boehnhardt et al. 2003; Peixinho et al. 2003).  Tegler et al. (2003) re-
ported a B�V color for (65489) Ceto/Phorcys of 0.86 ± 0.03 and a V�R color of 0.56 ± 0.03,
consistent with this result.
No lightcurve variability has been reported for this system and our data show no evidence
for it either.  The average magnitudes from the 4 visits reported in Table 2 differ by more than
the 1-� uncertainties, but that variability can be attributed to geometry.  After removing photo-
metric effects of the changing distances from the Sun to the target r and from the observer to the
target � and also the effect of the phase angle g (by assuming generic dark-object phase behavior
as represented by the H and G system of Bowell et al. 1989, with G = 0.15), we find that the
largest deviation from the 4-visit mean for either object or filter is only 1.5-� (for Ceto during
the May 10 UT visit in F606W).  With only four random epochs and ±0.04 mag photometric un-
certainties, the F606W data can only rule out a 0.15 mag sinusoidal lightcurve at about the 1-�
confidence level.  However, the observed F606W outlier is not mirrored in the F814W filter, as
would be expected if a lightcurve from an elongated shape were responsible, so noise is the like-
lier explanation for that point.  At least one deviation as large as 1.5-� is to be expected among
four sets of four measurements.
2.2. Orbit fitting and system mass
Our methods for fitting mutual orbits to relative astrometry of binaries have been described
previously (Noll et al. 2004a, 2004b, 2006, 2007).  We use the downhill simplex “amoeba” algo-
rithm (Nelder and Mead 1965; Press et al. 1992) to iteratively adjust a set of seven orbital ele-
ments to minimize the �2 statistic of residuals between observed and predicted sky plane relative
positions of the primary and secondary, accounting for light time delays and relative motion be-
tween the observer and the binary pair.  For previous orbit fits we had used the date and argu-
ment of periapsis as two of the seven fitted orbital elements.  This choice had originally been
made because the orbit of the satellite of 1998 WW31 (Veillet et al. 2002) suggested to us that
very high eccentricities might be the norm.  Unfortunately, for circular orbits those two parame-
ters become degenerate, and as eccentricity approaches zero, their use produces numerical insta-
bilities which plagued our fits to the near-circular orbits of Pluto's satellites (Buie et al. 2006).
Accordingly, we have since modified our orbit-fitting code to fit the following seven elements:
period P, semimajor axis a, eccentricity e, inclination i, mean longitude at epoch �, longitude of
ascending node �, and longitude of periapsis �.  To estimate the uncertainty in each of these fit-
ted elements, we used two different methods.  First, we systematically varied each parameter
around its best fit value, allowing the other six to adjust themselves to re-minimize �2, creating
slices through the seven dimensional �2 space which enabling us to map out the 1-� confidence
contour.  Second, we fitted orbits to random sets of input astrometry data generated from the ob-
served astrometry by adding Gaussian noise consistent with the astrometric uncertainties.  The
bundle of Monte Carlo orbits generated in this way provides an alternate measure of how well
we have determined the orbital elements.  Both methods gave very similar 1-� uncertainties on
the fitted elements for the orbit of Phorcys around Ceto.  The elements are tabulated in Table 3
and the projection of the orbit on the sky plane at the average time of the HST observations is
shown in Fig. 3.
Table 3. Orbital elements and derived parameters with 1-� uncertainties or limits
Parameter Orbit 1 (�2 = 2.3) Orbit 2 (�2 = 2.4)
Fitted orbital elements
   Period (days) P  9.557 ± 0.008  9.551 ± 0.007
   Semimajor axis (km) a 1840 ± 41   1841 ± 47   
Parameter Orbit 1 (�2 = 2.3) Orbit 2 (�2 = 2.4)
   Eccentricity e  � 0.013  � 0.015
   Inclinationa (deg) i 68.8 ± 2.9 116.6 ± 3.0   
   Mean longitudea at epochb (deg) � 23.0 ± 2.7 53.5 ± 5.2 
   Longitude of asc. nodea (deg) � 105.5 ± 3.7   134.6 ± 3.4   
   Longitude of periapsisa (deg) �     40 ± 360c     70 ± 360c
Derived parameters
   System mass (1018 kg) Msys 5.40 ± 0.36 5.42 ± 0.42
   Orbit pole right ascensiona (deg) � 15.5 ± 5.2  44.6 ± 5.2  
   Orbit pole declinationa (deg) � 21.2 ± 4.0  −26.7 ± 4.1    
Referenced to J2000 equatorial frame.
The epoch is Julian date 2453880 (2006 May 24 12:00 UT).
The uncertainty of ±360
 indicates that
this parameter is unconstrained.
It can be difficult to distin-
guish between an orbit and its mirror
image through the plane of the sky
(e.g., Descamps 2005).  Parallaxes
from the differential motion of the
Earth and the object will eventually
enable a patient observer to break
the ambiguity between an orbit and
its mirror, as the observer's sky
plane gradually rotates with respect
to the orbit.  More face-on orbits,
with their smaller excursions of the
satellite in the direction radial to the
observer, are relatively slow to re-
veal which solution is the real one.
At the time of our observations, the
Ceto/Phorcys orbit was tilted about
28
 from face-on.  We list both solu-
tions, noting that �2 is slightly better
for the first one, but does not ex-
clude the second one.  For both or-
bits, the longitude of periapsis � is
unconstrained, in that it can take any
value from 0 to 360
 without pushing
�2 over the 1-� threshold.  However,
there is a shallow �2 minimum for �
at about 40
 for Orbit 1 and about 70
 for Orbit 2.  Neither orbit will be oriented edge-on to the
Fig. 3: Projection of the orbit of Phorcys (gray oval) relative to Ce-
to's location (black dot) onto the sky plane at the average time of the
five HST observations.  Points with 1-� error bars indicate relative
astrometry between Ceto and Phorcys measured from the ensemble
of dithered frames during each HST visit.  Open circles are relative
positions of Phorcys at the times of the observations as calculated
from orbit 1 in Table 3.  The spot at the origin and the open circles
are scaled to the sizes of Ceto and Phorcys, respectively, derived in
Section 4.
inner solar system within the next century, so use of mutual events to obtain more detailed infor-
mation about the system geometry (e.g., Noll et al. 2007) is a distant future prospect.
The mutual orbit of Ceto/Phorcys can be compared with orbits of satellites of other small
outer Solar System bodies (see Noll et al. 2007 Table 2).  It is noteworthy that this is the least
massive system with a near-circular orbit by some three orders of magnitude.  All known semi-
major axes for transneptunian binaries are larger except for that of Typhon/Echidna (Grundy et
al. in preparation) and all periods are longer except for that of Charon's orbit about Pluto.  Al-
though these characteristics sound exceptional, we do not believe this system to be unusual.
Closer systems such as this one are simply more difficult to discovery and to study.
From the semimajor axis a and period P, we can compute the mass of the combined system
Msys, according to
4�2 a3
, (1)
where G is the gravitational constant which we take to be 6.6742 × 10-11 m3 s-2 kg-1.  Since we
have two possible orbits, we adopt values of P = 9.554 ± 0.011 days, a = 1840 ± 48 km, and
Msys = (5.41 ± 0.42) × 1018 kg to encompass the 1-� uncertainties from both solutions.  The
semimajor axis is measured to much lower fractional precision than the period is and it is raised
to a higher power in the mass equation, so it is the dominant source of uncertainty in the
Ceto/Phorcys system mass.
3. Spitzer Space Telescope Observations and Analysis
Spitzer Space Telescope ob-
served (65489) Ceto/Phorcys in
2006 July with the Multiband Imag-
ing Photometer for Spitzer (MIPS,
Rieke et al. 2004) in its 24 and
70 µm bands, which have effective
wavelengths of 23.68 and 71.42 µm.
These observations were part of Cy-
cle 3 program 30081 (led by JAS).
Data were collected using the pho-
tometry observing template, which is
tailored for photometry of point
sources.  The observatory tracked
the target during the observations,
although the motion was negligible
relative to the size of the point-
spread function (PSF) at these wave-
lengths.  The target was imaged in
both bands during two visits separat-
ed by 37 hours, over which time
(65489) Ceto/Phorcys moved 38 arcsec relative to the background stars, allowing us to identify
Fig. 4: Spitzer Space Telescope MIPS images of Ceto+Phorcys at
24 µm (left) and 70 µm (right) from 2006 July 18 UT.  Each image is
180 arcsec square, and is oriented North up, East left.  The circles
are centered at the ephemeris position of the object, and have diame-
ters equal to four times the FWHM of the Spitzer PSF in each band.
While the object is not observed at exactly the ephemeris position,
the offsets are consistent in the data from this and the other epoch,
the object motion vector relative to the background objects is as pre-
dicted, and it is the only moving object visible at both epochs.  Data
from the second epoch were used to remove background sources
from the first epoch, and vice versa.
the target with certainty.  Since the images from the two epochs have significant spatial overlap,
we could use the image pairs to confirm that no strong background sources were present at the
target position at either epoch and to subtract off the effect of weak background sources.  The
two visits would also help average over any possible thermal lightcurve variability.  Images from
the first epoch are shown in Fig. 4.
We reduced the raw data and mosaicked them using the MIPS instrument team data analy-
sis tools (Gordon et al. 2007).  For the 24 µm data, basic processing included slope fitting, flat-
fielding, and corrections for droop.  All of these steps are currently implemented in the Spitzer
Science Center (SSC) pipeline products.  Additional corrections were made to remove readout
offset (a jailbar pattern in the images), the effects of scattered light (which introduces a pointing-
dependent background gradient and slightly degrades the sensitivity), and the application of a
second-order flat field, derived from the data itself, to remove latents from previous observa-
tions. 
The photometric repeatability of MIPS observations of moderately bright sources is better
than 1% at 24 µm, and is 5% at 70 µm.  The uncertainty in the absolute calibration of these bands
is 4% and 8% respectively (Engelbracht et al. 2007; Gordon et al. 2007).  For purposes of fitting
models to our photometry, we use uncertainties that are the root-square-sum of the absolute cali-
bration uncertainties and the measurement uncertainties determined from the images themselves.
We adopt slightly larger 1-� calibration uncertainties, 5% and 10%, to account for uncertainties
in color and aperture corrections.  The widths of the filter bandpasses are about 25%, resulting in
modest color corrections.  We iteratively applied color corrections to our photometry, which con-
verged to give a color temperature of 73.2 K, and color corrections of +2.6% and +8.6% at 24
and 70 µm, respectively (see Stansberry et al. 2007b).  The uncertainties on the correction factors
are perhaps a few percent of the factors themselves, and so are negligible for our study.
We measured the flux density of (65489) Ceto/Phorcys using 9.96 and 29.6 arcsec diame-
ter apertures (about 4 and 3 native pixels) at 24 and 70 µm; the PSF full-width at half-max is 6.5
and 20 arcsec in those bands.  The apertures were positioned at the center-of-light centroid.  Mo-
saics were constructed using 1.245 arcsec and 4.925 arcsec pixels at 24 and 70 µm (about half the
native pixel scale of those arrays).  We applied aperture corrections of 1.91 and 1.85 to the 24
and 70 µm photometry to compute the total flux (see Gordon et al. 2007; Engelbracht et al. 2007
for details).  Uncertainties in the aperture corrections are approximately 1%.  Table 4 summa-
rizes the circumstances of our Spitzer MIPS observations and the measured, color-corrected flux
densities.
Table 4. Spitzer Space Telescope MIPS observational circumstances and thermal fluxes
Average UT date r � g 24 µm flux 70 µm flux
and hour (AU) (degrees) (mJy)
2006/07/18 10.23 27.990 27.662 1.99 1.47 ± 0.02a 14.9 ± 1.0a
2006/07/19 19.46 27.993 27.686 2.00 1.48 ± 0.02a 14.5 ± 1.2a
Adopted 27.991 27.674 2.00 1.473 ± 0.076b 14.69 ± 1.84b
Errors reflect the signal to noise ratios in the observations, which were about 70 and 13, resulting from integra-
tions of 900 and 2640 seconds, at 24 and 70 µm, respectively.
The adopted 1-� flux errors include additional absolute calibration uncertainties.
4. Size, Albedo, and Density
The thermal fluxes measured by Spitzer can be used to constrain the size of Ceto/Phorcys
and also the albedo if they can be combined with suitable visible photometry.  Tegler et al.
(2003) reported a V magnitude of 20.70 ± 0.03 from Vatican Observatory 1.8 m telescope obser-
vations when the system was at heliocentric distance r = 25.190 AU, geocentric distance
� = 24.298 AU, and phase angle g = 1.09
.  Assuming typical phase behavior for low albedo
objects (G = 0.15 in the H and G system of Bowell et al. 1989; see also Sheppard and Jewitt
2002; Rousselot et al. 2005), we can convert the Tegler et al. V photometry to absolute magni-
tude HV = 6.603 ± 0.030.  Under the same assumptions, our HST photometry (in Tables 1 and 2)
gives HV = 6.625 ± 0.030.  Combining these, we adopt the weighted average
HV = 6.614 ± 0.021.
Thermal fluxes are used to to constrain an object's size via a variety of thermal models
(e.g., Lebofsky and Spencer 1989).  We used the approach described by Stansberry et al. (2006),
which takes advantage of the existence of visual photometry plus two well-separated thermal in-
frared wavelengths from Spitzer/MIPS to simultaneously fit the size, albedo, and beaming pa-
rameter �, using the standard thermal model (STM), which assumes instantaneous thermal equi-
librium with sunlight illuminating a spherical surface.  We also assumed unit emissivity.  A wide
range of real-world complications such as rotation, pole orientation, surface roughness, and ther-
mal inertia can strongly influence observable thermal fluxes relative to what would be predicted
by the simple STM, but in general, the effects of these complications look spectrally similar to
the effect of changing the beaming parameter �.  If � is constrained by the data, the large model
uncertainties in size and albedo which would otherwise flow from lack of knowledge of these
other physical properties are greatly diminished.  Using this model, we are able to match the ob-
served thermal and visible photometry of (65489) Ceto/Phorcys with an effective radius
Reff = 109
�11  km, along with beaming parameter � = 0.77
�0.08
�0.09 , and geometric albedo
Ap = 0.084
�0.021
�0.014 .  Uncertainties on the derived parameters were determined by means of Monte
Carlo methods.  Thousands of random sets of input fluxes were generated, consistent with the
observational uncertainties.  Each set resulted in slightly different values of the derived parame-
ters, creating a population of solutions from which 1-� uncertainties could be estimated.  Errors
from possible lightcurve variations are small enough to be neglected.  For example, with thermal
observations at two effectively random times, the 1-� upper limit 0.15 mag lightcurve mentioned
earlier would contribute about a 1.4% average radius error, well below our 
�11 %  reported uncer-
tainty.
The derived value of � = 0.77 �0.08�0.09  is on the low side of what has been seen for other TNOs
and Centaurs, suggesting that Ceto and Phorcys have some combination of relatively low thermal
inertias, slow rotation rates, especially rough surfaces, or their poles oriented toward the Sun.
For comparison, Stansberry et al. (2007a) found � values ranging from 0.6 to 2.3, with an aver-
age of 1.3, for a sample of 23 TNOs and Centaurs detected with good signal precision at both 24
and 70 µm wavelengths by Spitzer/MIPS.
