Physical Prop erties of

K. J. Meech

Institute for Astronomy, University of Hawai`i, 2680 Wood lawn Drive, Honolulu, HI 96822, USA

ABSTRACT

There have b een several recent reviews of the physical prop erties of cometary nuclei, most concentrating on

the sp eci cs of the rotation p erio ds, shap es, sizes and the surface prop erties. This review will presentan

up dated summary of these prop erties based on recent observations. There are nucleus parameters known for

 26 nuclei. These nuclei are relatively small prolate ellipsoids of low alb edo. The axis ratios range

between 1.1{2.6 which when combined with rotation p erio ds constrains the densitylower limits. Typically

the nuclei are found to havevery small fractional active areas. Little direct observational evidence exists

for the internal physical prop erties, however, the results to date suggest a strengthless agglomeration of

3

gravitationally b ound with a bulk densitybetween 0.5-1.0 gm cm .

INTRODUCTION

With recent advances in theoretical mo dels of the early it is b ecoming increasingly imp ortant

to have a go o d understanding of the physical prop erties of cometary nuclei, so that they may b e used to

constrain mo dels of solar nebula evolution. Early mo dels of the comet formation environment suggested

that most comets formed in the Uranus- zone at temp eratures b etween 25{60K. Our current un-

derstanding of the early solar system suggests that the proto{planetary disks are much more massive than

previously b elieved. Lissauer 1987 shows that the accumulation of Jupiter's core required a solar nebula

surface density many times larger than the minimum mass solar nebula. Furthermore, observations show

that 25-50 of pre{main sequence have massive circumstellar disks which extend to b eyond 100 AU

from the central with masses up to 1 M Beckwith and Sargent, 1993. In these more massive mo dels,

the innermost region for comet formation o ccurs b etween the helio centric distances r = 14{16 AUi.e. near

60K as determined by the volatile comp osition of comets, and the most distant region b etween 80{110 AU

Yamamoto, 1985. As summarized byWeissman 1995, the current comet formation paradigm is that the

comets which originated in the Uranus{Neptune zone were dynamically ejected out to the , while

comets forming further out in the region now known as the Kuip er Belt KB, remained in{situ. As shown

by Levison and Duncan 1993 and Holman and Wisdom 1993, the KB comets are the most predominant

source of the observable short{p erio d comets. While there is nowa much b etter understanding of the general

comet formation environment, there is presently no self{consistent scenario leading from the coagulation of

the m{sized interstellar grains to the km{scale planetesimals. Lunine et al. 1991 have argued that

with the thicker disks it is probable that sho ck heating during infall to the disk mid{plane will cause some

sublimation of the primordial ices the extent to which this o ccurs will b e a function of radial distance from

the protostar. Furthermore, turbulence in the nebula will not allow formation via simple

Van der Waals sticking and gravitational collapse Weidenschilli ng, 1988. Weidenschilli ng and Cuzzi 1993

have shown that turbulent mo dels for m-sized to m{sized planetesimal growth may b e develop ed that pre-

dict p ossible radial and vertical mixing in the nebula. These e ects might b e observable as comp ositional

di erences in meteorites or comets. However, the stage of planetesimal formation from m{sized to km{sized

is not understo o d at all, and is sensitive to the disk turbulence hence disk mass and convection within the

disk. The still p o orly understo o d km{scale planetesimal stage of evolution is accessible through observa-

tions of to day's comets, and by assessing their physical prop erties as a function of formation lo cation, we

can place some invaluable constraints on the solar nebula mo dels. The rate of the protoplanetary growth 1

as a function of r dep ended on the size and mass distribution of the km-sized planetesimals whichhave

survived as to day's comets, their surface density in the nebula and their velo city distributions Lissauer

and Stewart, 1993. Unfortunately, as observations and detectors are b ecoming more sophisticated, we are

nding that comets exhibit activity and dust comae out to much larger distances than previously b elieved

Meech, 1994, so that probably most historical comet observations do not p ertain to the nuclei. In fact,

until recently,we probably had very little direct knowledge of the nucleus prop erties.

