Deduction of the possible excited spin states of 2P/Encke
Michael J.S. Belton ([email protected]) Belton Space Exploration Initiatives,
LLC 430 S. Randolph Way, Tucson AZ 85716
The determination of the spin state of an active cometary nucleus presents a somewhat
different problem than the determination of the spin state of an asteroid — although there
is also much in common in the two cases. To date the complete spin state has only been
determined for two cometary nuclei — and at least one of them - 1P/Halley - remains
controversial (Samarasinha et al. 2004). Partial information is available for about
two-dozen more comets, but this information is mainly limited to the primary periodicity
in the lightcurve and pole solutions are generally not available. This state of affairs is
regrettable for those who wish to explore the implications of observable coma structures
and global gas production rates for the properties of specific active regions on the surface.
It is knowledge of the spin state that allows such phenomena to be traced back to
particular localities on the cometary surface (e.g. Belton et al. 1991). 2P/Encke is a
well-observed comet with a short orbital period that displays variable coma structure and
also peculiarities in the production rates around perihelion. Its spin state is therefore of
considerable interest. Several photometric studies in the late 80’s seemed to indicate a fully
relaxed spin state with a period near 15 hr, however not all workers agreed pointing out
problems with the observed amplitudes of the lightcurves. More recently, observations in
2000 and 2001 have been reported with a period near 11 hr and all signs of a 15 hr period
seem to have disappeared. In this paper I revisit these many data sets and show that the
many periods latent in the data (not just the two mentioned above) can be consistently
explained in terms of an excited spin state. I also show how the pole determinations of
Sekanina (1988) and Festou and Barale (2000) can be generalized to give an estimate of the
direction of the total angular momentum vector. More difficult is a choice between spin
states in the short (SAM) or long (LAM) axis mode (both are allowed by the periodicities).
A low-excitation SAM state is the preferred solution, although a highly excited LAM state
with rather special properties is also a possibility. While not yet fully specified, four
(possibly five) of the parameters describing the spin state are deduced. The rest could, in
principle, be determined from radar observations and/or future high quality light curves in
the thermal infrared.
Acknowledgements: Much of this work has been done in consultation with N.H. Samarasinha, Y.
Fernandez, and K.J. Meech
Belton, M.J.S., Mueller, B.E.A., Julian, W.H., and Anderson, A.J. 1991. The Spin State and Homogeneity
of Comet Halley’s Nucleus. Icarus 93, 183-193.
1
Festou, M.C., and Barale, O. 2000. The Asymmetric Coma of Comets. I. Asymmetric Outgassing from the
Nucleus of Comet 2P/Encke. Astron. J. 119, 3119-3132.
Samarasinha, N.H., Mueller, B.E.A., Belton, M.J.S., and Jorda, L. 2004. Rotation of Cometary Nuclei. In
Comets II. Ed. M.C. Festou. In press.
Sekanina, Z. 1988b. Outgassing Asymmetry of Periodic Comet Encke. II. Apparitions 1868-1918 and a
Study of the Nucleus Evolution. Astron. J. 95, 911-924
3
Searching for the Long Lost Precursors of the Primordial Earth
William Bottke (Southwest Research Institute) David Nesvorny (Southwest Research Institute)
It is frequently assumed that planetesimals formed at 1 AU, presumably the precursors of
our heavily-evolved Earth, could not have survived to the present day. Dynamical models
indicate that most objects on planetary crossing orbits have a very short dynamical
lifetimes (<10 Myr) compared to the age of the solar system (Gladman et al. 1997; Icarus),
while cosmochemical models suggest the Earth’s bulk chemistry was unlikely to come from
any combination of chondritic meteorites in our current collection (e.g., Burbine et al.
2003; LPSC). This is unfortunate, given that samples taken from planetesimals formed at 1
AU could help answer numerous unsolved questions about the formation and evolution of
our Earth (e.g., did Earth’s water come from 1 AU or was it delivered by primitive
asteroids/comets).
Results from recent dynamical models, however, are somewhat less pessimistic; they hint at
the possibility that a few Earth precursors may still be found, provided we know where to
look. For example, Morbidelli et al. (2001; MAPS) showed that during the late stages of
planet formation, perturbations with planetary embryos chased a few percent of the initial
planetesimal population in the 1-2 AU zone onto highly-inclined orbits in the inner solar
system. According to their dynamical model, these bodies could have been long-lived
enough to cause an extended bombardment of all of the terrestrial planets for hundreds of
Myr. We hypothesize that a very small fraction of this population may have survived all
the way to today, provided that: (i) the initial population was large, (ii) the dynamical
decay rate of this material was slow (i.e., some of this precursor material found its way into
long-lived orbits within the inner solar system), and (iii) these survivors turn out to be
protected from extensive comminution.
To test our hypothesis, we numerically integrated the known high-inclination NEOs (and
their clones) using the code SWIFT-RMVS3 (Levison and Duncan 1994). In our
simulation, whenever our initial population decays to less than 10% of the starting
population, we clone the remnants and continue the integration. Our goal is to push out
the integrations to several Gyr while searching for a long-lived tail to the original
population. We believe our method has certain advantages over that used by Morbidelli et
al. (2001) because we use the present-day orbital parameters of the planets; Morbidelli et
al. (2001) integrated their particles using model-derived planetary parameters that do not
match our current solar system.
Preliminary results suggest
2 that some clones of our initial population reach orbits near the
periphery of the modern-day Hungarias and Phocaeas populations, where their dynamical
lifetimes can reach many hundreds of Myr, far longer than typical NEOs (Bottke et al.