Our 0.084
�0.021
�0.014  albedo of Ceto/Phorcys is consistent with albedos of other Centaurs.
Stansberry et al. (2007a) report albedos for 11 other Centaurs (by the DES classification) detect-
ed with good signal precision at both 24 and 70 µm by Spitzer/MIPS.  That sample has an aver-
age albedo of 0.06 and a standard deviation of 0.04.  Considerable albedo diversity is also appar-
ent among other small outer Solar System objects (e.g., Grundy et al. 2005; Cruikshank et al.
2007; Stansberry et al. 2007a), but correlations between albedo and dynamical class or color re-
main poorly established, except for a general trend of progressively lower average albedos from
TNOs to Centaurs to comet nuclei, and a trend of higher albedos for the redder Centaurs (Stans-
berry et al. 2007a).
By assuming the albedos of Ceto and Phorcys are similar to one another, we can use the
0.584 ± 0.030 average magnitude difference between them to work out their individual radii, ob-
taining RCeto = 87
�9  km and RPhorcys = 66
�7  km.  Computing the total system volume from these
two radii, and combining that with the total system mass from the mutual orbit, we obtain an av-
erage bulk density of 1.37
�0.66
�0.32  g cm
-3.  The assumption of equal albedos is consistent with the
observation of indistinguishable colors for the two components, but we can also explore how
sensitive we are to that assumption.  Assume, for instance, that the albedo of Phorcys was actual-
ly twice that of Ceto.  We would then have overestimated the average bulk density by a factor of
9%.  If Ceto's albedo were double that of Phorcys, we would have underestimated the average
bulk density by 2%.  Unless the albedo contrast between Ceto and Phorcys is very extreme in-
deed, the density is relatively insensitive to our assumption of equal albedos.  Our conclusions
are comparably insensitive to possible lightcurve variations, as mentioned previously.
Bulk densities 	 of icy objects are often interpreted in terms of a rock fraction
	rock
, (2)
where 	ice is taken to be 0.937 g cm-3 for low temperature crystalline ice Ih (Lupo and Lewis
1979) and 	rock could range from 2.5 g cm-3 for hydrated silicates to 3.5 g cm-3 for anhydrous sili-
cates (e.g., Schubert et al. 1986).  For 	rock = 2.5 g cm-3, our average bulk density of Ceto/Phor-
cys yields a rock fraction frock = 0.51
�0.29
�0.39 , a value intermediate between the rock-rich composi-
tions of Triton and Pluto and the more ice-rich compositions of some of the smaller satellites of
Saturn.  However, this rock fraction calculation only makes sense in the absence of void space,
or of other possible interior components, such as carbonaceous materials.
We estimate the hydrostatic pressure at the cores of Ceto and Phorcys according to
�G	2 R2 (3)
(e.g., Stansberry et al. 2006) as 2.0
�0.6  and 1.1
�0.4  MPa, respectively.  These pressures are insuf-
ficient to squeeze much void space out of cold, particulate H2O ice.  Laboratory experiments by
Durham et al. (2005) show that at pressures in the 5 to 10 MPa range, appreciable compaction
begins to occur in cold ice, but as much as 10% void space remains even at pressures as high as
100 MPa.  If Ceto and Phorcys have remained cold since their accretion, we can anticipate rela-
tively high fractions of void space within them, complicating interpretation of their densities in
terms of ice and rock fractions.
Bulk densities are known for several much larger outer Solar System bodies, including
Pluto and Charon (2.03 ± 0.06 and 1.65 ± 0.06 g cm-3, respectively; Buie et al. 2006), Eris
(2.26 ± 0.25 g cm-3; Brown 2006), and (136108) 2003 EL61 (3.0 ± 0.4 g cm-3; Rabinowitz et al.
2006).  These higher densities are consistent
with expectation for rock-rich and possibly
differentiated objects which probably expe-
rienced warm interior temperatures at some
time in their histories.  Two other small bi-
nary TNOs have recently had their average
bulk densities determined via the technique
used in this paper.  Stansberry et al. (2006)
reported a bulk density of 0.50
�0.30
�0.20  g cm
for (47171) 1999 TC36 and Spencer et al.
(2006) reported a bulk density of 0.70
�0.32
�0.21  
g cm-3 for (26308) 1998 SM165.  These much
lower densities require significant void
space, even for pure ice compositions.  Low
densities compared with likely bulk compo-
sitions have also been determined recently
for the Trojan asteroid (617) Patroclus
(Marchis et al. 2006) and for main belt as-
teroids (e.g., (90) Antiope; Descamps et al.
2007) as well as for much smaller comet
nuclei (e.g., A'Hearn et al. 2005; Davidsson
and Gutiérrez 2006).  However, the irregu-
lar saturnian satellite Phoebe, with a size
similar to that of Ceto+Phorcys, has a high-
er bulk density of 1.630 ± 0.033 g cm-3
(Johnson and Lunine 2005).  These diverse
densities (shown in Figure 5) point to con-
siderable variety in bulk compositions and
interior structures among small outer Solar System bodies.
Apart from bulk compositional differences, thermal history is another potential source of
density diversity among TNOs.  Objects in the outer parts of the protoplanetary disk could ini-
tially accrete ice mostly in the amorphous phase, with a fluffy structure that includes consider-
able void space (e.g., Jenniskens et al. 1998).  Subsequent thermal pulses, from whatever source
(impacts, tidal dissipation, Al26 decay, etc.), could crystallize amorphous ice.  The crystallization
would liberate additional heat as well as potentially reducing void space (e.g., Jewitt et al. 2007).
The presence of varying amounts of NH3 could also lead to considerable diversity of thermal
evolution and thus density (e.g., Leliwa-Kopystyński and Kossacki 2000).
5. Tidal evolution
Since gravitational attraction falls off as the square of separation, Ceto and Phorcys both
produce differential gravitational accelerations across the bodies of their partners, slightly dis-
torting their equipotential figures.  If their mutual orbit is eccentric, or either of their rotation
states differs from the orbital rotation rate and orientation, this distortion will change over time,
Fig. 5: Comparison of the average bulk density of (65489)
Ceto/Phorcys (star) with densities for binary outer Solar
System objects discussed in the text (black dots) and icy
satellites of Saturn, Uranus, and Neptune (gray points, from
Burns 1986 and McKinnon et al. 1995).  For the binaries
with unknown mass ratios, the radius shown is that of the
primary, since it is likely to dominate the average density.
The dashed curve is a theoretical bulk density for non-
porous, pure H2O ice subject to self-compression at 77 K
(Lupo and Lewis 1979).  The dotted curve allows for poros-
ity in pure, cold, granular H2O ice Ih, based on compaction
data from Durham et al. (2005) as modeled by McKinnon et
al. (2005).  An expected trend of smaller objects having sys-
tematically lower densities than their larger counterparts
(Lacerda and Jewitt 2007) is not cleanly supported by the
present data for (65489) Ceto/Phorcys.
100 1000
Radius (km)
resulting in frictional dissipation of energy and leading to tidal evolution of their orbit and spin
states.  The rate of energy dissipation and tidal evolution depends on the specific tidal dissipation
factor Q, which is a complicated function of interior structure and composition that describes the
degree to which tidal friction is deposited in a given body.  Q is approximately equal to 1/(2�),
where � is the angle between the tidal bulge of the object and the line of centers between the two
objects.  Because Ceto and Phorcys have similar sizes and probably similar compositions, we as-
sume that Q1 � Q2 � Q (where subscripts 1 and 2 to refer to Ceto and Phorcys, respectively).
Typical Q values for solid planets and icy satellites range from 10 to 100 (e.g., Goldreich and
Soter 1966; Yoder 1982; Hubbard 1984).  We take Q = 100, to minimize dissipation and thus
compute upper limits on tidal evolution timescales.
Small solid objects require a correction to Q because their rigidity can be large compared
to their self-gravity (Hubbard 1984).  In this case, the small body may not be able to relax to hy-
drostatic equilibrium over a tidal cycle, but instead acts elastically.  Thus, the deformation of the
body's surface is smaller than it would be in hydrostatic equilibrium as elastic forces tend to
maintain the body's shape.  The correction to Q takes the form
Q' = Q �1�19�2 g 	R � , (4)
where µ is the rigidity, 	 is the density, R is the radius, and g is the surface gravity (Goldreich
and Soter 1966).  Values adopted for use in our calculations are tabulated in Table 5.  The rigidi-
ties of Ceto and Phorcys are, of course, unknown.  If they are un-fractured monoliths, their
rigidities could be as high as 1011 dyn cm-2, intermediate between values for solid ice and solid
rock (Gladman et al. 1996).  In this extreme case, the correction to Q would be large, with
Q' = 3 × 106.  At the other extreme, if Ceto and Phorcys are unconsolidated “sand piles” their
rigidities could be as low as 107 dyn cm-2 (Yoder 1982).  In this case, the correction to Q is small,
giving Q' = 300.  We use these bracketing values of Q' to explore the range of possible
timescales for tidal spin-locking and orbital evolution in the Ceto/Phorcys system.
Table 5. Physical parameters adopted.
Parameter Ceto Phorcys
Radius R 87 km 66 km
Mass M 3.74 × 1018 kg 1.67 × 1018 kg
Density 	 1.37 g cm-3 1.37 g cm-3
Surface gravity g 3.3 cm s-2 2.5 cm s-2
Table note: These values are derived from the effective radius Reff, system mass Msys, and magnitude difference,
subject to the assumption of equal albedos and equal densities.
Over time, tidal effects can synchonize the spin rate of Phorcys to its orbital period (as for
the Earth's Moon, which keeps one face oriented toward Earth) and, on a longer timescale, syn-
chronize Ceto's spin rate as well (analogous to the Pluto-Charon system, where both members
keep the same face toward each other).  The timescale for spin-locking Ceto (slowing its spin
rate to match the mutual orbital period) is given by
spin , 1
Q'��1 M1 a
G M 2
, (5)
where subscripts 1 and 2 refers to Ceto and Phorcys, respectively, M is mass, R is radius, and 
�� is the difference between an initial angular rotation rate and the final, synchronized rate
(Goldreich and Soter 1966; Trilling 2000).  The timescale for spin-locking Phorcys can be found
simply by swapping all the subscripts in Equation 5.  A typical rotation period for TNOs is
around 10 hours (e.g., Trilling and Bernstein 2006).  The current orbital period is much longer
than this, so we set ��1 (and ��2) to correspond to this rate (one could equally start with the
breakup rotation rate, in the 2 to 3 hour period range).  We find that the spin-locking timescale
for Ceto ranges from 106 to 1010 years and the timescale for spin-locking Phorcys is about a fac-
tor of three shorter.  We conclude that unless these bodies are rigid monoliths, Phorcys should be
spin-locked to Ceto and Ceto to Phorcys as well, or nearly so.  (Recall that if Q is smaller than
our assumed maximum value of 100, the spin-lock timescale decreases, increasing the likelihood
of spin-locking.)
The eccentricity of the Ceto/Phorcys mutual orbit can also evolve due to tides raised on ei-
ther object by the other.  Following Goldreich and Soter (1966) we can write the contributions of
the two terms as
= � dedt �
�� dedt �
, (6)
where (de/dt)1 accounts for the effect of tides raised on the primary by the secondary and (de/dt)2
accounts for tides raised on the secondary by the primary.  The two contibutions can be ex-
pressed as
e � dedt �1 =
16 � GM 1 � R1
6.5 � sign �2�1�3n2 � (7)
where n2 is the mean orbital motion of the secondary and
e � dedt �2 = �
�G M 13� R2
6.5 � . (8)
Employing our previous result that Ceto and Phorcys should be spin-locked (or nearly so), �1
should be equal (or close) to n1 so (de/dt)1 is negative, implying that de/dt must also be negative
(since (de/dt)2 is always negative)
2.  A negative de/dt indicates circularization of the orbit.
Using the values for Ceto and Phorcys in Table 5, we find
7×10�12�1.4×10�11
Equating e with �de and solving for dt to estimate the timescale to reduce an initial eccentricity
to zero, we find that the circularization timescale ranges from 5 × 105 to 5 × 109 years for the
2 For bodies of equal density, (de/dt)2/(de/dt)1 � 1.5 (R1/R2), so (de/dt)2 always dominates, and the first term on the
right hand side of Equation 6 is often ignored (e.g., Rasio et al. 1996; Trilling 2000).  Thus, even when P1 < 2/3 P2,
giving positive (de/dt)1, |(de/dt)1| can never be larger than |(de/dt)2|, so de/dt will always be negative.
previously discussed range of Q'.  Again, unless Ceto and Phorcys are rigid monoliths, this
timescale is much less than the age of the Solar System (and, presumably, the age of the Ceto/
Phorcys binary) so we expect the system to have lost most (or all) of its primordial orbital eccen-
tricity.
The average density of (65489) Ceto/Phorcys is relatively high compared with two other
small TNOs with eccentric mutual orbits (26308) 1998 SM165 (Spencer et al. 2006) and (47171)
1999 TC36 (Stansberry et al. 2006), leading us to ask whether the tidal evolution of the
Ceto/Phorcys system could have driven internal temperatures high enough to enable ductile com-
paction and loss of void space.  What temperature would be required is not clear, but for crys-
talline ice Ih, it must exceed 120 K, since ice Ih remains brittle and can maintain its pore space up
to at least that temperature (e.g., Durham et al. 2005).  This temperature is considerably higher
than equilibrium temperatures in the Kuiper belt.  Energy from both circularization and spin-
locking would contribute to internal heating.  The specific energy (i.e., per unit mass) available
from a change in orbital semimajor axis is
�Ecirc
G M 1
�a initial
�1�afinal
�1� , (10)
where ainitial and afinal are the initial and final semimajor axes.  If the orbit changes by ~10% in the
process of circularization, then the total energy deposited is GM1/(20af), and we may take af as
the presently observed value of a.  Rotational kinetic energy of a spinning body is 
I�2 where �
is the angular rotation rate and I = 2
MR2 is the moment of inertia for a homogeneous spherical
body.  The specific energy deposited in each body via spin locking is thus
�E spin
��initial
2��final
2� , (11)
where �initial and �final are the initial and final rotation rates.  Taking the initial spin periods to be
10 hours and final spin periods to be 9.5 days, we obtain an energy input smaller than that from
circularization by a factor of a few.  Combining the above parts, the total specific energy deposit-
ed in the system is
2� ��
initial
final
, (12)
which is approximately 105 erg g-1.  Lunine and Tittemore (1993) present an alternate derivation
of the tidal heating of a synchronously rotating satellite.  Rewriting their expression for energy
deposition, we have
�G M13� R2
��G M 1 M2 e
a � (13)
which gives dE/dt ranging from 1010 to 1014 erg s-1 for our bracketing Q' assumptions.  The total
energy input is independent of rigidity and is around 1027 erg, or 105 erg g-1, in agreement with
our derivation above.
The heat capacity of cold water ice Ih depends on temperature, ranging from 3 × 106 erg g-1
K-1 at 30 K to over 107 erg g-1 K-1 at 60 K (Giauque and Stout 1936), so even if all 105 erg g-1 of
heat were deposited instantaneously instead of over a 106 year or longer timescale, the tempera-
ture rise would be much less than a degree, far too small for viscous creep to assist compaction
and loss of pore space.  Comparable arguments can be made to show that heat tidally deposited
by any close encounter with a giant planet which does not completely disrupt the system will
also produce a negligible temperature rise.  However, if tidal heating were highly localized, as
might happen if energy dissipation was confined to the intersections of large scale internal frac-
tures, the local temperature rise could be higher.