Techniques for Measurement of Nucleus Prop erties

Not only are the global physical prop erties imp ortant for the understanding of the early solar system accre-

tion mo dels, but the nucleus size, alb edo and rotational p erio ds are critical parameters which a ect the solar

energy distribution on the surface which will dictate the nature of a comet's activity.Even more dicult

to observe, but more imp ortant to the understanding of cometary activity and ultimately to the origins of

the comets, are the internal physical prop erties, including the volatile comp osition, dust{to{gas mass ratios,

and the thermo{physical prop erties of the nucleus: thermal conductivity, p ore size, p orosity and nucleus

bulk density. The evolution of activity in the nucleus is closely tied to the rate at which heat p enetrates

into the interior, as dictated by the thermal parameters. The p orosity, tensile strength and nucleus density

play critical roles in outbursts, splitting and tidal disruption, as well as in the observed non{gravitational

motions. However, as will b e shown b elow, information ab out the internal prop erties of nuclei is much less

well{constrained than for the external prop erties. In this review, the discussion will b e restricted to the

external physical prop erties and the thermo{physical prop erties.

Nucleus Size Distributions

Nucleus sizes were rst estimated from photographic measurements at large r when the nucleus was b elieved

to b e inactive Ro emer, 1966. By making assumptions ab out the visual alb edo, p , the nucleus radius could

v

b e estimated from the observed magnitude, m:

2 22 2 2 0:4m m

p R =2:24  10 r  10 [1]

v

N

where R is in [m], r andin[AU] and m is the 's magnitude. The disadvantage of this technique

N

was that the photographic plates are not very sensitive to the extremely low surface{brightness comae which

might b e present. Often the nucleus radii so determined were upp er limits Sekanina, 1976. Additionally,

the unknown nucleus alb edo created a range of size estimates. The rst application of the technique using

mo dern linear CCD detectors was with the recovery of comet P/Halley Jewitt & Danielson, 1984. This

technique was subsequently used extensively by Jewitt and Meech 1985, 1987, 1988a. This is the most

reliable easily applied means of remote determination of R when the nucleus is inactive. Nevertheless, it is

N

dep endent up on the unknown nucleus alb edo. The sensitivity of CCD detectors is required to measure the

scattered radiation of these relatively small low{alb edo ob jects when they are far from the sun. Radiometry,

a direct metho d for determining the Bond alb edo of an ob ject was rst applied to in the 1970s

Allen, 1970, and a second technique utilizing thermal ux measurements and optical photometry of active

comets was used to determine the alb edo of the dust grains O'Dell, 1971. The rst technique allows both

the alb edo and diameter to b e determined from a simultaneous IR and optical detection if a comet is large

enough and suciently close to the sun that it can b e detected in the IR, but b efore the observations are

contaminated by dust. These techniques have b een applied to only a few nuclei. A summary of alb edos

of material Meech, 1987, shows that the alb edo of the dust is generally low 0.03

v

Finally, Lamy and Toth 1995 have recently develop ed an indirect technique to mo del and remove the

coma contribution from high{resolution HST images of active comets in order to infer the nucleus size.

In total, wehave reasonable physical size estimates for  2 dozen comet nuclei cf. Table 1. The nuclei

are quite small, and in fact, estimates of sizes have continued to decrease as b etter techniques emerge, and

it is likely that we are seeing cometary activity at larger distances than previously b elieved Meech, 1994.

This forces the observations to b e made at large r where they are more dicult. This evolution of nucleus

size estimates, which is leading to a decrease in the inferred sizes is shown in Fig. 1. The top panel plots

the directly measured radii from Table 1. Recently, large telescop e time has b een dedicated to obtaining

upp er limits on the radii of p erio dic comets with well{known Hainaut et al., 1994. This technique

uses a non{detection or a measurementofnucleus plus coma as an upp er limit to the nucleus ux. The

distribution for these directly measured upp er limits is shown in Fig. 1b. While the distribution is wider than 2

Fig. 1 | Comparison of nucleus size

distributions determined by several di-

rect and indirect techniques: a direct

measurements of bare nuclei cf. Ta-

ble 1; b p erio dic comet and dynami-

cally new nucleus upp er limits Hainaut

et al., 1994; Meech, 1994; c coma cor-

rected measurements Scotti, 1994; d

CLICC visual observation extrap olation s

data from Kam el, 1992; and e normal-

ized comparison of the direct observation

technique [a-c] with the CLICC metho d,

showing that the \traditional" estimates

of nucleus size tend to b e to o large b e-

cause of coma contamination.

that of the directly observed nuclei, it is clear that the p opulations show similar sizes. Scotti 1994 has

b een using the SpacewatchTelescop e on Kitt Peak to make astrometric observations of a large number of

comets, and has extracted \nuclear magnitudes from the data by estimating and removing any coma con-

tribution. The measurements of over 60 comets whichwere made by this technique are shown in Fig. 1c. A

fourth technique for nucleus size estimatation uses the data of Kam el 1992 who has pro duced an enormous

p erio dic comet light{curve catalogue/atlas CLICC covering the p erio d from 1899{1989. By plotting the