2002; Icarus). Even so, it is not yet clear whether these lifetimes are long enough to be
consistent with our hypothesis. Our latest results on this topic will be presented at the
workshop.
4
Using Multi-Polarization Radar to Search for Regolith on Asteroids
Lynn M. Carter, Donald B. Campbell and Michael C. Nolan
The presence of regolith material will alter an asteroid’s thermal properties and can affect its
dynamical history via Yarkovsky forces [1]. It is not clear what sized asteroids have regolith;
small asteroids have lower escape velocities, but internal strength and the presence of
previously ejected material also determine how much volume is lost to space during an impact
[2]. High resolution spacecraft images, such as the NEAR images of Eros, have confirmed that
some asteroids possess regoliths [3]. Although many asteroids likely have a regolith, it is hard
to detect such surface coverings at the resolutions typically achieved by ground-based optical
imaging. At infrared wavelengths, thermal models can be used to extract a value for the
thermal inertia, which is related to the density of the surface. However, shape, surface
roughness, rotation state and thermal inertia are strongly connected in thermal models, and it
is difficult to derive the thermal inertia from observed fluxes without some prior knowledge of
the asteroid’s physical properties.
Multi-polarization radar imaging provides a unique method to search for regolith. In radar
experiments, an analysis of the degree of linear polarization in the received echo can be used
to investigate whether there is a surface covering on an object. A circularly polarized wave,
such as that transmitted by the Arecibo radar, can be thought of as a combination of two
linearly polarized waves of equal magnitude, one perpendicular to the plane of incidence and
one parallel to the plane of incidence. If a circularly polarized radar wave refracts into a
surface that is smooth at wavelength scales and is reflected by embedded scatterers or by an
underlying structure, the returned radar echo will have a net linearly polarized component (it
will be elliptically polarized). The linear polarization is produced because the horizontally
and vertically polarized components of the incident wave have different transmission
coefficients into and out of the surface layer. This technique has been used by Stacy [4] to
study the lunar regolith and by Carter et al. [5] to study surface deposits on Venus.
Benner et al. [6] used the Arecibo and Goldstone radars to observe the asteroid 1999 JM8
during its close approach to Earth. The asteroid is about 7 km in diameter, and
delay-Doppler images from these radar runs have resolutions as small as 15 m/pixel, which
gives thousands of pixels on the asteroid [6]. The Stokes parameter analysis reveals a
significant linearly polarized echo component, which demonstrates that there is some
penetration of the radar wave into a surface layer. JM8 has an irregular shape, and the
resulting radar ambiguity makes it difficult to model physical properties, such as the dielectric
constant and depth, of the regolith. However, the values of the degree of linear polarization
also follow the incidence angle trend expected from the transmission coefficients: at near
normal incidence angles,3 no linear polarized echo power is produced, and the values are higher
elsewhere on the asteroid. This linear polarization technique can be used with other asteroids,
provided that the radar data have sufficient signal-to-noise. We hope to compare the linear
polarization properties of different size, shape and perhaps different composition asteroids.
References: [1] Bottke et al. 2002. in Asteroids III, p. 395. [2] Scheeres et al. 2002, in Asteroids III, p 527. [3]
Veverka et al. 2000, Science, 292, 485. [4] Stacy 1993, Ph.D. Thesis, Cornell University [5] Carter et al. 2003,
LPSC XXXIV, 1809 [6] Benner et al. 2002, Meteoritics and Planetary Science, 37, 779.
6
The First Direct Measurement of Yarkovsky Acceleration on an Asteroid
Steven R. Chesley (JPL), Steven J. Ostro (JPL), David Vokrouhlický (Charles Univ.,
Prague), David Čapek (Charles Univ., Prague), Jon D. Giorgini (JPL), Michael C. Nolan
(Arecibo Obs.), Jean-Luc Margot (UCLA), Alice A. Hine (Arecibo Obs.), Lance A. M. Benner (JPL), Alan B. Chamberlin (JPL)
Radar ranging at three apparitions over twelve years has unambiguously revealed the
action of the Yarkovsky Effect on near-Earth asteroid 6489 Golevka. The most recent
measurements, from Arecibo in May 2003, indicate a 15 km displacement that cannot be
reconciled with a purely gravitational force model. This kind of detection requires careful
consideration of astrometric uncertainties and potential mismodeling of gravitational
perturbations. Indeed, uncertainty in the masses of perturbing asteroids has the potential
to completely obscure Yarkovsky-induced deflections in some cases.
The magnitude of the displacement is consistent with the predictions from simplified
Yarkovsky models, and thus many previous theoretical studies that relied on such models
are substantially validated by this detection. Moreover, the Yarkovsky measurement
permits us to place constraints on the mass and bulk density of the asteroid. However the
quality of the mass estimate is degraded by uncertainty in the surface thermal
characteristics. A Yarkovsky detection, along with independent measurement of the surface
thermal conductivity would allow a much more precise estimate of the asteroid’s mass.
Conversely, if the mass can be independently determined, such as for a binary asteroid
system, then a Yarkovsky detection would allow a precise estimate of the surface thermal
properties.