That the Ceto/Phorcys system is expected to be tidally spin-locked and circularized sug-
gests that the spin axes of both objects could also have become aligned with the orbit pole.  Such
a configuration would help explain why no lightcurve has been reported for this object, and why
there is no evidence for it in our ACS/HRC photometry in Table 2 nor in our Spitzer/MIPS pho-
tometry in Table 4.  If the spin axes are aligned with the orbit pole, which was tilted about 28
from the line of sight from Earth at the time of the observations (as seen in Fig. 3), a lightcurve
observable when the system was near equator-on would be reduced in amplitude by the current
geometry by a factor of sin(28
), equal to 0.47.  A more pole-on configuration is also consistent
with the small beaming parameter �.  Smaller values of � correspond to warmer surface tempera-
tures, as would be expected when observing a hemisphere mostly in continuous sunlight.  Unfor-
tunately, we cannot use the assumption of aligned spin orientations to constrain the thermal iner-
tia of the surfaces of Ceto and Phorcys, since observable thermal flux becomes independent of
thermal inertia in pole-on geometry (e.g., Lebofsky and Spencer 1989).
6. Effect of encounters
In its current heliocentric orbit, Ceto/Phorcys is most likely to encounter Uranus, since its
perihelion is just inside the orbit of Uranus and its argument of perihelion is near 180
 (see
Fig. 1).  Tidal disruption becomes probable for planetary encounters with closest approach dis-
tances within
= a � 3 M planetM
, (14)
where a is the binary's semimajor axis and Mplanet and Msys are the masses of the planet and the bi-
nary system, respectively (Agnor and Hamilton 2006).  For encounters between Ceto/Phorcys
and Uranus, rtd is about 0.0045 AU, equivalent to 26 times the radius of Uranus or 360 times the
Ceto/Phorcys separation a.  For an encounter with Jupiter, rtd would be 0.013 AU, or 1000 times
a.  The probability that Ceto/Phorcys would have had an encounter closer than rtd with any of the
giant planets on its way to being perturbed into its current orbit is not known, but by analogy
with (42355) Typhon/Echidna (Noll et al. 2006), it is perhaps not surprising that the Ceto/Phor-
cys binary survived the sequence of planetary encounters which put it on its present-day orbit.
Although these encounters are unlikely to have been close enough to disrupt the binary, as evi-
denced by the simple fact of its existence, they could possibly be expected to have had some ef-
fect on the eccentricity of the binary orbit.  If so, a future survey of comparable TNBs with orbits
sampling the range from zero to non-zero eccentricity may enable statistical limits to be placed
on their Q values.
Trilling (2007) explores the possibility of binary disruption by encounters with other
TNOs.  For Ceto/Phorcys, the most likely time for such an encounter to have taken place would
have been prior to perturbation into a short-lived Centaur orbit.  The “hardness” H of the binary
can be expressed as a function of the mass M3 of a third body being encountered as
G M1 M 2
2 a M
2  (15)
(Binney and Tremaine 1987; Trilling 2007) where M1 and M2 are the masses of Ceto and Phorcys
(assuming both have the same density), a is the semimajor axis of their mutual orbit, and �v is
the velocity dispersion of potential interlopers, which is unknown, because we do not know what
heliocentric orbit the system was on prior to its becoming a Centaur.  For H(M3) greater than uni-
ty, the system is “hard” against disruption by interlopers of mass M3.  Assuming a velocity dis-
persion of 1 km s-1 (Jewitt et al. 1996), we find that H(M3) is unity for interlopers in the 3 km size
range, assuming an average density of 1 g cm-3.  For smaller interlopers, the Ceto/Phorcys system
is “hard” but for larger interlopers, it is “soft” and could be disrupted.  Durda and Stern (2000)
estimated rates of impacts in the Kuiper belt as a function of impactor size, finding that on aver-
age, an object the size of Ceto+Phorcys should be struck by one interloper of this size over the
age of the solar system.  Additional close, but non-impacting encounters would also be expected.
A possible consequence could be that binaries at least as widely separated as Ceto and Phorcys
(i.e., all currently known TNBs other than the near-contact binaries) represent a remnant popula-
tion which has lost many of its members over the age of Solar System, but that even tighter bina-
ries could be immune to disruption in the present collisional environment, and so could reveal
the primordial binary abundance.  This argument supports the ideas of Goldreich et al. (2002)
and Petit and Mousis (2004) that closer binaries could be considerably more abundant than the
comparatively widely separated ones currently being discovered by ground-based and even HST
searches (e.g., Kern and Elliot 2006; Noll et al. 2007).
7. Conclusion
Combined Hubble Space Telescope and Spitzer Space Telescope observations reveal the
Centaur (65489) Ceto/Phorcys to be a binary system with a separation of 1840 ± 48 km.  The
average geometric albedo is 0.084
�0.021
�0.014 , consistent with radiometrically determined albedos of
other Centaurs.  If both components have equal albedos, as suggested by their shared colors, the
radii of Ceto and Phorcys are 87
�9  and 66
�7  km, respectively.  The average bulk density of the
system is then 1.37
�0.66
�0.32  g cm
-3, higher than recent densities for other comparably-sized binary
outer Solar System objects, but smaller than the densities of much larger icy worlds such as Plu-
to, Triton, and Eris.  Despite probable recent encounters with gas giants, the mutual orbit of Ceto
and Phorcys is nearly circular, consistent with calculations showing that the system should be-
come tidally circularized and synchronized on timescales shorter than the age of the Solar Sys-
Acknowledgments
This work is based in part on NASA/ESA Hubble Space Telescope Cycle 14 program
10508 and 10514 observations.  Support for these programs was provided by NASA through a
grant from the Space Telescope Science Institute (STScI), which is operated by the Association
of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555.  We are
especially grateful to Tony Roman and Tricia Royle at STScI for their rapid reactions in schedul-
ing the HST follow-up observations.  STSDAS and PyRAF are products of STScI. This work is
also based in part on Spitzer Space Telescope Cycle 3 program 30081 observations.  Spitzer is
operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract
with NASA through an award issued by JPL/Caltech.  We thank two anonymous reviewers for
numerous constructive suggestions on how to improve this manuscript. Finally, we are grateful
to the free and open source software communities for empowering us with many of the tools
used to complete this project, notably Linux, the GNU tools, OpenOffice.org, MySQL, FVWM,
Python, IRAF, STSDAS, PyRAF, and TkRat.
REFERENCES
Agnor, C.B., and D.P. Hamilton 2006.  Neptune's capture of its moon Triton in a binary-planet
gravitational encounter. Nature 441, 192-194.
A'Hearn, M.F., M.J.S. Belton, W.A. Delamere, J. Kissel, K.P. Klaasen, L.A. McFadden, K.J.
Meech, H.J. Melosh, P.H. Schultz, J.M. Sunshine, P.C. Thomas, J. Veverka, D.K. Yeo-
mans, M.W. Baca, I. Busko, C.J. Crockett, S.M. Collins, M. Desnoyer, C.A. Eberhardy,
C.M. Ernst, T.L. Farnham, L. Feaga, O. Groussin, D. Hampton, S.I. Ipatov, J.Y. Li, D.
Lindler, C.M. Lisse, N. Mastrodemos, W.M. Owen Jr., J.E. Richardson, D.D. Wellnitz, and
R.L. White 2005.  Deep Impact: Excavating comet Tempel 1. Science 310, 258-264.
Binney, J., and S. Tremaine 1987.  Galactic dynamics.  Princeton Univ. Press, Princeton NJ.
Boehnhardt, H., A. Barucci, A. Delsanti, C. de Bergh, A. Doressoundiram, J. Romon, E. Dotto,
G. Tozzi, M. Lazzarin, S. Fornasier, N. Peixinho, O. Hainaut, J. Davies, P. Rousselot, L.
Barrera, K. Birkle, K. Meech, J. Ortiz, T. Sekiguchi, J.I. Watanabe, N. Thomas, and R.
West 2003.  Results from the ESO large program on transneptunian objects and centaurs.
Earth, Moon, and Planets 92, 145-156.
Bowell, E., B. Hapke, D. Domingue, K. Lumme, J. Peltoniemi, and A. Harris 1989. Application
of photometric models to asteroids.  In Asteroids II, Eds. R.P. Binzel, T. Gehrels, and M.S.
Matthews, Univ. of Arizona Press, Tucson AZ.
Brown, M.E. 2006. The largest Kuiper belt objects.  Invited talk at AAS/DPS meeting, Pasadena
CA, 2006 October 9-13.
Buie, M.W., W.M. Grundy, E.F. Young, L.Y. Young, and S.A. Stern 2006.  Orbits and photome-
try of Pluto's satellites: Charon, S/2005 P1, and S/2005 P2. Astron. J. 132, 290-298.
Burns, J.A. 1986.  Some background about satellites. In Satellites, Eds. J.A. Burns, and M.S.
Matthews, Univ. of Arizona Press, Tucson AZ.
Cooper, J.F., E.R. Christian, J.D. Richardson, and C. Wang 2003.  Proton irradiation of Centaur,
Kuiper belt, and Oort cloud objects at plasma to cosmic ray energy.  Earth, Moon, and
Planets 92, 261-277.
Cruikshank, D.P., M.A. Barucci, J.P. Emery, Y.R. Fernández, W.M. Grundy, K.S. Noll, and J.A.
Stansberry 2007.  Physical properties of trans-neptunian objects.  In Protostars and Planets
V. Eds. B. Reipurth, D. Jewitt, and K. Keil, Univ. of Arizona Press, Tucson AZ.
Davidsson, B.J.R., and P.J. Gutiérrez 2006.  Non-gravitational force modeling of Comet
81P/Wild 2 I. A nucleus bulk density estimate. Icarus 180, 224-242.
Descamps, P. 2005.  Orbit of an astrometric binary system. Celestial Mech. and Dynamical As-
tron. 92, 381-402.
Descamps, P., F. Marchis, T. Michalowski, F. Vachier, F. Colas, J. Berthier, M. Assafin, P.B.
Dunckel, M. Polinska, W. Pych, D. Hestroffer, K.P.M. Miller, R. Vieira-Martins, M. Bir-
lan, J.-P. Teng-Chuen-Yu, A. Peyrot, B. Payet, J. Dorseuil, Y. Léonie, and T. Dijoux 2007.
Figure of the double asteroid 90 Antiope from adaptive optics and lightcurve observations.
Icarus 187, 482-499.
Decker, R.B., S.M. Krimigis, E.C. Roelof, M.E. Hill, T.P. Armstrong, G. Gloeckler, D.C. Hamil-
ton, and L.J. Lanzerotti 2005.  Voyager 1 in the foreshock, termination shock, and he-
liosheath. Science 309, 2020-2024.
Duncan, M.J., and H.F. Levison 1997.  A scattered disk of icy objects and the origin of Jupiter-
family comets. Science 276, 1670-1672.
Duncan, M., T. Quinn, and S. Tremaine 1988.  The origin of short-period comets. Astrophys. J.
328, L69-L73.
Durda, D.D., and S.A. Stern 2000.  Collision rates in the present-day Kuiper belt and Centaur re-
gions: Applications to surface activation and modification on Comets, Kuiper belt objects,
Centaurs, and Pluto-Charon. Icarus 145, 220-229.
Durham, W.B., W.B. McKinnon, and L.A. Stern 2005.  Cold compaction of water ice. Geophys.
Res. Lett. 32, L18202.1-5.
Elliot, J.L., S.D. Kern, K.B. Clancy, A.A.S. Gulbis, R.L. Millis, M.W. Buie, L.H. Wasserman,
E.I. Chiang, A.B. Jordan, D.E. Trilling, and K.J. Meech 2005.  The Deep Ecliptic Survey:
A search for Kuiper belt objects and Centaurs. II. Dynamical classification, the Kuiper belt
plane, and the core population. Astron. J. 129, 1117-1162.
Engelbracht, C.W., M. Blaylock, K.Y.L. Su, J. Rho, and G.H. Rieke 2007.  Absolute calibration
and characterization of the Multiband Imaging Photometer for Spitzer. I. The stellar cali-
brator sample and the 24 µm calibration. Publ. Astron. Soc. Pacific (submitted).
Ford, H.C., and the ACS Science Team 1996.  The Advanced Camera for the Hubble Space
Telescope.  In Space Telescopes and Instruments IV.  Eds. P. Bely and J. Breckinridge,
SPIE 2807, 184-196.
Giauque, W.F., and J.W. Stout 1936.  The entropy of water and the third law of thermo-dynam-
ics: The heat capacity of ice from 15 to 273
K. J. Amer. Chem. Soc. 58, 1144-1150.
Gladman, B., D.D. Quinn, P. Nicholson, and R. Rand 1996.  Synchronous locking of tidally
evolving satellites. Icarus 122, 166-192.
Gladman, B., B.G. Marsden, and C. VanLaerhoven 2007.  Nomenclature in the outer Solar Sys-
tem.  In Kuiper Belt.  Eds. A. Barucci, H. Boehnhardt, D. Cruikshank, and A. Morbidelli.
Univ. of Arizona Press, Tucson AZ (in press).
Goldreich, P., and S. Soter 1966.  Q in the solar system. Icarus 5, 375-389.
Goldreich, P., Y. Lithwick, and R. Sari 2002.  Formation of Kuiper-belt binaries by dynamical
friction and three-body encounters. Nature, 420, 643-646.
Gordon, K.D., C.W. Engelbracht, D. Fadda, J.A. Stansberry, and S. Wachter 2007.  Absolute cal-
ibration and characterization of the Multiband Imaging Photometer for Spitzer. II. 70 mi-
cron imaging. Publ. Astron. Soc. Pacific (submitted).
Grundy, W.M., K.S. Noll, and D.C. Stephens 2005.  Diverse albedos of small transneptunian ob-
jects. Icarus 176, 184-191.
Holman, M.J. 1997.  A possible long-lived belt of objects between Uranus and Neptune. Nature
387, 785-788.
Horner, J., N.W. Evans, and M.E. Bailey 2004.  Simulations of the population of Centaurs - I.
The bulk statistics. Mon. Not. Royal Astron. Soc. 354, 798-810.
Hubbard, W.B. 1984.  Planetary interiors.  Van Nostrand Reinhold Co., New York NY.
Jenniskens, P, D.F. Blake, and K. Kouchi 1998.  Amorphous water ice: A solar system material.
In Solar System Ices, Eds. B. Schmitt, C. de Bergh, and K. Kouchi, Kluwer Academic Pub-
lishers, Boston MA.
Jewitt, D., J. Luu, and J. Chen 1996.  The Mauna Kea-Cerro-Tololo (MKCT) Kuiper belt and
Centaur survey. Astron. J. 112, 1225-1238.
Jewitt, D., L. Chizmadia, R. Grimm, and D. Prialnik 2007.  Water in Small Bodies of the Solar
System.  In Protostars and Planets V, Eds. B. Reipurth, D. Jewitt, and K. Keil, Univ. of
Arizona Press, Tucson AZ.
Johnson, T.V., and J.I. Lunine 2005.  Saturn's moon Phoebe as a captured body from the outer
Solar System. Nature 435, 69-71.