2

light curves as a function of r and comparing them with the exp ected r light curve dep endence for a bare

nucleus, one can estimate at which p oint in the the comet

is inactive and from this estimate the nucleus size for an assumed

alb edo. This has traditionally b een the basis for many estimates

of nucleus sizes. The results of this are shown in Fig. 1d. A com-

parison of the directly estimated bare nucleus measurements and

the inferred nucleus sizes from Kam el are shown in Fig. 1e. The

size distribution for the CLICC comets is clearly broader than the

other distributions, which probably re ects the fact that this is not

a reliable way to infer the absence of a dust coma. In particular,

for many of these comets, observations don't extend muchbeyond

r =3AU, and clearly exp erience with comet P/Halley has shown

that H O{ice activity can b egin as early as r =6AU Meech et

2

al., 1986.

The exciting new discoveries of the Trans{Neptunian TNO or

Kuip er Belt KB Ob jects Jewitt and Luu, 1995 are giving us

our rst lo ok at the physical prop erties e.g. sizes and colors of

Fig. 2 | Comparison of the IRAS the small b o dies comets p opulating the outer solar system. The

size distribution scaled to 1/20, with those of size distributions of the comets from Table 1 and the TNOs are

the TNOs, and directly measured short-p erio d plotted in Fig. 2 in comparison with that of the asteroids which

comet nuclei. represent a collisionally evolved p opulation, although the curvein 3

Table 1. MEASURED PROPERTIES

1 2 3 4 5 6 7

Comet q[AU] R p Rot [hrs] A:B Frac Ref

N v

Arend-Rigaux 1.385 5.2 0.03 13.56 1.9 0.001 1,2

Borrelly 1.365 24.7 2.5 0.1 3

Chiron 8.454 90 0.13 5.9178 1.1 0.00015 4-9

d'Arrest 1.346 2.7 5.17 10,11

Encke 0.331 3.1 15.08 1.8 0.002 12,13

Faye 1.655 2.7 1.3 14

Giacobini-Zinner 1.035 3.0 11

Grigg-Skjellerup 0.997 2.9 11

Halley 0.596 5.5 0.04 88.6 2.0 0.2 15,16

Honda-Mrkos-Padj. 0.532 0.35 0.1 17

Hyakutake 0.230 6.3 18

IRAS-Araki-Alco ck 0.991 3.5 51.0 2.3 0.002-0.01 19,20

Kop 1.579 2.8,1.8 12.91 1.4 0.1 11,17

Levy P/1991 L3 0.983 8.2 8.34 1.3 21

Machholz 1 0.125 2.8 6.38 1.4 0.005 11,22

Neujmin 1 1.549 10.4 0.03 12.67 1.6 0.001 23-25

5

Phaethon 0.139 2.6 0.09 3.604 1.4 3.5x10 26

SW1 5.743 15.4 0.13 14 2.6 0.06 27,28

SW2 2.027 3.1 5.58 1.6 0.1 29

Swift-Tuttle 0.962 11.8 69.36 0.03 30,31

Temp el 2 1.482 5.9 0.02 8.876 1.7 32,33

Wild 2 1.582 2.0 11

Wild 3 2.301 3.1 11

Wilson 1.199 <6.0 34

Wilson-Harrington 1.000 2.0 6.1 1.2 0.0002 11,35-36

Wirtanen 1.064 1.0 >6 0.25 37-39

1 2 3 4

Notes: Perihelion distance; Nucleus radius in km; Measured visible geometric alb edo; Nucleus rotation p erio d in hours;

5 6 7

Nucleus axis ratio; Fractional nucleus active area; References: [1] Jewitt & Meech 1985; [2] Millis et al. 1988; [3] Lamy

1995; [4] Bus, et al. 1989; [5] Bus et al. 1996; [6] Meech et al. 1996; [7] Marciales & Buratti 1993; [8] Meech & Belton

1990; [9] Altenho & Stump 1995; [10] Fay & Wisniewski 1978; [11] Meech, unpublished ; [12] Jewitt & Meech 1987;

[13] Luu & Jewitt 1990; [14] Lamy&Toth 1995; [15] Belton 1990; [16] Keller et al. 1987; [17] Lamy et al. 1996; [18]

Osip et al. 1996; [19] Hanner et al. 1985; [20] Sekanina 1987; [21] Fitzsimmons & Williams 1994; [22] Sekanina 1990;