4
7
that
is an for
orderSynchronous
of magnitude shorter
than thatSatellites
for YORP acting on an ideal Ida. Of
YORP
Asteroidal
course, real asteroids have very different shapes; nevertheless this exercise demonstrates
Matija Cuk, Cornell University
Many of the lesser components in binary asteroid pairs are expected to be in synchronous
rotation. Geometrically, such satellites appear to be rigidly attached to their primaries,
since they always keep the same orientations relative to their primary’s center of mass
(assuming the satellite’s orbit is circular). Recently, YORP – the non-gravitational force
affecting an asteroid’s rotation – has received considerable attention (Rubincam 2000,
Vokrouhlicky and Capek 2002, Vokrouhlicky et al. 2003). I argue that a similar effect
should influence the orbits of at least some synchronous asteroidal satellites, owing to their
similarity to promontories of the primary. To illustrate this mechanism, we visualize an
irregularly shaped asteroid as a sphere with a wedge-shaped attachment (cf. Rubincam
2000, but we assume only a single attachment). This appendage is shaped like a prism
with a right triangular base, which is attached to sphere’s equator, with one of the smaller
rectangular sides perpendicular to the sphere’s rotation axis. This attachment reflects
sunlight directly back off one side but out-of-plane off the other; each side has the same
vertical cross-section. The infrared radiation re-emitted by the body itself has a similar
distribution. Hence a torque, which can change spins, arises.
I now consider an identically shaped asteroidal satellite in synchronous rotation, with the
prism glued to the satellite’s long axis, which is assumed to point toward the primary. In
this way one side of the prism is always facing forward relative to the satellite’s orbital
motion, while the other faces backwards. Depending on the prism’s exact placement and
its orientation, re-radiated energy from the prism can produce a positive or negative torque
on the satellite’s orbit. To estimate roughly the significance of this effect, we compare the
timescales for YORP acting on the primary and “satellite YORP” acting on a secondary,
assuming our “sphere-plus-wedge” shape and taking binary parameters like those of the
Ida-Dactyl system. The YORP’s magnitude varies with the prism’s size, and therefore with
radius squared, while the torque is the product of this force times the distance from the
center of motion (the primary’s radius for the usual YORP, but the binary’s separation for
the satellite YORP). The timescales for these two effects are estimated by dividing the
relevant angular momenta by the respective torques. For YORP, the timescale
ty = const ∗ 2/5 ∗ M ∗ R2 ∗ Wrot /(R ∗ R2 ) = const ∗ R2 ∗ Wrot
(where M, R and Wrot are the primary’s mass, radius and rotation rate). For satellite
YORP,
ts = const ∗ m ∗ a2 ∗ Worb /(a ∗ r2 ) = const ∗ a ∗ r ∗ Worb
(where m, r, a, Worb are the satellite’s mass, radius, semimajor axis and mean motion).
Assuming identical densities, the ratio of timescales is:
(ts )/(ty ) = 2.5 ∗ (a/R) ∗ (r/R) ∗ (Worb )/(Wrot )
5
For the Ida-Dactyl pair, (a/R) = 7, (r/R) = 1/22, (Worb /Wrot ) = 1/8, so the timescale ratio
should be (ts /ty )= 0.1. Therefore, our ideal Dactyl would change its orbit on a timescale
89
the√potential importance of the satellite YORP. Since the orbital angular momentum varies
as a, and the satellite YORP torque is proportional to a, a satellite’s outward migration
is a runaway process (at least until the synchronous rotation is broken), quite unlike tidal
evolution. Also, for some close binaries with similar-sized, mutually-synchronous
components (“contact binaries”), YORP and satellite YORP should become
indistinguishable.
6
9
Does Microporosity or Macroporosity Dominate in Stone Asteroids?:
Evidence from Stone Meteorites
George J. Flynn, Dept. of Physics, SUNY-Plattsburgh, 101 Broad St., Plattsburgh, NY
12901
Comparison of the densities of asteroids with the densities of the minerals presumed to
dominate their composition (based on reflection spectroscopy) indicates that most asteroids
exhibit significant porosity (Flynn, 1994). The type of porosity ranging from microporosity
to macroporosity (in the extreme case, a rubble pile) determines the physical behavior of
the asteroids, e.g., the response to collisions, the maximum rotation rate, etc.
Since the meteorites are generally accepted to be samples of the asteroids, the study of
porosity in meteorites can provide constraints on the type and amount of microporosity in
the asteroids. Britt and Consolmagno (2003) reviewed the density and porosity
measurements on stone meteorites obtained by several groups. The lowest bulk density in
their tabulation is 1.5 gm/cc for a large (47.2 gm) sample of the hydrated CI carbonaceous
chondrite Orgueil. Four of the hydrated CM carbonaceous chondrites in the tabulation
have bulk density values < 2.0 gm/cc (ranging from 1.79 gm/cc for Santa Cruz to 1.96
gm/cc for Nogoya), but other hydrated CM meteorites Cold Bokkeveld, Kivesvaara, and
Murchison have bulk densities ranging from 2.3 to 2.4 gm/cc. The lowest bulk density
reported for an anhydrous meteorite is 2.38 gm/cc for the LL ordinary chondrite Y-75258.
However, we might reasonably expect that the bulk density of the parent asteroid would be
significantly lower than that of the meteorite derived from that parent since objects tend to
break into their strongest subunits, thus minimizing their microporosity. This trend is
evident in the Orgueil data (Britt and Consolmagno, 2003), where the sample having the
lowest bulk density (1.5 gm/cc) is the largest one measured, while the smaller Orgueil
samples have much higher bulk densities (averaging 2.1 gm/cc).
Recent asteroid flyby missions have permitted accurate determinations of the bulk densities
of several asteroids: Mathilda at 1.3 gm/cc, Ida at 2.7 gm/cc, and Eros at 2.67 gm/cc.
Each of these bulk densities is high enough to be explained entirely by microporosity,
especially when the measured bulk densities of the meteorites are adjusted down to
account for objects breaking into their strongest (most likely least porous) subunits.