Kern, S.D., and J.L. Elliot 2006.  The frequency of binary Kuiper belt objects. Astrophys. J. 643,
L57-L60.
Kowal, C.T., W. Liller, and B.G. Marsden 1979. The discovery and orbit of 2060 Chiron. IAU
Symp. 81: Dynamics of the Solar System 81, 245-250.
Krist, J.E., and R.N. Hook 2004.  The Tiny Tim user's guide. Version 6.3 is available from
http://www.stsci.edu/software/tinytim/.
Lacerda, P., and D.C. Jewitt 2007.  Densities of Solar System objects from their rotational
lightcurves. Astron. J. 133, 1393-1408.
Lebofsky, L.A., and J.R. Spencer 1989.  Radiometry and thermal modeling of asteroids.  In As-
teroids II, Eds. R.P. Binzel, T. Gehrels, and M.S. Matthews, Univ. of Arizona Press, Tuc-
son AZ.
Leliwa-Kopystyński, J., and K.J. Kossacki 2000.  Evolution of porosity in small icy bodies.
Planet. Space Sci. 48, 727-745.
Levison, H.F., and M.J. Duncan 1997.  From the Kuiper belt to Jupiter-family comets: The spa-
tial distribution of ecliptic comets. Icarus 127, 13-32.
Lunine, J.I., and W.C. Tittemore 1993.  Origins of outer-planet satellites.  In Protostars and
Planets III, Eds. E.H. Levy, and J.I. Lunine, Univ. of Arizona Press, Tucson AZ.
Lupo, M.J., and J.S. Lewis 1979.  Mass-radius relationships in icy satellites. Icarus 40, 157-170.
Marchis, F., D. Hestroffer, P. Descamps, J. Berthier, A.H. Bouchez, R.D. Campbell, J.C.Y. Chin,
M.A. van Dam, S.K. Hartman, E.M. Johansson, R.E. Lafon, D. Le Mignant, I. de Pater,
P.J. Stomski, D.M. Summers, F. Vachier, P.L. Wizinovich, and M.H. Wong 2006.  A low
density of 0.8 g cm-3 for the Trojan binary asteroid 617 Patroclus. Nature 439, 565-567.
McKinnon, W.B., J.I. Lunine, and D. Banfield 1995.  Origin and evolution of Triton.  In Neptune
and Triton, Ed. D.P. Cruikshank, Univ. of Arizona Press, Tucson AZ.
McKinnon, W.B., W.B. Durham, and L.A. Stern 2005.  Cold compaction of porous ice, and the
densities of Kuiper belt objects.  Paper presented at Asteroids, Comets, and Meteors 2005
August 7-12, Rio de Janeiro, Brazil.
Nelder, J., and R. Mead 1965.  A simplex method for function minimization. Computer J. 7, 308-
Noll, K.S., D.C. Stephens, W.M. Grundy, and I. Griffin 2004a.  The orbit, mass, and albedo of
(66652) 1999 RZ253. Icarus 172, 402-407.
Noll, K.S., D.C. Stephens, W.M. Grundy, D.J. Osip, and I. Griffin 2004b.  The orbit and albedo
of trans-neptunian binary (58534) 1997 CQ29. Astron. J. 128, 2547-2552.
Noll, K.S., H.F. Levison, W.M. Grundy, and D.C. Stephens 2006.  Discovery of a binary Cen-
taur. Icarus 184, 611-618.
Noll, K.S., W.M. Grundy, E. Chiang, and J.L. Margot 2007.  Binaries in the Kuiper belt.  In
Kuiper Belt.  Eds. A. Barucci, H. Boehnhardt, D. Cruikshank, and A. Morbidelli. Univ. of
Arizona Press, Tucson AZ (in press).
Peixinho, N., A. Doressoundiram, A. Delsanti, H. Boehnhardt, M.A. Barucci, and I. Belskaya
2003.  Reopening the TNOs color controversy: Centaurs bimodality and TNOs unimodali-
ty.  Astron. & Astrophys. 410, L29-L32.
Petit, J.M., and O. Mousis 2004.  KBO binaries: How numerous are they? Icarus 168, 409-419.
Press, W.H., S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery 1992. Numerical Recipes in C.
Cambridge Univ. Press, New York NY.
Rabinowitz, D.L., K. Barkume, M.E. Brown, H. Roe, M. Schwartz, S. Tourtellotte, and C. Trujil-
lo 2006.  Photometric observations constraining the size, shape, and albedo of 2003 EL61, a
rapidly rotating, Pluto-sized object in the Kuiper belt. Astrophys. J. 639, 1238-1251.
Rasio, F.A., C.A. Tout, S.H. Lubow, and M. Livio 1996, Tidal decay of close planetary orbits.
Astrophys. J. 470, 1187-1191.
Rieke, G.H., and 42 co-authors 2004.  The Multiband Imaging Photometer for Spitzer (MIPS).
Astrophys. J. 154, 25-29.
Rousselot, P., J.M. Petit, F. Poulet, and A. Sergeev 2005.  Photometric study of Centaur (60558)
2000 EC98 and trans-neptunian object (55637) 2002 UX25 at different phase angles. Icarus
176, 478-491.
Schubert, G., T. Spohn, and R.T. Reynolds 1986.  Thermal histories, compositions, and internal
structures of the moons of the solar system.  In Satellites, Univ. of Arizona Press, Tucson
Sheppard, S.S., and D.C. Jewitt 2002.  Time-resolved photometry of Kuiper belt objects: Rota-
tions, shapes, and phase functions. Astron. J. 124, 1757-1775.
Spencer, J.R., J.A. Stansberry, W.M. Grundy, and K.S. Noll 2006.  A low density for binary
Kuiper belt object (26308) 1998 SM165. Bull. Amer. Astron. Soc. 38, 546 (abstract).
Sirianni, M.,  M.J. Jee, N. Benítez, J.P. Blakeslee, A.R. Martel, G. Meurer, M. Clampin, G. De
Marchi, H.C. Ford, R. Gilliland, G.F. Hartig, G.D. Illingworth, J. Mack, and W.J. McCann
2005.  The photometric performance and calibration of the HST Advanced Camera for
Surveys. Publ. Astron. Soc. Pacific 117, 1049-1112.
Stansberry, J.A., W.M. Grundy, J.L. Margot, D.P. Cruikshank, J.P. Emery, G.H. Rieke, and D.T.
Trilling 2006.  The albedo, size, and density of binary Kuiper belt object (47171) 1999
TC36. Astrophys. J. 643, 556-566.
Stansberry, J., W. Grundy, M. Brown, D. Cruikshank, J. Spencer, D. Trilling, and J.L. Margot
2007a.  Physical properties of Kuiper belt objects and Centaurs: Constraints from Spitzer
Space Telescope.  In Kuiper Belt.  Eds. A. Barucci, H. Boehnhardt, D. Cruikshank, and A.
Morbidelli.  Univ. of Arizona Press, Tucson AZ (in press).
Stansberry J.A., K.D. Gordon, B. Bhattacharya, C.W. Engelbracht, G.H. Rieke, M. Blaylock,
F.R. Marleau, D. Fadda, D.T. Frayer, A. Noriega-Crespo, S. Wachter, D. Henderson, D.M.
Kelly, and G. Neugebauer 2007b.  Absolute calibration and characterization of the Multi-
band Imaging Photometer for Spitzer III. An asteroid-based calibration at 160 microns.
Publ. Astron. Soc. Pacific (submitted).
Stephens, D.C., and K.S. Noll 2006.  Detection of six trans-neptunian binaries with NICMOS: A
high fraction of binaries in the cold classical disk. Astron. J. 131, 1142-1148.
Tegler, S.C., W. Romanishin, and G.J. Consolmagno, S.J. 2003.  Color patterns in the Kuiper
belt: A possible primordial origin. Astrophys. J. 599, L49-L52.
Trilling, D.E. 2000.  Tidal constraints on the masses of extrasolar planets. Astrophys. J. 537,
L61-L64.
Trilling, D.E. 2007.  The evolution of Kuiper belt object and Centaur binaries. Astrophys. J. (sub-
mitted).
Trilling, D.E., and G.M. Bernstein 2006.  Lightcurves of 20-100 kilometer Kuiper belt objects
using the Hubble Space Telescope. Astron. J. 131, 1149-1162.
Veillet, C., J.W. Parker, I. Griffin, B. Marsden, A. Doressoundiram, M. Buie, D.J. Tholen, M.
Connelley, and M.J. Holman 2002.  The binary Kuiper-belt object 1998 WW31. Nature 416,
711-713.
Virtanen, J., K. Muinonen, and E. Bowell 2001.  Statistical ranging of asteroid orbits. Icarus 154,
412-431.
Virtanen, J., G. Tancredi, K. Muinonen, and E. Bowell 2003.  Orbit computation for trans-
neptunian objects. Icarus 161, 419-430.
Yoder, C.F. 1982.  Tidal rigidity of Phobos. Icarus 49, 327-346.
Figure 5.  

  Hubble Space Telescope observations of Uranus- and Neptune-crossing object
(65489) Ceto/Phorcys (provisionally designated 2003 FX128) reveal it to be a
close binary system. The mutual orbit has a period of 9.554 +/- 0.011 days and
a semimajor axis of 1840 +/- 48 km. These values enable computation of a system
mass of (5.41 +/- 0.42) 10^18 kg. Spitzer Space Telescope observations of
thermal emission at 24 and 70 microns are combined with visible photometry to
constrain the system's effective radius (109 +10/-11 km) and geometric albedo
(0.084 +0.021/-0.014). We estimate the average bulk density to be 1.37
+0.66/-0.32 g cm^-3, consistent with ice plus rocky and/or carbonaceous
materials. This density contrasts with lower densities recently measured with
the same technique for three other comparably-sized outer Solar System binaries
(617) Patroclus, (26308) 1998 SM165, and (47171) 1999 TC36, and is closer to
the density of the saturnian irregular satellite Phoebe. The mutual orbit of
Ceto and Phorcys is nearly circular, with an eccentricity <= 0.015. This
observation is consistent with calculations suggesting that the system should
tidally evolve on a timescale shorter than the age of the solar system.

Introduction
Objects following unstable, giant-planet crossing orbits in the outer solar system have been
termed Centaurs
 (e.g., Kowal et al. 1979; Elliot et al. 2005).  They are thought to be bodies per-
turbed from the transneptunian region, evolving on timescales of the order of ~10
 years to either
being ejected from the solar system, suffering catastrophic impacts, roasting in the heat of the
Sun as comets, or getting parked in cold-storage in the Oort cloud (e.g., Duncan and Levison
1997; Holman 1997; Levison and Duncan 1997; Horner et al. 2004).  Centaurs offer a sample
from the transneptunian region that is closer and more accessible to Earth-bound observers.
They are less accessible than comets, but could have surfaces more pristine than those of comets
which have spent more time closer to the Sun.
A typical member of the Centaur population has experienced numerous close encounters
with one or more of the giant planets (e.g., Duncan et al. 1988; Levison and Duncan 1997).  Such
events might be expected to induce observable effects on the mutual orbits of binary Centaurs,
when compared statistically with the mutual orbits of binary transneptunian objects (TNOs) in
1 In this paper we use the Deep Ecliptic Survey (DES) definition of Centaurs as non-resonant objects with perihelia
between the orbits of Jupiter and Neptune (Elliot et al. 2005).  The Minor Planet Center defines transneptunian
dynamical classes somewhat differently, and would classify some DES Centaurs, including (65489) Ceto/Phorcys,
as members of the scattered disk (e.g., Gladman et al. 2007).  The Committee on Small Body Nomenclature of the
International Astronomical Union has recently adopted a naming convention for objects on unstable, non-resonant,
giant-planet-crossing orbits with semimajor axes greater than Neptune's.   Befitting their Centaur-like transitional
orbits between TNOs and comets, they are to be named for other hybrid and shape-shifting mythical creatures.
Some 30 objects are currently known to fall into this category, although only Ceto/Phorcys and (42355) Typhon/
Echidna have been named according to the new policy, so far.  The names (announced without explanation in
IAUC 8778) come from classical Greek mythology.  The primary body is named for Ceto (K����), an enormous
sea monster, born of Gaia.  English words like “cetacean” derive from her name.  The secondary is named for
Phorcys (�ó	
��), her brother and husband, depicted as part man, part crab, and part fish.  Together, they begot
numerous terrible monsters, including the Gorgons.
stable heliocentric orbits.  For several years, Noll et al. (2004a, 2004b, 2006, 2007) have been
carrying out a deep search for binaries among various dynamical classes of TNOs, most recently
using the Advanced Camera for Surveys High Resolution Camera (ACS/HRC, Ford et al. 1996)
aboard the Hubble Space Telescope (HST).  An important result from this work is the finding
that the dynamically cold “Classical” sub-population has relatively high binary rates compared
with other transneptunian sub-populations (Stephens and Noll 2006).  Recently, we (KSN,
WMG, DCS, and HFL) have put greater emphasis on searching for binaries among the more dy-
namically excited sub-populations, including the Centaurs.  Prior to its untimely demise, we used
ACS/HRC to search for satellites around 22 Centaurs (as per the DES definition), finding com-
panions for two of them.  The first, (42355) Ty-
phon/Echidna (provisionally designated 2002 CR46),
was discovered in 2006 January and a second,
(65489) Ceto/Phorcys (provisionally designated
2003 FX128), was discovered in 2006 April (Noll et
al. 2006).  The latter system is the subject of this pa-
The initial discovery of (65489) Ceto/Phorcys
was 2003 March 22 at the Palomar 1.2 m Schmidt
camera by C. Trujillo and the Near-Earth Asteroid
Tracking (NEAT) team (MPEC 2003-H33).  It was
soon identified in a series of pre-discovery images
dating back to 1987, enabling its elongated helio-
centric orbit (shown in Fig. 1) to be determined,
with osculating heliocentric elements: semimajor
axis a� = 102 AU, inclination i� = 22
, and eccen-
tricity e� = 0.82.  The orbit crosses the orbits of
both Uranus and Neptune and also extends far be-
yond the solar wind radiation environment to an
aphelion of about 186 AU, well beyond the 94 AU
distance where Voyager 1 crossed (or was crossed
by) the heliosphere termination shock (e.g., Decker
et al. 2005) with important implications for radi-
olytic processing of its surface (Cooper et al. 2003).
2. Hubble Space Telescope Observations and Analysis
The binary nature of (65489) Ceto/Phorcys was discovered in HST ACS/HRC images ob-
tained 2006 April 11 UT (see Fig. 2), as part of Cycle 14 program 10514 (led by KSN).  Details
of the clear filter combination and dithering techniques used in program 10514 are described by
Noll et al. (2006).
Follow up ACS/HRC images were obtained on May 6, 10, 30, and 31 UT as part of Cy-
cle 14 program 10508 (led by WMG).  The scheduling of these observations benefited from a
statistical ranging Monte Carlo type of analysis inspired by the work of J. Virtanen and col-
leagues (e.g., Virtanen et al. 2001, 2003).  This approach enabled us to optimize the timing of
Fig. 1: Plan view of the Solar System, showing the
heliocentric orbit of (65489) Ceto/Phorcys (dotted
curve) compared with orbits of the four gas giants
(solid curves), with points indicating positions as of
2007 July.  The orbit crosses the orbits of both
Uranus and Neptune, but considerable time is also
spent well beyond 94 AU from the Sun, the dis-
tance at which Voyager 1 crossed the heliosphere
termination shock (e.g., Decker et al. 2005)..