The meteorites exhibit three distinct types of porosity on the microscale – cracks, vugs, and
gaps or low density regions separating chondrules from the matrix (Flynn et al., 2000). But
the dominant type of porosity is cracks, which, in some cases, may not reflect the condition
of their parent body. Meteorites are believed to be ejected from their parent body by
collisions, which can induce
new cracks through shock or fill pre-existing cracks through
7
injection of melted material into the interior of the rock. In addition, we have performed
Computed MicroTomography (CMT) on several small whole stone meteorites. We found
cracks that cut the fusion crust on two meteorites. Once the cracks were identified using
CMT, we were able to locate these microscopic cracks on the exterior surface of these stones
using a low-power magnifying lens. Thus, at least in some cases, the cracks in meteorites
were either produced or significantly enlarged after production of the fusion crust.
10
Britt, D. T. and G. J. Consolmagno (2003) Stony meteorite porosities and densities: A
review of the data through 2001, Meteoritics & Planetary Science, 38, 1161-1180.
Flynn, G. J. (1994) Interplanetary dust particles collected from the stratosphere: Physical,
chemical, and mineralogical properties and implications for their sources, Planetary and
Space Science, 42, 1151-1161.
Flynn, G. J.; Rivers, M.; Sutton, S. R.; Eng, P.; Klock, W. (2000) X-Ray Computed
Microtomography (CMT): A Non-invasive Screening Tool for Characterization of Returned
Rock Cores from Mars and Other Solar System Bodies, 31st Annual Lunar and Planetary
Science Conference, March 13-17, 2000, Houston, Texas, Abstract no. 1893.
8
11
Asteroid Orbit Determination and Radar Astrometry:
Small Forces and Long-Term Prediction
Jon D. Giorgini
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA
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Asteroid Lightcurve Parameters Data File
Alan W. Harris1, Brian D. Warner2, Petr Pravec3
1. Space Science Institute, La Canada, CA-91011, U.S.A.
2. Palmer Divide Observatory, Colorado Springs, CO 80908 U.S.A.
3. Astronomical Institute AS CR, Ondrejov, CZ-25165, Czech Republic
Beginning about the time of the first Asteroids conference in Tucson in 1979, I (AWH) began compiling
data on asteroid rotations from literature reports of lightcurve observations. The first research based on
that list was published that year (Harris and Burns, Icarus 40, 115-144, 1979). Along with the statistical
analysis of rotations, we published the entire list, which consisted of 304 entries referring to 191 different
asteroids. Of these, 182 asteroids had some indication of rotational properties, and 151 had "reliable"
rotation periods published. The entire list fit on six partial pages of the old small Icarus page layout. In
following years, numerous papers have been published analyzing the data contained on various updates
of the data file, and updates of the file itself have been published in the Asteroids II book, an Icarus paper
in 1983, and in abridged form in the annual Ephemeredes of Minor Planets (EMP), and is posted on the
MPC and CALL web sites. Here we present the latest revision, which has now grown to a file with 6,183
entries referring to 1,813 different asteroids, and including 1,371 reliable rotation periods. The current
data file, if published in format similar to the original Icarus publication, would occupy a fair fraction of a
single issue of the journal. Fortunately electronic publication has come to the rescue of the data
explosion, so it is again possible to publish one's underlying data. This file, and updates thereof, will
continue to be available on the CALL and MPC web sites, or available for download, or CD copy on
request (to AWH). However, it is desirable from time to time to "freeze" a version of the data file so that
analyses based on that set can be examined, checked and compared against other analyses using the same
data. With that in mind, we offer the data set as used in the analyses presented at this conference (Pravec
et al.; Harris and Pravec) and invite others to use the same data set for related analyses or checking of our
results. This version of the data file will also be archived on the NASA Planetary Data System Small
Bodies Node (http://pdssbn.astro.umd.edu/).
A further use of this data file is for observation planning, particularly for radar or other complimentary
physical observations, or to identify targets in need of confirmation or further study. With that in mind
the data file contains entries indicating unpublished results and identifying the observers who have made
those observations so that one can inquire directly with other observers to determine what further
observations are needed. These unpublished entries are not listed in the EMP or MPC versions of the list,
but are indicated in the compressed files on the CALL website
(http://www.minorplanetobserver.com/astlc/default.htm). Following is a brief non-random sample from
the file:
Asteroid
Class
dia.
H
Alb.
2921 Sophocles
Birlan 96
C*
12.1
13.3 *.058
2929 Harris
Harris
T
26.4
11.6 *.058
2945*Zanstra
*Behrend 03w
10
21.12 12.2
.0522
Per.
4.778
4.778
Ampl.
0.16
0.16
Rel Com
2
2
2 *
2 *
19.414
19.414
0.20
0.20
1
1
The first entry is a published result, with the full journal citation given in a companion file; the third entry
refers to a result posted on a web page (indicated by a "03w" citation). The second entry is of an
unpublished observation. You'll have to ask the observer for numerical results relating to this object.
Fast and Slow Spins Revisited: YORP alteration
Alan W. Harris1, Petr Pravec2
1. Space Science Institute, La Canada, CA-91011, U.S.A.
2. Astronomical Institute AS CR, Ondrejov, CZ-25165, Czech Republic
At the ACM 2002 meeting in Berlin, I (AWH) congratulated Bottke et al. for finding the "smoking gun"
of the Yarkovsky Effect, in the form of the odd orbital structure of the Koronis family, and challenged
them to find a similar "smoking gun" of the claimed YORP effect. Less than a year later, they obliged
with the evidence of spin alteration of the members of the Koronis family (Vokrouhlicky et al, 2003).