-50 0 50 100 150
Distance from Sun (AU)
subsequent observations for satellite orbit determination, within the limitations of HST schedul-
ing and the restricted visibility windows imposed by the two-gyro mode in which HST is cur-
rently operating.  Our implementation of the technique is described in a forthcoming paper
(Grundy et al. in preparation).  The follow up observations used the F606W and F814W filters of
the ACS/HRC camera.  For each visit, eight 223 second exposures (four in each filter) were ob-
tained, dithered over a four-point box pattern so that images with defects such as hot pixels or
cosmic rays contaminating the flux of the binary system could be easily identified and excluded
from further analysis.
2.1. Photometry and astrometry
Data were processed through the standard CAL ACS pipeline at Space Telescope Science
Institute (STScI), producing dark-subtracted, flat-fielded images (for details, refer to http://
www.stsci.edu/hst/acs/documents/handbooks/cycle16).  Astrometry and pho-
tometry were calculated from these images by fitting model point spread functions (PSFs) gener-
ated by Tiny Tim (Krist and Hook 2004) and correcting the results for the geometric distortion
arising from the separation between the ACS camera and the optical axis of the telescope.  De-
tails of the binary-PSF fitting procedure are described in Stephens and Noll (2006).  The PyRAF
program xytosky in the STSDAS package (http://www.stsci.edu/resources/soft-
ware_hardware) was used to translate the pixel coordinates found for Ceto and Phorcys to
their true right ascension and declination values.  Accurate separations and position angles for
the binary pair could then be calculated, and measurements from the multiple images combined
to get the average relative sky plane astrometry for each visit in Table 1.
Table 1. HST ACS/HRC observational circumstances and 1-� relative astrometry
Average UT date and
a ��b ��b
(AU) (degrees) (arcsec)
2006/04/11 21.691 27.753 26.785 0.542 +0.0172 ± 0.002 +0.0833 ± 0.003
2006/05/06   7.447 27.813 26.881 0.812 �0.0475 ± 0.002 �0.0687 ± 0.001
2006/05/10   4.510 27.822 26.912 0.916 �0.0032 ± 0.001 +0.0860 ± 0.002
2006/05/30   0.217 27.870 27.129 1.440 +0.0362 ± 0.001 +0.0747 ± 0.001
2006/05/31   1.692 27.873 27.143 1.466 +0.0829 ± 0.002 +0.0295 ± 0.002
Fig. 2: Example Hubble Space Telescope ACS/HRC single frames of Ceto and Phorcys (centered on Ceto), tak-
en 2006 April 11, May 5, May 10, May 30, and May 31 UT, from left to right.  The HRC pixels are projected to
sky-plane geometry with North up and East to the left, revealing the geometric distortion at the HRC focal
plane.  For scale, the mosaic of images is 2.0 × 0.4 arcsec.  The left-most image was one of the binary discov-
ery sequence of images, obtained through the CLEAR filter as part of program 10514.  The other four images
were obtained through the F814W filter as part of program 10508.                                                      
                      
The distance from the Sun to the target is r and from the observer to the target is �.  The phase angle, the an-
gular separation between the observer and Sun as seen from the target, is g.
Relative right ascension �� and relative declination �� are computed as �� = (�2 − �1)cos(�) and �� = �
2 − �1, where subscripts 1 and 2 refer to Ceto and Phorcys, respectively.
The PSF model binary solutions were also used to calculate individual magnitudes for Ceto
and Phorcys.  To get the magnitude of one object, we subtracted the model PSF of the other from
each image and then used the PyRAF multidrizzle task in the STSDAS package to remove the  ge-
ometric distortion.  For each resulting undistorted image, the total flux within a 3 pixel radius
was measured and corrected to an aperture of 20 pixels (0.5 arcsec) computed for an undistorted
model PSF.  We then applied the Sirianni et al. (2005) AC05 (0.5 arcsec to ∞) aperture correc-
tion coefficients, the photometric zero point for each filter, and the charge transfer efficiency cor-
rection to get the final HST magnitude in each image.
To compare the HST magnitudes with ground based results and to help constrain the size
and albedo of (65489) Ceto/Phorcys, transformation coefficients were derived to convert the
F606W and F814W magnitudes to Johnson-Cousins V and I magnitudes.  The ACS and Johnson-
Cousins filters are not exact counterparts, so assumptions had to be made about the spectral ener-
gy distribution of Ceto/Phorcys.  We applied a reddening coefficient to a solar spectrum until it
had the same F606W�F814W color as (65489) Ceto/Phorcys.  We then convolved this spectrum
with the HST and Johnson-Cousins filters using the synphot task under STSDAS to get transfor-
mation coefficients specific to Ceto/Phorcys.  These coefficients were used to transform the HST
magnitudes of Ceto and Phorcys in each image to the Johnson-Cousins system.  For each visit
the F606W, F814W, V, and I magnitudes were averaged to produce Table 2.
Table 2. Photometry from Hubble Space Telescope ACS/HRC observations
Observation                       Ceto                                          Phorcys                    
Date (UT) F606W F814W V I F606W F814W V I
2006/05/06 21.43 20.54 21.68 20.56 21.94 21.12 22.15 21.14
2006/05/10 21.35 20.53 21.57 20.55 21.94 21.10 22.18 21.13
2006/05/30 21.49 20.61 21.74 20.63 22.10 21.24 22.35 21.26
2006/05/31 21.49 20.63 21.72 20.65 22.07 21.24 22.29 21.26
Table note: Photometric 1-� uncertainties in F606W and F814W filters are about ±0.04 mag.  Color transfor-
mation uncertainties inflate the V and I uncertainties to about ±0.06 mag.
Two filters were used in the follow-up observations to search for color differences between
Ceto and Phorcys.  The average F606W�F814W colors were 0.867 ± 0.028 and
0.836 ± 0.028 mag for Ceto and Phorcys, respectively.  Ceto's measured color is slightly redder
than that of Phorcys, but the difference is statistically insignificant.  Our average V�I color for
the system is 1.07 ± 0.04, corresponding to a spectral slope of 15.3 ± 1.5 (% rise per 100 nm
relative to V), putting Ceto/Phorcys among the gray color clump of Centaurs, albeit at the red
edge of that clump (e.g., Boehnhardt et al. 2003; Peixinho et al. 2003).  Tegler et al. (2003) re-
ported a B�V color for (65489) Ceto/Phorcys of 0.86 ± 0.03 and a V�R color of 0.56 ± 0.03,
consistent with this result.
No lightcurve variability has been reported for this system and our data show no evidence
for it either.  The average magnitudes from the 4 visits reported in Table 2 differ by more than
the 1-� uncertainties, but that variability can be attributed to geometry.  After removing photo-
metric effects of the changing distances from the Sun to the target r and from the observer to the
target � and also the effect of the phase angle g (by assuming generic dark-object phase behavior
as represented by the H and G system of Bowell et al. 1989, with G = 0.15), we find that the
largest deviation from the 4-visit mean for either object or filter is only 1.5-� (for Ceto during
the May 10 UT visit in F606W).  With only four random epochs and ±0.04 mag photometric un-
certainties, the F606W data can only rule out a 0.15 mag sinusoidal lightcurve at about the 1-�
confidence level.  However, the observed F606W outlier is not mirrored in the F814W filter, as
would be expected if a lightcurve from an elongated shape were responsible, so noise is the like-
lier explanation for that point.  At least one deviation as large as 1.5-� is to be expected among
four sets of four measurements.
2.2. Orbit fitting and system mass
Our methods for fitting mutual orbits to relative astrometry of binaries have been described
previously (Noll et al. 2004a, 2004b, 2006, 2007).  We use the downhill simplex “amoeba” algo-
rithm (Nelder and Mead 1965; Press et al. 1992) to iteratively adjust a set of seven orbital ele-
ments to minimize the �2 statistic of residuals between observed and predicted sky plane relative
positions of the primary and secondary, accounting for light time delays and relative motion be-
tween the observer and the binary pair.  For previous orbit fits we had used the date and argu-
ment of periapsis as two of the seven fitted orbital elements.  This choice had originally been
made because the orbit of the satellite of 1998 WW31 (Veillet et al. 2002) suggested to us that
very high eccentricities might be the norm.  Unfortunately, for circular orbits those two parame-
ters become degenerate, and as eccentricity approaches zero, their use produces numerical insta-
bilities which plagued our fits to the near-circular orbits of Pluto's satellites (Buie et al. 2006).
Accordingly, we have since modified our orbit-fitting code to fit the following seven elements:
period P, semimajor axis a, eccentricity e, inclination i, mean longitude at epoch �, longitude of
ascending node �, and longitude of periapsis �.  To estimate the uncertainty in each of these fit-
ted elements, we used two different methods.  First, we systematically varied each parameter
around its best fit value, allowing the other six to adjust themselves to re-minimize �2, creating
slices through the seven dimensional �2 space which enabling us to map out the 1-� confidence
contour.  Second, we fitted orbits to random sets of input astrometry data generated from the ob-
served astrometry by adding Gaussian noise consistent with the astrometric uncertainties.  The
bundle of Monte Carlo orbits generated in this way provides an alternate measure of how well
we have determined the orbital elements.  Both methods gave very similar 1-� uncertainties on
the fitted elements for the orbit of Phorcys around Ceto.  The elements are tabulated in Table 3
and the projection of the orbit on the sky plane at the average time of the HST observations is
shown in Fig. 3.
Table 3. Orbital elements and derived parameters with 1-� uncertainties or limits
Parameter Orbit 1 (�2 = 2.3) Orbit 2 (�2 = 2.4)
Fitted orbital elements
   Period (days) P  9.557 ± 0.008  9.551 ± 0.007
   Semimajor axis (km) a 1840 ± 41   1841 ± 47   
Parameter Orbit 1 (�2 = 2.3) Orbit 2 (�2 = 2.4)
   Eccentricity e  � 0.013  � 0.015
   Inclinationa (deg) i 68.8 ± 2.9 116.6 ± 3.0   
   Mean longitudea at epochb (deg) � 23.0 ± 2.7 53.5 ± 5.2 
   Longitude of asc. nodea (deg) � 105.5 ± 3.7   134.6 ± 3.4   
   Longitude of periapsisa (deg) �     40 ± 360c     70 ± 360c
Derived parameters
   System mass (1018 kg) Msys 5.40 ± 0.36 5.42 ± 0.42
   Orbit pole right ascensiona (deg) � 15.5 ± 5.2  44.6 ± 5.2  
   Orbit pole declinationa (deg) � 21.2 ± 4.0  −26.7 ± 4.1    
Referenced to J2000 equatorial frame.
The epoch is Julian date 2453880 (2006 May 24 12:00 UT).
The uncertainty of ±360
 indicates that
this parameter is unconstrained.
It can be difficult to distin-
guish between an orbit and its mirror
image through the plane of the sky
(e.g., Descamps 2005).  Parallaxes
from the differential motion of the
Earth and the object will eventually
enable a patient observer to break
the ambiguity between an orbit and
its mirror, as the observer's sky
plane gradually rotates with respect
to the orbit.  More face-on orbits,
with their smaller excursions of the
satellite in the direction radial to the
observer, are relatively slow to re-
veal which solution is the real one.
At the time of our observations, the
Ceto/Phorcys orbit was tilted about
28
 from face-on.  We list both solu-
tions, noting that �2 is slightly better
for the first one, but does not ex-
clude the second one.  For both or-
bits, the longitude of periapsis � is
unconstrained, in that it can take any
value from 0 to 360
 without pushing
�2 over the 1-� threshold.  However,
there is a shallow �2 minimum for �
at about 40
 for Orbit 1 and about 70
 for Orbit 2.  Neither orbit will be oriented edge-on to the
Fig. 3: Projection of the orbit of Phorcys (gray oval) relative to Ce-
to's location (black dot) onto the sky plane at the average time of the
five HST observations.  Points with 1-� error bars indicate relative
astrometry between Ceto and Phorcys measured from the ensemble
of dithered frames during each HST visit.  Open circles are relative
positions of Phorcys at the times of the observations as calculated
from orbit 1 in Table 3.  The spot at the origin and the open circles
are scaled to the sizes of Ceto and Phorcys, respectively, derived in
Section 4.
inner solar system within the next century, so use of mutual events to obtain more detailed infor-
mation about the system geometry (e.g., Noll et al. 2007) is a distant future prospect.
The mutual orbit of Ceto/Phorcys can be compared with orbits of satellites of other small
outer Solar System bodies (see Noll et al. 2007 Table 2).  It is noteworthy that this is the least
massive system with a near-circular orbit by some three orders of magnitude.  All known semi-
major axes for transneptunian binaries are larger except for that of Typhon/Echidna (Grundy et
al. in preparation) and all periods are longer except for that of Charon's orbit about Pluto.  Al-
though these characteristics sound exceptional, we do not believe this system to be unusual.
Closer systems such as this one are simply more difficult to discovery and to study.
From the semimajor axis a and period P, we can compute the mass of the combined system
Msys, according to
4�2 a3
, (1)
where G is the gravitational constant which we take to be 6.6742 × 10-11 m3 s-2 kg-1.  Since we
have two possible orbits, we adopt values of P = 9.554 ± 0.011 days, a = 1840 ± 48 km, and
Msys = (5.41 ± 0.42) × 1018 kg to encompass the 1-� uncertainties from both solutions.  The
semimajor axis is measured to much lower fractional precision than the period is and it is raised
to a higher power in the mass equation, so it is the dominant source of uncertainty in the
Ceto/Phorcys system mass.
3. Spitzer Space Telescope Observations and Analysis
Spitzer Space Telescope ob-
served (65489) Ceto/Phorcys in
2006 July with the Multiband Imag-
ing Photometer for Spitzer (MIPS,
Rieke et al. 2004) in its 24 and
70 µm bands, which have effective
wavelengths of 23.68 and 71.42 µm.
These observations were part of Cy-
cle 3 program 30081 (led by JAS).
Data were collected using the pho-
tometry observing template, which is
tailored for photometry of point
sources.  The observatory tracked
the target during the observations,
although the motion was negligible
relative to the size of the point-
spread function (PSF) at these wave-
lengths.  The target was imaged in
both bands during two visits separat-
ed by 37 hours, over which time
(65489) Ceto/Phorcys moved 38 arcsec relative to the background stars, allowing us to identify
Fig. 4: Spitzer Space Telescope MIPS images of Ceto+Phorcys at
24 µm (left) and 70 µm (right) from 2006 July 18 UT.  Each image is
180 arcsec square, and is oriented North up, East left.  The circles
are centered at the ephemeris position of the object, and have diame-
ters equal to four times the FWHM of the Spitzer PSF in each band.
While the object is not observed at exactly the ephemeris position,
the offsets are consistent in the data from this and the other epoch,
the object motion vector relative to the background objects is as pre-
dicted, and it is the only moving object visible at both epochs.  Data
from the second epoch were used to remove background sources
from the first epoch, and vice versa.
the target with certainty.  Since the images from the two epochs have significant spatial overlap,
we could use the image pairs to confirm that no strong background sources were present at the
target position at either epoch and to subtract off the effect of weak background sources.  The
two visits would also help average over any possible thermal lightcurve variability.  Images from
the first epoch are shown in Fig. 4.