The compelling aspect of this evidence is not only the dispersion of spin rates, but also most strikingly
the clustering of spin axis orientations, leaving little doubt that the YORP effect is capable of altering the
spin states of asteroids up to a size of 30-40 km in diameter. With this new insight in hand, and utilizing
the new compilation of asteroid rotation rates of nearly 1400 asteroids (Harris et al., this conference), we
return to the problem of slow rotators among asteroids, which has been an unsolved mystery for two
decades, since the discovery of the record slow rotator, 288 Glauke, with a rotation period exceeding
1000 hours. The hypothesis that slow rotators are the result of YORP despinning is supported by the fact
that most slow rotators are also very irregular bodies with large amplitudes of lightcurve variation (but
that could also be in part a selection effect of what can be observed). It is further supported by the
absence of slow rotators at larger sizes: 253 Mathilde is the largest at nearly 60 km diameter. However
the numbers of yet larger asteroids decreases rapidly so that one can't be sure if there is a real cutoff with
larger size, or if there are just too few asteroids for a chance outlier. Nevertheless, it can be noted that the
rate of YORP despinning is inversely proportional to diameter squared, so the difference from ~30 km
where we see clear evidence in the Koronis family, and Mathilde is only a factor of about four in rate of
spin evolution. Furthermore, the spin evolution looks more like "sliding friction" than "aerodynamic
drag" (cf., evolution plots in Vokrouhlicky et al, 2003, where we see that rotation rates simply "skid to a
halt," rather than slowing exponentially), thus if an asteroid like Mathilde happened to start out with a
somewhat slow rotation rate, say 20-30 hours, it could plausibly be brought to a near halt by YORP drag
in the same time as a 30-km diameter asteroid starting from an average spin rate.
Turning to the smaller end of the size distribution, it has long been apparent that the spin distribution of
asteroids becomes increasingly dispersed with decreasing size. This is even more apparent in the "higher
resolution" view of the new data set. YORP is a suitable explanation for the ever-increasing numbers of
slow rotators as we go to smaller sizes, as the inverse-square with diameter power of the effect allows
less irregular bodies to evolve to greater degrees. The slow trend toward faster rotation among the bulk
of asteroids may also be due to YORP effect in the opposite direction. As we have noted previously, the
"spin barrier" for rubble pile asteroids sets an upper limit to spin rate, but YORP could lead to mass
shedding leading to binary formation as objects are spun up to the barrier. The statistics of small (mostly
NEA) binaries are consistent with splitting of bodies rotating at nearly critical rates, then evolving by
tidal evolution to stable end states. An important observational test is whether NEAs are unusual in their
spin states and fraction of binaries, compared to main-belt asteroids where tidal disruptions by close
planetary encounters are not a viable mode of spin alteration or binary formation.
11
Hungaria asteroids provide a possibility to compare spin statistics of non-planet crossers with planet
crossing asteroids. Hungarias are extreme inner main-belt objects just beyond Mars, and also high
albedo, thus typically very small for their apparent brightness. These asteroids offer an opportunity to
study main-belt asteroids nearly as small as NEAs to compare rotation statistics, pole orientations, and
incidence of binaries to see if planet-crossing (tidal interactions) significantly alter these properties.
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13
16
Asteroid spins and shapes from multidatainversion:
the big picture
Mikko Kaasalainen (1,2), Markku Lehtinen (2), Daniel Hestroffer (3),
Chris Magri (4), et al.
(1)
(2)
(3)
(4)
Rolf Nevanlinna Institute, U. Helsinki, Finland
Sodankylä Geoph. Obs. and EISCAT Radar Stn., U. Oulu, Finland
IMCCE, Paris, France
U. Maine at Farmington, USA
A large set of comprehensive physical asteroid models can be and is now being
built with combined analysis of photo- and interferometric and radar observations, occultation timings, and other data. In addition to optimizing the models
to fit the data, it is useful to optimize the data acquisition events themselves
(timing, design of radar experiments, etc.). This is a joint effort with several
observers and research groups. We have now compiled a population sample of
nearly 100 targets, including MBAs, NEAs, and Jupiter Trojans. This group
displays a wide variety of shapes, spin states, and structures. It is possible to
obtain hundreds of such models in the relatively near future.
This sample can be analyzed in the collective sense by investigating crosscorrelations between quantities such as size, rotation period, pole latitude, shape
irregularity, deviation from an equilibrium shape, etc. This should provide us
with new insights into asteroid structures and evolution. Potential trends such
as YORP spin clustering will also provide information for choosing the objects
that should be targeted for observations (Koronis/Hungarias/NEAs/slow rotators/etc.).
Instead of professing to give answers, we present a list of open questions on
which we hope to evoke lively discussion:
1. What should we observe (especially for fewer biasing effects)?
2. How should we observe (for maximal information)?
3. How should we analyze the ensemble?
4. Should we be looking for something (en masse or á la Itokawa)?
5. Should we not be looking for anything?
6. Should we have something to drink?
References and links: www.astro.helsinki.fi/∼kaselain
14
17
Topics in asteroid dynamics
Donald Korycansky, CODEP, UC Santa Cruz
I discuss some recent and ongoing work by our group (CODEP) at UC Santa Cruz. The
first two topics concern the role played by impacts and secondary ejecta in determining the
regolith distribution on asteroids such as 433 Eros, and the possible effect of the same in
determining their shape. Finally I present work on the dynamics of rigid bodies and the
application to modeling the structure and dynamics of gravitational aggregates (“rubble
piles”).
For the first two areas, we used many-faced polyhedral models and their gravitational
potentials as calculated by the “polyhedron gravity” algorithm of Werner and Scheeres
(Werner 1994, Werner and Scheeres 1996). In 2003 we published a study (Korycansky and
Asphaug, Icarus v. 163, 374-288) of the role that small impacts might play in reshaping
asteroids. In this paper, we modeled small impacts, the craters that they produced, and
their ejecta, to see how the cumulative effect of many such impacts might change the shape
of an initially-spherical asteroid. We found that oblate shapes dominated the outcomes of
this process for rotating bodies, unlike the prolate or irregular shapes that are often seen.
More recent work (Korycansky and Asphaug, submitted to Icarus) is a study of the ejecta
blanket produced by small impacts on Eros. Here we integrated the orbits of test particles
produced at the locations of primary impacts and mapped the distribution of those
particles that re-impacted the asteroid. We found that ejecta tend to “pile up” in low-lying
regions such as the craters Psyche, Himeros, and in Shoemaker Regio. Conversely, high
spots, (the two long ends of the asteroid) were net losers of ejecta.
Both of our studies suggest that small impacts (and resulting ejecta) act to smooth or
“round down” asteroids toward quasi-spherical or oblate shapes. In turn, this suggests that
asteroid shapes, in particular the often rather extreme shapes of many small objects, are
determined by catastrophic events such as large impacts or tidal encounters.
Some recently completed work (Korycansky, Astrophysics and Space Science in press)
focuses on rigid body dynamics of self-gravitating polyhedra (of arbitrary shape). Mutual
forces and torques exerted by bodies are calculated by means of appropriate surface
integrals, and collisions are included as well. Collisions can be elastic, inelastic, or
frictional, depending on the specification of coefficients of restitution. Our ongoing work is
aimed at modeling “rubble pile” asteroids made of individual sub-components of general
shapes and sizes. We hope to test some ideas in the literature about rubble-piles and arrive
at predictions for the internal structure of asteroids.
15
18
Yarkovsky Effect Measured for Main-Belt Asteroids
David Nesvorny, William F. Bottke, Jr., Southwest Research Institute
The Karin cluster is a remarkably young asteroid family. Using N-body gravitational
models and backward numerical integrations, we showed that all family members had
nearly identical orbits at 5.8 ± 0.2 My ago. To make the orbits converge exactly, the orbital
histories of the family members must be corrected for thermal effects. Using this novel
method, we measured, for the first time, the semimajor axis drift that 2 to 6-km-diameter
asteroids experience in the main belt due to the Yarkovsky effect. As a by-product, we
determined obliquities for ∼ 100 members of the Karin cluster which gives us an insight
into physics of the 5.8-Ma impact event that produced the family.
16
19
Radar Observations of Binary Near-Earth Asteroid 66391 (1999 KW4)
Steven J. Ostro, Lance A. M. Benner, Jon D. Giorgini, Raymond F. Jurgens (JPL/Caltech),
Jean-Luc Margot (UCLA), Michael C. Nolan (Arecibo Observatory),
Petr Pravec (Astronomical Institute, Academy of Sciences of the Czech Republic),
and Daniel J. Scheeres (U. Michigan)
The Mercury crosser 66391 (1999 KW4) has an orbit (a,e,i = 0.64 AU, 0.69, 39°) that is unique
among known asteroids for its combination of small perihelion distance (q = 0.200 AU) and high
inclination.
Only four known objects, all comets, have both a smaller perihelion distance and a larger inclination. The asteroid’s 2001 approach to within 0.032 AU from Earth was its closest until 2036, and
we conducted extended observations using the Goldstone X-band (8560-MHz,
3.5-cm) and Arecibo S-band (2380-MHz, 13-cm) radar systems. The Goldstone sequences
revealed the binary nature of this asteroid and provide our longest continuous imaging coverage,
while the Arecibo images are much stronger and have finer resolution.
I’ll describe the state of our analyses.
17
Page 1
Tumbling Asteroids
P. Pravec1 , A. W. Harris2 , P. Scheirich1 , P. Kusnirak1 , L. Sarounova1 , C. W. Hergenrother3 ,
S. Mottola4 , G. Masi5,6 , M. Nolan7 , E. Howell7 , P. Brown8 , D. R. DeGraff9 , A. Galad10 , J.
V. Lambert11 , S. Foglia12
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Astronomical Institute AS CR, Ondrejov, CZ-25165, Czech Republic
Space Science Institute, La Canada, CA 91011, USA
Lunar and Planetary Laboratory, Univ. of Arizona, Tucson, AZ 85721, USA
DLR, Institute of Planetary Research, D-12489 Berlin, Germany
Physics Dept., University of Rome ”Tor Vergata”, Italy
Campocatino Astronomical Observatory, Italy
Arecibo Observatory, NAIC, PR 00612, USA
Dept. of Physics and Astronomy, Univ. of Western Ontario, Canada
Alfred University, Alfred, NY 14802, USA
Modra Observatory, Astronomical Institute, FMFI Comenius University, Bratislava, Slovak
Republic
11. Air Force Maui Optical and Supercomputing Facility, Kihei, HI 96753 USA
12. Serafino Zani Observatory, Lumezzane, I-25065, Italy
We present both a review of earlier data and new results on non-principal axis rotators
(tumblers) among asteroids. Among new tumblers found, the best data we have are for
2002 TD60, 2000 WL107 and 54789 2001 MZ7 — each of them shows a lightcurve with two
frequencies (full terms with linear combinations of the two frequencies are present in the
lightcurve). For 2002 TD60, we will present a physical model of the NPA rotation. Other
recent objects which have been found to be likely tumblers based on their lightcurves that
don’t fit with a single periodicity are 2002 NY40, 16067 1999 RH27, and 5645 1990 SP.