We reduced the raw data and mosaicked them using the MIPS instrument team data analy-
sis tools (Gordon et al. 2007).  For the 24 µm data, basic processing included slope fitting, flat-
fielding, and corrections for droop.  All of these steps are currently implemented in the Spitzer
Science Center (SSC) pipeline products.  Additional corrections were made to remove readout
offset (a jailbar pattern in the images), the effects of scattered light (which introduces a pointing-
dependent background gradient and slightly degrades the sensitivity), and the application of a
second-order flat field, derived from the data itself, to remove latents from previous observa-
tions. 
The photometric repeatability of MIPS observations of moderately bright sources is better
than 1% at 24 µm, and is 5% at 70 µm.  The uncertainty in the absolute calibration of these bands
is 4% and 8% respectively (Engelbracht et al. 2007; Gordon et al. 2007).  For purposes of fitting
models to our photometry, we use uncertainties that are the root-square-sum of the absolute cali-
bration uncertainties and the measurement uncertainties determined from the images themselves.
We adopt slightly larger 1-� calibration uncertainties, 5% and 10%, to account for uncertainties
in color and aperture corrections.  The widths of the filter bandpasses are about 25%, resulting in
modest color corrections.  We iteratively applied color corrections to our photometry, which con-
verged to give a color temperature of 73.2 K, and color corrections of +2.6% and +8.6% at 24
and 70 µm, respectively (see Stansberry et al. 2007b).  The uncertainties on the correction factors
are perhaps a few percent of the factors themselves, and so are negligible for our study.
We measured the flux density of (65489) Ceto/Phorcys using 9.96 and 29.6 arcsec diame-
ter apertures (about 4 and 3 native pixels) at 24 and 70 µm; the PSF full-width at half-max is 6.5
and 20 arcsec in those bands.  The apertures were positioned at the center-of-light centroid.  Mo-
saics were constructed using 1.245 arcsec and 4.925 arcsec pixels at 24 and 70 µm (about half the
native pixel scale of those arrays).  We applied aperture corrections of 1.91 and 1.85 to the 24
and 70 µm photometry to compute the total flux (see Gordon et al. 2007; Engelbracht et al. 2007
for details).  Uncertainties in the aperture corrections are approximately 1%.  Table 4 summa-
rizes the circumstances of our Spitzer MIPS observations and the measured, color-corrected flux
densities.
Table 4. Spitzer Space Telescope MIPS observational circumstances and thermal fluxes
Average UT date r � g 24 µm flux 70 µm flux
and hour (AU) (degrees) (mJy)
2006/07/18 10.23 27.990 27.662 1.99 1.47 ± 0.02a 14.9 ± 1.0a
2006/07/19 19.46 27.993 27.686 2.00 1.48 ± 0.02a 14.5 ± 1.2a
Adopted 27.991 27.674 2.00 1.473 ± 0.076b 14.69 ± 1.84b
Errors reflect the signal to noise ratios in the observations, which were about 70 and 13, resulting from integra-
tions of 900 and 2640 seconds, at 24 and 70 µm, respectively.
The adopted 1-� flux errors include additional absolute calibration uncertainties.
4. Size, Albedo, and Density
The thermal fluxes measured by Spitzer can be used to constrain the size of Ceto/Phorcys
and also the albedo if they can be combined with suitable visible photometry.  Tegler et al.
(2003) reported a V magnitude of 20.70 ± 0.03 from Vatican Observatory 1.8 m telescope obser-
vations when the system was at heliocentric distance r = 25.190 AU, geocentric distance
� = 24.298 AU, and phase angle g = 1.09
.  Assuming typical phase behavior for low albedo
objects (G = 0.15 in the H and G system of Bowell et al. 1989; see also Sheppard and Jewitt
2002; Rousselot et al. 2005), we can convert the Tegler et al. V photometry to absolute magni-
tude HV = 6.603 ± 0.030.  Under the same assumptions, our HST photometry (in Tables 1 and 2)
gives HV = 6.625 ± 0.030.  Combining these, we adopt the weighted average
HV = 6.614 ± 0.021.
Thermal fluxes are used to to constrain an object's size via a variety of thermal models
(e.g., Lebofsky and Spencer 1989).  We used the approach described by Stansberry et al. (2006),
which takes advantage of the existence of visual photometry plus two well-separated thermal in-
frared wavelengths from Spitzer/MIPS to simultaneously fit the size, albedo, and beaming pa-
rameter �, using the standard thermal model (STM), which assumes instantaneous thermal equi-
librium with sunlight illuminating a spherical surface.  We also assumed unit emissivity.  A wide
range of real-world complications such as rotation, pole orientation, surface roughness, and ther-
mal inertia can strongly influence observable thermal fluxes relative to what would be predicted
by the simple STM, but in general, the effects of these complications look spectrally similar to
the effect of changing the beaming parameter �.  If � is constrained by the data, the large model
uncertainties in size and albedo which would otherwise flow from lack of knowledge of these
other physical properties are greatly diminished.  Using this model, we are able to match the ob-
served thermal and visible photometry of (65489) Ceto/Phorcys with an effective radius
Reff = 109
�11  km, along with beaming parameter � = 0.77
�0.08
�0.09 , and geometric albedo
Ap = 0.084
�0.021
�0.014 .  Uncertainties on the derived parameters were determined by means of Monte
Carlo methods.  Thousands of random sets of input fluxes were generated, consistent with the
observational uncertainties.  Each set resulted in slightly different values of the derived parame-
ters, creating a population of solutions from which 1-� uncertainties could be estimated.  Errors
from possible lightcurve variations are small enough to be neglected.  For example, with thermal
observations at two effectively random times, the 1-� upper limit 0.15 mag lightcurve mentioned
earlier would contribute about a 1.4% average radius error, well below our 
�11 %  reported uncer-
tainty.
The derived value of � = 0.77 �0.08�0.09  is on the low side of what has been seen for other TNOs
and Centaurs, suggesting that Ceto and Phorcys have some combination of relatively low thermal
inertias, slow rotation rates, especially rough surfaces, or their poles oriented toward the Sun.
For comparison, Stansberry et al. (2007a) found � values ranging from 0.6 to 2.3, with an aver-
age of 1.3, for a sample of 23 TNOs and Centaurs detected with good signal precision at both 24
and 70 µm wavelengths by Spitzer/MIPS.
Our 0.084
�0.021
�0.014  albedo of Ceto/Phorcys is consistent with albedos of other Centaurs.
Stansberry et al. (2007a) report albedos for 11 other Centaurs (by the DES classification) detect-
ed with good signal precision at both 24 and 70 µm by Spitzer/MIPS.  That sample has an aver-
age albedo of 0.06 and a standard deviation of 0.04.  Considerable albedo diversity is also appar-
ent among other small outer Solar System objects (e.g., Grundy et al. 2005; Cruikshank et al.
2007; Stansberry et al. 2007a), but correlations between albedo and dynamical class or color re-
main poorly established, except for a general trend of progressively lower average albedos from
TNOs to Centaurs to comet nuclei, and a trend of higher albedos for the redder Centaurs (Stans-
berry et al. 2007a).
By assuming the albedos of Ceto and Phorcys are similar to one another, we can use the
0.584 ± 0.030 average magnitude difference between them to work out their individual radii, ob-
taining RCeto = 87
�9  km and RPhorcys = 66
�7  km.  Computing the total system volume from these
two radii, and combining that with the total system mass from the mutual orbit, we obtain an av-
erage bulk density of 1.37
�0.66
�0.32  g cm
-3.  The assumption of equal albedos is consistent with the
observation of indistinguishable colors for the two components, but we can also explore how
sensitive we are to that assumption.  Assume, for instance, that the albedo of Phorcys was actual-
ly twice that of Ceto.  We would then have overestimated the average bulk density by a factor of
9%.  If Ceto's albedo were double that of Phorcys, we would have underestimated the average
bulk density by 2%.  Unless the albedo contrast between Ceto and Phorcys is very extreme in-
deed, the density is relatively insensitive to our assumption of equal albedos.  Our conclusions
are comparably insensitive to possible lightcurve variations, as mentioned previously.
Bulk densities 	 of icy objects are often interpreted in terms of a rock fraction
	rock
, (2)
where 	ice is taken to be 0.937 g cm-3 for low temperature crystalline ice Ih (Lupo and Lewis
1979) and 	rock could range from 2.5 g cm-3 for hydrated silicates to 3.5 g cm-3 for anhydrous sili-
cates (e.g., Schubert et al. 1986).  For 	rock = 2.5 g cm-3, our average bulk density of Ceto/Phor-
cys yields a rock fraction frock = 0.51
�0.29
�0.39 , a value intermediate between the rock-rich composi-
tions of Triton and Pluto and the more ice-rich compositions of some of the smaller satellites of
Saturn.  However, this rock fraction calculation only makes sense in the absence of void space,
or of other possible interior components, such as carbonaceous materials.
We estimate the hydrostatic pressure at the cores of Ceto and Phorcys according to
�G	2 R2 (3)
(e.g., Stansberry et al. 2006) as 2.0
�0.6  and 1.1
�0.4  MPa, respectively.  These pressures are insuf-
ficient to squeeze much void space out of cold, particulate H2O ice.  Laboratory experiments by
Durham et al. (2005) show that at pressures in the 5 to 10 MPa range, appreciable compaction
begins to occur in cold ice, but as much as 10% void space remains even at pressures as high as
100 MPa.  If Ceto and Phorcys have remained cold since their accretion, we can anticipate rela-
tively high fractions of void space within them, complicating interpretation of their densities in
terms of ice and rock fractions.
Bulk densities are known for several much larger outer Solar System bodies, including
Pluto and Charon (2.03 ± 0.06 and 1.65 ± 0.06 g cm-3, respectively; Buie et al. 2006), Eris
(2.26 ± 0.25 g cm-3; Brown 2006), and (136108) 2003 EL61 (3.0 ± 0.4 g cm-3; Rabinowitz et al.
2006).  These higher densities are consistent
with expectation for rock-rich and possibly
differentiated objects which probably expe-
rienced warm interior temperatures at some
time in their histories.  Two other small bi-
nary TNOs have recently had their average
bulk densities determined via the technique
used in this paper.  Stansberry et al. (2006)
reported a bulk density of 0.50
�0.30
�0.20  g cm
for (47171) 1999 TC36 and Spencer et al.
(2006) reported a bulk density of 0.70
�0.32
�0.21  
g cm-3 for (26308) 1998 SM165.  These much
lower densities require significant void
space, even for pure ice compositions.  Low
densities compared with likely bulk compo-
sitions have also been determined recently
for the Trojan asteroid (617) Patroclus
(Marchis et al. 2006) and for main belt as-
teroids (e.g., (90) Antiope; Descamps et al.
2007) as well as for much smaller comet
nuclei (e.g., A'Hearn et al. 2005; Davidsson
and Gutiérrez 2006).  However, the irregu-
lar saturnian satellite Phoebe, with a size
similar to that of Ceto+Phorcys, has a high-
er bulk density of 1.630 ± 0.033 g cm-3
(Johnson and Lunine 2005).  These diverse
densities (shown in Figure 5) point to con-
siderable variety in bulk compositions and
interior structures among small outer Solar System bodies.
Apart from bulk compositional differences, thermal history is another potential source of
density diversity among TNOs.  Objects in the outer parts of the protoplanetary disk could ini-
tially accrete ice mostly in the amorphous phase, with a fluffy structure that includes consider-
able void space (e.g., Jenniskens et al. 1998).  Subsequent thermal pulses, from whatever source
(impacts, tidal dissipation, Al26 decay, etc.), could crystallize amorphous ice.  The crystallization
would liberate additional heat as well as potentially reducing void space (e.g., Jewitt et al. 2007).
The presence of varying amounts of NH3 could also lead to considerable diversity of thermal
evolution and thus density (e.g., Leliwa-Kopystyński and Kossacki 2000).
5. Tidal evolution
Since gravitational attraction falls off as the square of separation, Ceto and Phorcys both
produce differential gravitational accelerations across the bodies of their partners, slightly dis-
torting their equipotential figures.  If their mutual orbit is eccentric, or either of their rotation
states differs from the orbital rotation rate and orientation, this distortion will change over time,
Fig. 5: Comparison of the average bulk density of (65489)
Ceto/Phorcys (star) with densities for binary outer Solar
System objects discussed in the text (black dots) and icy
satellites of Saturn, Uranus, and Neptune (gray points, from
Burns 1986 and McKinnon et al. 1995).  For the binaries
with unknown mass ratios, the radius shown is that of the
primary, since it is likely to dominate the average density.
The dashed curve is a theoretical bulk density for non-
porous, pure H2O ice subject to self-compression at 77 K
(Lupo and Lewis 1979).  The dotted curve allows for poros-
ity in pure, cold, granular H2O ice Ih, based on compaction
data from Durham et al. (2005) as modeled by McKinnon et
al. (2005).  An expected trend of smaller objects having sys-
tematically lower densities than their larger counterparts
(Lacerda and Jewitt 2007) is not cleanly supported by the
present data for (65489) Ceto/Phorcys.
100 1000
Radius (km)
resulting in frictional dissipation of energy and leading to tidal evolution of their orbit and spin
states.  The rate of energy dissipation and tidal evolution depends on the specific tidal dissipation
factor Q, which is a complicated function of interior structure and composition that describes the
degree to which tidal friction is deposited in a given body.  Q is approximately equal to 1/(2�),
where � is the angle between the tidal bulge of the object and the line of centers between the two
objects.  Because Ceto and Phorcys have similar sizes and probably similar compositions, we as-
sume that Q1 � Q2 � Q (where subscripts 1 and 2 to refer to Ceto and Phorcys, respectively).
Typical Q values for solid planets and icy satellites range from 10 to 100 (e.g., Goldreich and
Soter 1966; Yoder 1982; Hubbard 1984).  We take Q = 100, to minimize dissipation and thus
compute upper limits on tidal evolution timescales.
Small solid objects require a correction to Q because their rigidity can be large compared
to their self-gravity (Hubbard 1984).  In this case, the small body may not be able to relax to hy-
drostatic equilibrium over a tidal cycle, but instead acts elastically.  Thus, the deformation of the
body's surface is smaller than it would be in hydrostatic equilibrium as elastic forces tend to
maintain the body's shape.  The correction to Q takes the form
Q' = Q �1�19�2 g 	R � , (4)
where µ is the rigidity, 	 is the density, R is the radius, and g is the surface gravity (Goldreich
and Soter 1966).  Values adopted for use in our calculations are tabulated in Table 5.  The rigidi-
ties of Ceto and Phorcys are, of course, unknown.  If they are un-fractured monoliths, their
rigidities could be as high as 1011 dyn cm-2, intermediate between values for solid ice and solid
rock (Gladman et al. 1996).  In this extreme case, the correction to Q would be large, with
Q' = 3 × 106.  At the other extreme, if Ceto and Phorcys are unconsolidated “sand piles” their
rigidities could be as low as 107 dyn cm-2 (Yoder 1982).  In this case, the correction to Q is small,
giving Q' = 300.  We use these bracketing values of Q' to explore the range of possible
timescales for tidal spin-locking and orbital evolution in the Ceto/Phorcys system.
Table 5. Physical parameters adopted.
Parameter Ceto Phorcys
Radius R 87 km 66 km
Mass M 3.74 × 1018 kg 1.67 × 1018 kg
Density 	 1.37 g cm-3 1.37 g cm-3
Surface gravity g 3.3 cm s-2 2.5 cm s-2
Table note: These values are derived from the effective radius Reff, system mass Msys, and magnitude difference,
subject to the assumption of equal albedos and equal densities.
Over time, tidal effects can synchonize the spin rate of Phorcys to its orbital period (as for
the Earth's Moon, which keeps one face oriented toward Earth) and, on a longer timescale, syn-
chronize Ceto's spin rate as well (analogous to the Pluto-Charon system, where both members
keep the same face toward each other).  The timescale for spin-locking Ceto (slowing its spin
rate to match the mutual orbital period) is given by
spin , 1
Q'��1 M1 a
G M 2
, (5)
where subscripts 1 and 2 refers to Ceto and Phorcys, respectively, M is mass, R is radius, and 
�� is the difference between an initial angular rotation rate and the final, synchronized rate
(Goldreich and Soter 1966; Trilling 2000).  The timescale for spin-locking Phorcys can be found
simply by swapping all the subscripts in Equation 5.  A typical rotation period for TNOs is
around 10 hours (e.g., Trilling and Bernstein 2006).  The current orbital period is much longer
than this, so we set ��1 (and ��2) to correspond to this rate (one could equally start with the
breakup rotation rate, in the 2 to 3 hour period range).  We find that the spin-locking timescale
for Ceto ranges from 106 to 1010 years and the timescale for spin-locking Phorcys is about a fac-
tor of three shorter.  We conclude that unless these bodies are rigid monoliths, Phorcys should be
spin-locked to Ceto and Ceto to Phorcys as well, or nearly so.  (Recall that if Q is smaller than
our assumed maximum value of 100, the spin-lock timescale decreases, increasing the likelihood
of spin-locking.)
The eccentricity of the Ceto/Phorcys mutual orbit can also evolve due to tides raised on ei-
ther object by the other.  Following Goldreich and Soter (1966) we can write the contributions of
the two terms as
= � dedt �
�� dedt �
, (6)
where (de/dt)1 accounts for the effect of tides raised on the primary by the secondary and (de/dt)2
accounts for tides raised on the secondary by the primary.  The two contibutions can be ex-
pressed as
e � dedt �1 =
16 � GM 1 � R1
6.5 � sign �2�1�3n2 � (7)
where n2 is the mean orbital motion of the secondary and
e � dedt �2 = �
�G M 13� R2
6.5 � . (8)
Employing our previous result that Ceto and Phorcys should be spin-locked (or nearly so), �1
should be equal (or close) to n1 so (de/dt)1 is negative, implying that de/dt must also be negative
(since (de/dt)2 is always negative)
2.  A negative de/dt indicates circularization of the orbit.
Using the values for Ceto and Phorcys in Table 5, we find
7×10�12�1.4×10�11
Equating e with �de and solving for dt to estimate the timescale to reduce an initial eccentricity
to zero, we find that the circularization timescale ranges from 5 × 105 to 5 × 109 years for the
2 For bodies of equal density, (de/dt)2/(de/dt)1 � 1.5 (R1/R2), so (de/dt)2 always dominates, and the first term on the
right hand side of Equation 6 is often ignored (e.g., Rasio et al. 1996; Trilling 2000).  Thus, even when P1 < 2/3 P2,
giving positive (de/dt)1, |(de/dt)1| can never be larger than |(de/dt)2|, so de/dt will always be negative.
previously discussed range of Q'.  Again, unless Ceto and Phorcys are rigid monoliths, this
timescale is much less than the age of the Solar System (and, presumably, the age of the Ceto/
Phorcys binary) so we expect the system to have lost most (or all) of its primordial orbital eccen-
tricity.
The average density of (65489) Ceto/Phorcys is relatively high compared with two other
small TNOs with eccentric mutual orbits (26308) 1998 SM165 (Spencer et al. 2006) and (47171)
1999 TC36 (Stansberry et al. 2006), leading us to ask whether the tidal evolution of the
Ceto/Phorcys system could have driven internal temperatures high enough to enable ductile com-
paction and loss of void space.  What temperature would be required is not clear, but for crys-
talline ice Ih, it must exceed 120 K, since ice Ih remains brittle and can maintain its pore space up
to at least that temperature (e.g., Durham et al. 2005).  This temperature is considerably higher
than equilibrium temperatures in the Kuiper belt.  Energy from both circularization and spin-
locking would contribute to internal heating.  The specific energy (i.e., per unit mass) available
from a change in orbital semimajor axis is
�Ecirc
G M 1
�a initial
�1�afinal
�1� , (10)
where ainitial and afinal are the initial and final semimajor axes.  If the orbit changes by ~10% in the
process of circularization, then the total energy deposited is GM1/(20af), and we may take af as
the presently observed value of a.  Rotational kinetic energy of a spinning body is 
I�2 where �
is the angular rotation rate and I = 2
MR2 is the moment of inertia for a homogeneous spherical
body.  The specific energy deposited in each body via spin locking is thus
�E spin
��initial
2��final
2� , (11)
where �initial and �final are the initial and final rotation rates.  Taking the initial spin periods to be
10 hours and final spin periods to be 9.5 days, we obtain an energy input smaller than that from
circularization by a factor of a few.  Combining the above parts, the total specific energy deposit-
ed in the system is
2� ��
initial
final
, (12)
which is approximately 105 erg g-1.  Lunine and Tittemore (1993) present an alternate derivation
of the tidal heating of a synchronously rotating satellite.  Rewriting their expression for energy
deposition, we have
�G M13� R2
��G M 1 M2 e
a � (13)
which gives dE/dt ranging from 1010 to 1014 erg s-1 for our bracketing Q' assumptions.  The total
energy input is independent of rigidity and is around 1027 erg, or 105 erg g-1, in agreement with
our derivation above.
The heat capacity of cold water ice Ih depends on temperature, ranging from 3 × 106 erg g-1
K-1 at 30 K to over 107 erg g-1 K-1 at 60 K (Giauque and Stout 1936), so even if all 105 erg g-1 of
heat were deposited instantaneously instead of over a 106 year or longer timescale, the tempera-
ture rise would be much less than a degree, far too small for viscous creep to assist compaction
and loss of pore space.  Comparable arguments can be made to show that heat tidally deposited
by any close encounter with a giant planet which does not completely disrupt the system will
also produce a negligible temperature rise.  However, if tidal heating were highly localized, as
might happen if energy dissipation was confined to the intersections of large scale internal frac-
tures, the local temperature rise could be higher.
That the Ceto/Phorcys system is expected to be tidally spin-locked and circularized sug-
gests that the spin axes of both objects could also have become aligned with the orbit pole.  Such
a configuration would help explain why no lightcurve has been reported for this object, and why
there is no evidence for it in our ACS/HRC photometry in Table 2 nor in our Spitzer/MIPS pho-
tometry in Table 4.  If the spin axes are aligned with the orbit pole, which was tilted about 28
from the line of sight from Earth at the time of the observations (as seen in Fig. 3), a lightcurve
observable when the system was near equator-on would be reduced in amplitude by the current
geometry by a factor of sin(28
), equal to 0.47.  A more pole-on configuration is also consistent
with the small beaming parameter �.  Smaller values of � correspond to warmer surface tempera-
tures, as would be expected when observing a hemisphere mostly in continuous sunlight.  Unfor-
tunately, we cannot use the assumption of aligned spin orientations to constrain the thermal iner-
tia of the surfaces of Ceto and Phorcys, since observable thermal flux becomes independent of
thermal inertia in pole-on geometry (e.g., Lebofsky and Spencer 1989).
6. Effect of encounters
In its current heliocentric orbit, Ceto/Phorcys is most likely to encounter Uranus, since its
perihelion is just inside the orbit of Uranus and its argument of perihelion is near 180
 (see
Fig. 1).  Tidal disruption becomes probable for planetary encounters with closest approach dis-
tances within
= a � 3 M planetM
, (14)
where a is the binary's semimajor axis and Mplanet and Msys are the masses of the planet and the bi-
nary system, respectively (Agnor and Hamilton 2006).  For encounters between Ceto/Phorcys
and Uranus, rtd is about 0.0045 AU, equivalent to 26 times the radius of Uranus or 360 times the
Ceto/Phorcys separation a.  For an encounter with Jupiter, rtd would be 0.013 AU, or 1000 times
a.  The probability that Ceto/Phorcys would have had an encounter closer than rtd with any of the
giant planets on its way to being perturbed into its current orbit is not known, but by analogy
with (42355) Typhon/Echidna (Noll et al. 2006), it is perhaps not surprising that the Ceto/Phor-
cys binary survived the sequence of planetary encounters which put it on its present-day orbit.
Although these encounters are unlikely to have been close enough to disrupt the binary, as evi-
denced by the simple fact of its existence, they could possibly be expected to have had some ef-
fect on the eccentricity of the binary orbit.  If so, a future survey of comparable TNBs with orbits
sampling the range from zero to non-zero eccentricity may enable statistical limits to be placed
on their Q values.
Trilling (2007) explores the possibility of binary disruption by encounters with other
TNOs.  For Ceto/Phorcys, the most likely time for such an encounter to have taken place would
have been prior to perturbation into a short-lived Centaur orbit.  The “hardness” H of the binary
can be expressed as a function of the mass M3 of a third body being encountered as
G M1 M 2
2 a M
2  (15)
(Binney and Tremaine 1987; Trilling 2007) where M1 and M2 are the masses of Ceto and Phorcys
(assuming both have the same density), a is the semimajor axis of their mutual orbit, and �v is
the velocity dispersion of potential interlopers, which is unknown, because we do not know what
heliocentric orbit the system was on prior to its becoming a Centaur.  For H(M3) greater than uni-
ty, the system is “hard” against disruption by interlopers of mass M3.  Assuming a velocity dis-
persion of 1 km s-1 (Jewitt et al. 1996), we find that H(M3) is unity for interlopers in the 3 km size
range, assuming an average density of 1 g cm-3.  For smaller interlopers, the Ceto/Phorcys system
is “hard” but for larger interlopers, it is “soft” and could be disrupted.  Durda and Stern (2000)
estimated rates of impacts in the Kuiper belt as a function of impactor size, finding that on aver-
age, an object the size of Ceto+Phorcys should be struck by one interloper of this size over the
age of the solar system.  Additional close, but non-impacting encounters would also be expected.
A possible consequence could be that binaries at least as widely separated as Ceto and Phorcys
(i.e., all currently known TNBs other than the near-contact binaries) represent a remnant popula-
tion which has lost many of its members over the age of Solar System, but that even tighter bina-
ries could be immune to disruption in the present collisional environment, and so could reveal
the primordial binary abundance.  This argument supports the ideas of Goldreich et al. (2002)
and Petit and Mousis (2004) that closer binaries could be considerably more abundant than the
comparatively widely separated ones currently being discovered by ground-based and even HST
searches (e.g., Kern and Elliot 2006; Noll et al. 2007).
7. Conclusion
Combined Hubble Space Telescope and Spitzer Space Telescope observations reveal the
Centaur (65489) Ceto/Phorcys to be a binary system with a separation of 1840 ± 48 km.  The
average geometric albedo is 0.084
�0.021
�0.014 , consistent with radiometrically determined albedos of
other Centaurs.  If both components have equal albedos, as suggested by their shared colors, the
radii of Ceto and Phorcys are 87
�9  and 66
�7  km, respectively.  The average bulk density of the
system is then 1.37
�0.66
�0.32  g cm
-3, higher than recent densities for other comparably-sized binary
outer Solar System objects, but smaller than the densities of much larger icy worlds such as Plu-
to, Triton, and Eris.  Despite probable recent encounters with gas giants, the mutual orbit of Ceto
and Phorcys is nearly circular, consistent with calculations showing that the system should be-
come tidally circularized and synchronized on timescales shorter than the age of the Solar Sys-
Acknowledgments
This work is based in part on NASA/ESA Hubble Space Telescope Cycle 14 program
10508 and 10514 observations.  Support for these programs was provided by NASA through a
grant from the Space Telescope Science Institute (STScI), which is operated by the Association
of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555.  We are
especially grateful to Tony Roman and Tricia Royle at STScI for their rapid reactions in schedul-
ing the HST follow-up observations.  STSDAS and PyRAF are products of STScI. This work is
also based in part on Spitzer Space Telescope Cycle 3 program 30081 observations.  Spitzer is
operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract
with NASA through an award issued by JPL/Caltech.  We thank two anonymous reviewers for
numerous constructive suggestions on how to improve this manuscript. Finally, we are grateful
to the free and open source software communities for empowering us with many of the tools
used to complete this project, notably Linux, the GNU tools, OpenOffice.org, MySQL, FVWM,
Python, IRAF, STSDAS, PyRAF, and TkRat.
REFERENCES
Agnor, C.B., and D.P. Hamilton 2006.  Neptune's capture of its moon Triton in a binary-planet
gravitational encounter. Nature 441, 192-194.
A'Hearn, M.F., M.J.S. Belton, W.A. Delamere, J. Kissel, K.P. Klaasen, L.A. McFadden, K.J.
Meech, H.J. Melosh, P.H. Schultz, J.M. Sunshine, P.C. Thomas, J. Veverka, D.K. Yeo-
mans, M.W. Baca, I. Busko, C.J. Crockett, S.M. Collins, M. Desnoyer, C.A. Eberhardy,
C.M. Ernst, T.L. Farnham, L. Feaga, O. Groussin, D. Hampton, S.I. Ipatov, J.Y. Li, D.
Lindler, C.M. Lisse, N. Mastrodemos, W.M. Owen Jr., J.E. Richardson, D.D. Wellnitz, and
R.L. White 2005.  Deep Impact: Excavating comet Tempel 1. Science 310, 258-264.
Binney, J., and S. Tremaine 1987.  Galactic dynamics.  Princeton Univ. Press, Princeton NJ.
Boehnhardt, H., A. Barucci, A. Delsanti, C. de Bergh, A. Doressoundiram, J. Romon, E. Dotto,
G. Tozzi, M. Lazzarin, S. Fornasier, N. Peixinho, O. Hainaut, J. Davies, P. Rousselot, L.
Barrera, K. Birkle, K. Meech, J. Ortiz, T. Sekiguchi, J.I. Watanabe, N. Thomas, and R.
West 2003.  Results from the ESO large program on transneptunian objects and centaurs.
Earth, Moon, and Planets 92, 145-156.
Bowell, E., B. Hapke, D. Domingue, K. Lumme, J. Peltoniemi, and A. Harris 1989. Application
of photometric models to asteroids.  In Asteroids II, Eds. R.P. Binzel, T. Gehrels, and M.S.
Matthews, Univ. of Arizona Press, Tucson AZ.
Brown, M.E. 2006. The largest Kuiper belt objects.  Invited talk at AAS/DPS meeting, Pasadena
CA, 2006 October 9-13.
Buie, M.W., W.M. Grundy, E.F. Young, L.Y. Young, and S.A. Stern 2006.  Orbits and photome-
try of Pluto's satellites: Charon, S/2005 P1, and S/2005 P2. Astron. J. 132, 290-298.