Among observational conditions and selection effects affecting detections of NPA rotations,
there is a bias against detection of lower-amplitude (less elongated) tumblers. High
amplitude tumblers are easy to recognize when data covering at least a few rotation cycles
repeatedly in about constant geometric conditions are obtained.
We present a statistical analysis of the population of NPA rotators. We have found an
evidence that most asteroids larger than 0.5 km with estimated damping timescales of 4.5
b.y. and longer (according to the formula by Harris 1994) are NPA rotators. The statistic
of two tumblers (D=0.04 and 0.4 km) among monolithic asteroids suggests that they have
µ ∗ Q/T , where µ is the mechanical rigidity, Q is the elastic dissipation factor, and T is the
age of the object, greater by two to three orders of magnitude than the larger, rubble-pile
tumblers.
18
22
Equilibrium Shapes of Rubble Piles
Derek C. Richardson (U Maryland), Pradeep Elankumaran (U Maryland), Keith A. Holsapple (U Washington)
With increasing interest in the notion that many asteroids may be gravitational aggregates,
that is, loose collections of solid material held together mainly by gravity, it is important to
characterize the range of allowable equilibrium shapes such bodies may have in response to
properties like their spin states. These shapes may act as diagnostics of the internal
structure of the bodies. We have begun an investigation of the supportable configurations
of spinning rubble piles as a first step toward this goal. Our rubble piles are collections of
identical smooth spheres, representing idealizations of a medium-porosity gravitational
aggregates with low tensile strength. We find that even in this ideal case, which might be
construed as a good analog for a fluid, deviations from the classical limits described by
Maclaurin spheroids and Jacobi ellipsoids can be large. We report on the dependence of
equilibrium shape on the number of particles in the rubble pile (the “resolution”), and
whether shape approaches the fluid limit as the resolution is increased. We also determine
the maximum spin rate of the rubble piles before mass loss begins and compare the results
to recent observations of NEA spin periods. Future work will include a study of the effect
of interlocking between non-spherical particles.
19
23
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24
Dynamics of Deformable Asteroids
Ishan Sharma, James T. Jenkins and Joseph A. Burns
Department of Theoretical and Applied Mechanics
Cornell University, Ithaca, NY 14853
December 6, 2003
Abstract
Recent observations suggest that most asteroids might be granular
aggregates. Compared to solid objects, granular ones tend to deform
more and, possibly, to dissipate more energy. Both these facts might
have a significant influence on the dynamics and shape of granular
asteroids. To study the dynamics of a granular asteroid, we begin by
assuming that the asteroid deforms homogeneously. We then consider
different kinds of material behaviours. For example, we model the
asteroid as a collection of colliding, inelastic, rigid spheres or as a dense
packing of frictional spheres. In both cases the asteroid is held together
by gravity. The type of dynamical situations we consider include free
Eulerian precession and planetary fly-by’s. In these, we determine the
position and velocity of the center of mass and/or the homogeneous
deformation as functions of time.
21
25
26
Accurate ephemerides of Eros’ rotation
Jean Souchay (Observatoire de Paris)
To compute with precision the rotation of any celestial body as an asteroid, requires a deep
knowledge of physical and astrometrical parameters related to this body, as its moments of
inertia and its angular speed of rotation. This is now available in the case of the asteroid
Eros 433, which was recently abundantly observed by the NEAR (Near Earth Asteroid
Rendez-Vous) probe mission. After describing in some details the two components of the
motion (free and forced rotations) we show how very accurate ephemerides of Eros’rotation
could be obtained.
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1
Outlier detection
J. Virtanen, K. Muinonen, M. Granvik (Observatory, University of Helsinki)
We discuss the problem of identifying outlier observations in the case of sparse/exiguous
data. Outlier rejection is an important part of the orbit computation process, in particular,
in applications such as the linking of asteroid observations, evaluation of impact probability,
and analysis of high-precision data (e.g. the GAIA mission). Although algorithms exist for
identifying outliers in multiapparition data sets, the case of short observational arcs and
small numbers of observations has not been studied in detail. We propose a new outlier
detection algorithm, which makes use of the technique of statistical ranging.
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Next Yark Candidates
D. Vokrouhlicky1 , S.R. Chesley2 , D. Capek1 and S.J. Ostro2
1. Institute of Astronomy, Charles University, Prague V Holesovickach 2, CZ-18000 Prague 8,
Czech Republic
2. JPL, California Institute of Technology, Pasadena, CA 91109, USA
The first successful detection of the Yarkovsky effect acting on the orbit of a near-Earth
Asteroid (6489 Golevka) not only validated current models, but also demonstrated a
unique means of estimating an asteroid’s mass. We provide an overview of further
candidates for which the Yarkovsky effect is likely to be detected within next decade or
two. In all cases radar ranging to these targets during their next Earth close approaches is
crucial, and in some cases accurate pre-encounter optical astrometry is also needed.
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Tidal Reshaping of the Near Earth Asteroid Population
Kevin J. Walsh (U. of Maryland), Derek C. Richardson (U. of Maryland), William F. Bottke
(SwRI), Douglas P. Hamilton (U. of Maryland)
Radar observations show a surprising number of near-Earth asteroids (NEAs) have nearly
spherical shapes. While it is possible some of these objects were produced by the
reaccretion of debris after a catastrophic collision, collisional modeling work suggests such
outcomes should be relatively rare (e.g., Michel et al. 2004; Durda et al. 2004). We suggest
a different mechanism to explain these unusually-shaped objects.