Burns, J.A. 1986.  Some background about satellites. In Satellites, Eds. J.A. Burns, and M.S.
Matthews, Univ. of Arizona Press, Tucson AZ.
Cooper, J.F., E.R. Christian, J.D. Richardson, and C. Wang 2003.  Proton irradiation of Centaur,
Kuiper belt, and Oort cloud objects at plasma to cosmic ray energy.  Earth, Moon, and
Planets 92, 261-277.
Cruikshank, D.P., M.A. Barucci, J.P. Emery, Y.R. Fernández, W.M. Grundy, K.S. Noll, and J.A.
Stansberry 2007.  Physical properties of trans-neptunian objects.  In Protostars and Planets
V. Eds. B. Reipurth, D. Jewitt, and K. Keil, Univ. of Arizona Press, Tucson AZ.
Davidsson, B.J.R., and P.J. Gutiérrez 2006.  Non-gravitational force modeling of Comet
81P/Wild 2 I. A nucleus bulk density estimate. Icarus 180, 224-242.
Descamps, P. 2005.  Orbit of an astrometric binary system. Celestial Mech. and Dynamical As-
tron. 92, 381-402.
Descamps, P., F. Marchis, T. Michalowski, F. Vachier, F. Colas, J. Berthier, M. Assafin, P.B.
Dunckel, M. Polinska, W. Pych, D. Hestroffer, K.P.M. Miller, R. Vieira-Martins, M. Bir-
lan, J.-P. Teng-Chuen-Yu, A. Peyrot, B. Payet, J. Dorseuil, Y. Léonie, and T. Dijoux 2007.
Figure of the double asteroid 90 Antiope from adaptive optics and lightcurve observations.
Icarus 187, 482-499.
Decker, R.B., S.M. Krimigis, E.C. Roelof, M.E. Hill, T.P. Armstrong, G. Gloeckler, D.C. Hamil-
ton, and L.J. Lanzerotti 2005.  Voyager 1 in the foreshock, termination shock, and he-
liosheath. Science 309, 2020-2024.
Duncan, M.J., and H.F. Levison 1997.  A scattered disk of icy objects and the origin of Jupiter-
family comets. Science 276, 1670-1672.
Duncan, M., T. Quinn, and S. Tremaine 1988.  The origin of short-period comets. Astrophys. J.
328, L69-L73.
Durda, D.D., and S.A. Stern 2000.  Collision rates in the present-day Kuiper belt and Centaur re-
gions: Applications to surface activation and modification on Comets, Kuiper belt objects,
Centaurs, and Pluto-Charon. Icarus 145, 220-229.
Durham, W.B., W.B. McKinnon, and L.A. Stern 2005.  Cold compaction of water ice. Geophys.
Res. Lett. 32, L18202.1-5.
Elliot, J.L., S.D. Kern, K.B. Clancy, A.A.S. Gulbis, R.L. Millis, M.W. Buie, L.H. Wasserman,
E.I. Chiang, A.B. Jordan, D.E. Trilling, and K.J. Meech 2005.  The Deep Ecliptic Survey:
A search for Kuiper belt objects and Centaurs. II. Dynamical classification, the Kuiper belt
plane, and the core population. Astron. J. 129, 1117-1162.
Engelbracht, C.W., M. Blaylock, K.Y.L. Su, J. Rho, and G.H. Rieke 2007.  Absolute calibration
and characterization of the Multiband Imaging Photometer for Spitzer. I. The stellar cali-
brator sample and the 24 µm calibration. Publ. Astron. Soc. Pacific (submitted).
Ford, H.C., and the ACS Science Team 1996.  The Advanced Camera for the Hubble Space
Telescope.  In Space Telescopes and Instruments IV.  Eds. P. Bely and J. Breckinridge,
SPIE 2807, 184-196.
Giauque, W.F., and J.W. Stout 1936.  The entropy of water and the third law of thermo-dynam-
ics: The heat capacity of ice from 15 to 273
K. J. Amer. Chem. Soc. 58, 1144-1150.
Gladman, B., D.D. Quinn, P. Nicholson, and R. Rand 1996.  Synchronous locking of tidally
evolving satellites. Icarus 122, 166-192.
Gladman, B., B.G. Marsden, and C. VanLaerhoven 2007.  Nomenclature in the outer Solar Sys-
tem.  In Kuiper Belt.  Eds. A. Barucci, H. Boehnhardt, D. Cruikshank, and A. Morbidelli.
Univ. of Arizona Press, Tucson AZ (in press).
Goldreich, P., and S. Soter 1966.  Q in the solar system. Icarus 5, 375-389.
Goldreich, P., Y. Lithwick, and R. Sari 2002.  Formation of Kuiper-belt binaries by dynamical
friction and three-body encounters. Nature, 420, 643-646.
Gordon, K.D., C.W. Engelbracht, D. Fadda, J.A. Stansberry, and S. Wachter 2007.  Absolute cal-
ibration and characterization of the Multiband Imaging Photometer for Spitzer. II. 70 mi-
cron imaging. Publ. Astron. Soc. Pacific (submitted).
Grundy, W.M., K.S. Noll, and D.C. Stephens 2005.  Diverse albedos of small transneptunian ob-
jects. Icarus 176, 184-191.
Holman, M.J. 1997.  A possible long-lived belt of objects between Uranus and Neptune. Nature
387, 785-788.
Horner, J., N.W. Evans, and M.E. Bailey 2004.  Simulations of the population of Centaurs - I.
The bulk statistics. Mon. Not. Royal Astron. Soc. 354, 798-810.
Hubbard, W.B. 1984.  Planetary interiors.  Van Nostrand Reinhold Co., New York NY.
Jenniskens, P, D.F. Blake, and K. Kouchi 1998.  Amorphous water ice: A solar system material.
In Solar System Ices, Eds. B. Schmitt, C. de Bergh, and K. Kouchi, Kluwer Academic Pub-
lishers, Boston MA.
Jewitt, D., J. Luu, and J. Chen 1996.  The Mauna Kea-Cerro-Tololo (MKCT) Kuiper belt and
Centaur survey. Astron. J. 112, 1225-1238.
Jewitt, D., L. Chizmadia, R. Grimm, and D. Prialnik 2007.  Water in Small Bodies of the Solar
System.  In Protostars and Planets V, Eds. B. Reipurth, D. Jewitt, and K. Keil, Univ. of
Arizona Press, Tucson AZ.
Johnson, T.V., and J.I. Lunine 2005.  Saturn's moon Phoebe as a captured body from the outer
Solar System. Nature 435, 69-71.
Kern, S.D., and J.L. Elliot 2006.  The frequency of binary Kuiper belt objects. Astrophys. J. 643,
L57-L60.
Kowal, C.T., W. Liller, and B.G. Marsden 1979. The discovery and orbit of 2060 Chiron. IAU
Symp. 81: Dynamics of the Solar System 81, 245-250.
Krist, J.E., and R.N. Hook 2004.  The Tiny Tim user's guide. Version 6.3 is available from
http://www.stsci.edu/software/tinytim/.
Lacerda, P., and D.C. Jewitt 2007.  Densities of Solar System objects from their rotational
lightcurves. Astron. J. 133, 1393-1408.
Lebofsky, L.A., and J.R. Spencer 1989.  Radiometry and thermal modeling of asteroids.  In As-
teroids II, Eds. R.P. Binzel, T. Gehrels, and M.S. Matthews, Univ. of Arizona Press, Tuc-
son AZ.
Leliwa-Kopystyński, J., and K.J. Kossacki 2000.  Evolution of porosity in small icy bodies.
Planet. Space Sci. 48, 727-745.
Levison, H.F., and M.J. Duncan 1997.  From the Kuiper belt to Jupiter-family comets: The spa-
tial distribution of ecliptic comets. Icarus 127, 13-32.
Lunine, J.I., and W.C. Tittemore 1993.  Origins of outer-planet satellites.  In Protostars and
Planets III, Eds. E.H. Levy, and J.I. Lunine, Univ. of Arizona Press, Tucson AZ.
Lupo, M.J., and J.S. Lewis 1979.  Mass-radius relationships in icy satellites. Icarus 40, 157-170.
Marchis, F., D. Hestroffer, P. Descamps, J. Berthier, A.H. Bouchez, R.D. Campbell, J.C.Y. Chin,
M.A. van Dam, S.K. Hartman, E.M. Johansson, R.E. Lafon, D. Le Mignant, I. de Pater,
P.J. Stomski, D.M. Summers, F. Vachier, P.L. Wizinovich, and M.H. Wong 2006.  A low
density of 0.8 g cm-3 for the Trojan binary asteroid 617 Patroclus. Nature 439, 565-567.
McKinnon, W.B., J.I. Lunine, and D. Banfield 1995.  Origin and evolution of Triton.  In Neptune
and Triton, Ed. D.P. Cruikshank, Univ. of Arizona Press, Tucson AZ.
McKinnon, W.B., W.B. Durham, and L.A. Stern 2005.  Cold compaction of porous ice, and the
densities of Kuiper belt objects.  Paper presented at Asteroids, Comets, and Meteors 2005
August 7-12, Rio de Janeiro, Brazil.
Nelder, J., and R. Mead 1965.  A simplex method for function minimization. Computer J. 7, 308-
Noll, K.S., D.C. Stephens, W.M. Grundy, and I. Griffin 2004a.  The orbit, mass, and albedo of
(66652) 1999 RZ253. Icarus 172, 402-407.
Noll, K.S., D.C. Stephens, W.M. Grundy, D.J. Osip, and I. Griffin 2004b.  The orbit and albedo
of trans-neptunian binary (58534) 1997 CQ29. Astron. J. 128, 2547-2552.
Noll, K.S., H.F. Levison, W.M. Grundy, and D.C. Stephens 2006.  Discovery of a binary Cen-
taur. Icarus 184, 611-618.
Noll, K.S., W.M. Grundy, E. Chiang, and J.L. Margot 2007.  Binaries in the Kuiper belt.  In
Kuiper Belt.  Eds. A. Barucci, H. Boehnhardt, D. Cruikshank, and A. Morbidelli. Univ. of
Arizona Press, Tucson AZ (in press).
Peixinho, N., A. Doressoundiram, A. Delsanti, H. Boehnhardt, M.A. Barucci, and I. Belskaya
2003.  Reopening the TNOs color controversy: Centaurs bimodality and TNOs unimodali-
ty.  Astron. & Astrophys. 410, L29-L32.
Petit, J.M., and O. Mousis 2004.  KBO binaries: How numerous are they? Icarus 168, 409-419.
Press, W.H., S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery 1992. Numerical Recipes in C.
Cambridge Univ. Press, New York NY.
Rabinowitz, D.L., K. Barkume, M.E. Brown, H. Roe, M. Schwartz, S. Tourtellotte, and C. Trujil-
lo 2006.  Photometric observations constraining the size, shape, and albedo of 2003 EL61, a
rapidly rotating, Pluto-sized object in the Kuiper belt. Astrophys. J. 639, 1238-1251.
Rasio, F.A., C.A. Tout, S.H. Lubow, and M. Livio 1996, Tidal decay of close planetary orbits.
Astrophys. J. 470, 1187-1191.
Rieke, G.H., and 42 co-authors 2004.  The Multiband Imaging Photometer for Spitzer (MIPS).
Astrophys. J. 154, 25-29.
Rousselot, P., J.M. Petit, F. Poulet, and A. Sergeev 2005.  Photometric study of Centaur (60558)
2000 EC98 and trans-neptunian object (55637) 2002 UX25 at different phase angles. Icarus
176, 478-491.
Schubert, G., T. Spohn, and R.T. Reynolds 1986.  Thermal histories, compositions, and internal
structures of the moons of the solar system.  In Satellites, Univ. of Arizona Press, Tucson
Sheppard, S.S., and D.C. Jewitt 2002.  Time-resolved photometry of Kuiper belt objects: Rota-
tions, shapes, and phase functions. Astron. J. 124, 1757-1775.
Spencer, J.R., J.A. Stansberry, W.M. Grundy, and K.S. Noll 2006.  A low density for binary
Kuiper belt object (26308) 1998 SM165. Bull. Amer. Astron. Soc. 38, 546 (abstract).
Sirianni, M.,  M.J. Jee, N. Benítez, J.P. Blakeslee, A.R. Martel, G. Meurer, M. Clampin, G. De
Marchi, H.C. Ford, R. Gilliland, G.F. Hartig, G.D. Illingworth, J. Mack, and W.J. McCann
2005.  The photometric performance and calibration of the HST Advanced Camera for
Surveys. Publ. Astron. Soc. Pacific 117, 1049-1112.
Stansberry, J.A., W.M. Grundy, J.L. Margot, D.P. Cruikshank, J.P. Emery, G.H. Rieke, and D.T.
Trilling 2006.  The albedo, size, and density of binary Kuiper belt object (47171) 1999
TC36. Astrophys. J. 643, 556-566.
Stansberry, J., W. Grundy, M. Brown, D. Cruikshank, J. Spencer, D. Trilling, and J.L. Margot
2007a.  Physical properties of Kuiper belt objects and Centaurs: Constraints from Spitzer
Space Telescope.  In Kuiper Belt.  Eds. A. Barucci, H. Boehnhardt, D. Cruikshank, and A.
Morbidelli.  Univ. of Arizona Press, Tucson AZ (in press).
Stansberry J.A., K.D. Gordon, B. Bhattacharya, C.W. Engelbracht, G.H. Rieke, M. Blaylock,
F.R. Marleau, D. Fadda, D.T. Frayer, A. Noriega-Crespo, S. Wachter, D. Henderson, D.M.
Kelly, and G. Neugebauer 2007b.  Absolute calibration and characterization of the Multi-
band Imaging Photometer for Spitzer III. An asteroid-based calibration at 160 microns.
Publ. Astron. Soc. Pacific (submitted).
Stephens, D.C., and K.S. Noll 2006.  Detection of six trans-neptunian binaries with NICMOS: A
high fraction of binaries in the cold classical disk. Astron. J. 131, 1142-1148.
Tegler, S.C., W. Romanishin, and G.J. Consolmagno, S.J. 2003.  Color patterns in the Kuiper
belt: A possible primordial origin. Astrophys. J. 599, L49-L52.
Trilling, D.E. 2000.  Tidal constraints on the masses of extrasolar planets. Astrophys. J. 537,
L61-L64.
Trilling, D.E. 2007.  The evolution of Kuiper belt object and Centaur binaries. Astrophys. J. (sub-
mitted).
Trilling, D.E., and G.M. Bernstein 2006.  Lightcurves of 20-100 kilometer Kuiper belt objects
using the Hubble Space Telescope. Astron. J. 131, 1149-1162.
Veillet, C., J.W. Parker, I. Griffin, B. Marsden, A. Doressoundiram, M. Buie, D.J. Tholen, M.
Connelley, and M.J. Holman 2002.  The binary Kuiper-belt object 1998 WW31. Nature 416,
711-713.
Virtanen, J., K. Muinonen, and E. Bowell 2001.  Statistical ranging of asteroid orbits. Icarus 154,
412-431.
Virtanen, J., G. Tancredi, K. Muinonen, and E. Bowell 2003.  Orbit computation for trans-
neptunian objects. Icarus 161, 419-430.
Yoder, C.F. 1982.  Tidal rigidity of Phobos. Icarus 49, 327-346.
Figure 5.  