NEAs are known to have numerous close encounters with terrestrial planets during their
dynamical lifetimes. Together with evidence suggesting that most of the NEAs above 150
meters in diameter are gravitational aggregates, it is likely that many NEAs have been
distorted or disrupted via planetary tidal forces (Richardson et al. 1998). Accordingly, we
believe that many nearly-spherical NEAs may in fact be by-products of these same
processes.
To test this scenario we used an N-body code to numerically model close encounters
between rubble pile asteroids and the Earth. Our progenitor was constructed of identical
rigid spheres and held together by self-gravity rather than tensile strength. For a large
number of cases our results indicate that tidal forces can reshape elongated into nearly
spherical bodies. This mechanism relies on the tidal forces stretching the body and having
it collapse back on itself. Our plan is to compare these results with NEA lightcurve
amplitudes (to estimate elongation) and spin rates. Continuing efforts on this project
includes simulations towards the creation of a steady-state shape distribution for NEAs as
affected by tidal disruption.
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Brian D. Warner1
1. Palmer Divide Observatory, Colorado Springs, CO 80908 USA
The past few years has seen a dramatic increase in the number of quality asteroid lightcurves
produced by amateur observers. This has been clearly demonstrated in the number of curves
submitted to the Minor Planet Bulletin, which jumped from 3 in 1985 to 78 in 2003. It’s also
reflected in the number of curves in the list maintained by Alan Harris and the author, which now
has more than 1800 objects represented with almost 1400 of those having reliable curves.
The increased involvement by amateur observers, proven very capable of quality work, and who
are not under the telescope time constraints of professional astronomers, i.e., being able to
respond to situations on demand and/or work a given target for extended periods, is invaluable.
The increasing output of this pool provides the opportunity for more rapid development of
asteroid dynamics theories that center on spin axis rate and orientation or shape modeling. The
Collaborative Asteroid Lightcurve Link web site, maintained by the author since early 2000
(http://www.MinorPlanetObserver.com/astlc/default.htm), helps coordinate programs among
observers by providing a “reservation” system so that unnecessary duplication of effort is avoided
and allows results to be publicly posted prior to formal publication. It also provides links to other
observing programs such as the shape and spin axis modeling programs being conducted by
Mikko Kaasalainen and Steven Slivan.
The efforts at the Palmer Divide Observatory and others will be used as an exampl e of how
amateurs go about developing a lightcurve program, including measuring images and analyzing
results and working with professionals, optical and radar, to help build the statistical pool
required for ongoing studies in asteroid dynamics. Some specific case studies of successful proam collaborations will be included to demonstrate their effectiveness and see how they might be
improved.
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Photometric Observation of Karin Family Asteroids
Fumi Yoshida (National Astronomical Observatory of Japan), Takashi Ito (Lunar and Planetary Laboratory, University of Arizona), Renu Malhotra (Lunar and Planetary Laboratory,
University of Arizona), Budi Dermawan (University of Tokyo, ITB, Indonesia), Tsuko Nakamura (National Astronomical Observatory of Japan), Shigeru Takahashi (Institute of Astronomy, National Central University, Taiwan), Mansur A. Ibrahimov (Ulugh Beg Astronomical
Institute, Uzbekistan), Wing Huen Ip (Institute of Astronomy, National Central University,
Taiwan), Wen Ping Chen (Institute of Astronomy, National Central University, Taiwan)
In 2002, a very young asteroid family, the Karin family, was discovered by Nesvorny et al
(2002). This family consists of 39 members (their diameter range is between 1.5-20km) , and
is estimated to have been created by an asteroid breakup event only 5.8 Myr ago, while most
known asteroid families are considered very old (about a few Gyr), so the latter have
undergone significant collisional and dynamical evolution which mask the property of the
original collisional events. Meanwhile, the members of the young Karin family seem to still
preserve properties of the original collision. A part of collisional properties seems to appear
in the non-principal axis rotation and/or the wide-range distribution of their rotational
period, which possibly reflect the rotational status of asteroid fragments just after the
breakup event. The distribution of shape of the Karin family members is also interesting. If
we assume the spherical shape indicate a rubble pile asteroids and the elongate shape is
interpreted by the monolithic fragments, we can estimate the production rate of rubble pile
asteroids, monolithic asteroids on one breakup event. The YORP effect can alter the
orientation of asteroids’ spin axes to a specific direction. This phenomenon was discovered in
Koronis family asteroids (their diameter range is between 20-40km) by Slivan (2003). Just
after a catastrophic collision, the orientation of their spin axes must be random. We expect
to estimate the time scale that the YORP effect arranges the asteroids’ spin axes by the
Karin members. And also color distribution of their surface is important. We guess the
largest member “(832) Karin” has old region and fresh region which was exposed by
excavation of the collision on its surface.
So, based on the above view points, we intend to grasp the insight of the collisional
properties through the observations of their lightcurves.
We report here the results of the lightcurve observation for six Karin family asteroids. The
observations were performed from November 2002 to September 2003. We determined their
rotational periods and show the possibility of their non-principal axis rotation. Asteroid
(4507) 1990FV (main rotational period (MRP)) is 6.576 hr) doesn’t have the non-principal
axis rotation probably. Asteroids (832) Karin (MRP is 18.348 hr), (28271) 1999CK16
27 (MRP:3.912 hr), and (16706) Svojsik (MRP:5.880 hr) likely have
(MRP:5.640 hr), 2000VE21
multi-period rotation. However, we need more observations.
Our observation must be a unique opportunity to understand an asteroid disruption event.
We believe that our observation could be essentially important for the dynamical study of
the asteroid fragments formed by a family-forming collisional event, though the observations
are still in progress.
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