[23] Wisniewski et al. 1986; [24] Jewitt & Meech 1988a; [25] Campins et al. 1987; [26] Meech et al., in prep. 1996; [27]

Cruikshank 1983; [28] Meech et al. 1993; [29] Luu & Jewitt 1992; [30] OCeallaigh et al. 1995; [31] Yoshida et al. 1993;

[32] A'Hearn et al. 1989; [33] Mueller & Ferrin 1996; [34] Meech et al. 1995; [35] Osip et al. 1995; [36] Chamb erlain et

al. 1996; [37] Bauer et al. 1996; [38] Jorda et al. 1995; [39] Bo ehnhardt et al. 1996.

this gure has not b een corrected for observational bias and completeness. The KB sizes are large com-

pared to known short{p erio d comet nuclei, however, the statistics are so small on this p opulation that we

cannot draw meaningful conclusions yet as to the implications. Clearly the active p ortion of a comet's

3

lifetime will result in a decrease in nucleus size  1 m p er p erihelion passage, for mayb e a few x 10 orbits.

However, it seems unlikely that the present apparent di erence in sizes is due solely to cometary activity

in the short{p erio d comets, since the nucleus size limits for the dynamically new comets are comparable to

those of the short{p erio d comets, yet these comets have not sp entasmuch time in the inner Solar System.

Thus mass{loss cannot explain the size distributions. The size distributions of the icy planetesimals were

constrained by the material density in the nebula, however interpretation of the observed distributions must

takeinto account the nebula dynamics. Recent mo dels Duncan, et al., 1996; Malhotra, 1995 suggest that

the helio centric distance distribution of the KB ob jects was a ected by the orbital migration of the outer

planets. The fundamental outer solar system dynamics and pro cesses and our understanding of

the volatile distribtuion and chemistry in the solar nebula are not well understo o d, thus observations of the

small b o dy size distributions are imp ortant to constrain early solar system mo dels.

Nucleus Rotation

When nucleus observations are obtained with sucient time resolution, it is p ossible to determine the ro-

tation p erio d of the comet. The rst determination of nucleus rotation p erio ds utilized indirect techniques 4

e.g. the Halo metho d Whipple, 1982, and Sekanina's non{gravitational force mo dels 1981 whichwere

dep endent up on uncertain physical assumptions see A'Hearn, 1988; Belton, 1991 for a review of these

techniques. However, b ecause of the inherent assumptions, the p erio ds determined by indirect means don't

necessarily represent the true rotational state of the nucleus. Faye and Wisniewski 1978 obtained the

rst direct photometric rotational light curve of a comet | comet P/d'Arrest, and in the 1980's the more

sensitive CCD detectors were used to determine the rotational p erio ds from observations of bare nuclei.

The simultaneous in{phase visible and infra{red observations of comet P/Arend{Rigaux Millis et al., 1988

showed for the rst time that the rotational lightcurvewas due unambiguously to the prolate shap e of the

nucleus rather than to alb edo features. The range of the bare{nucleus light curve is related to the pro jected

axis ratio of the comet. All of the directly determined nucleus rotation p erio ds are summarized in Table 1,

the distribution of the p erio ds is shown in Fig. 3, and all the bare nucleus lightcurves are shown in Fig. 4.

The brightness mo dulation due to nucleus rotation can b e observed through some coma, as long as the coma

brightness do es not overwhelm the contribution from the nucleus. By decreasing the ap erture size used for

observation p ossible only under conditions of go o d seeing, the ratio of the nucleus ux to the total ux

can b e increased, allowing the rotational mo dulation to b e detected | as was the case for P/Schwassmann{

Wachmann 1 Meech et al., 1993. By observing how the light curve amplitude changes as a function of

ap erture size, and using the observed brightness distribution of the coma, it is p ossible to infer the axis ratio

of the comet and the pro duct of the nucleus cross section times the alb edo. The observed light curve range

for an active comet dep ends on:

B +B p

N C

2

[2] mp= 2:5 log

B +B p

N C

1

where B and B are the light scattered at minimum and maximum brightness, resp ectively, and B p

N N C

2 1

is the contribution from the coma within ap erture of radius p. This equation can b e parameterized in terms

of only the ratio of the scattered light from minimum to max-

imum nucleus cross section, , the average nucleus scattered

light, B , related to size and alb edo, and the measured

N

coma surface brightness gradient, G:

zB

G+2

N

+ p 

1+

[3] mp= 2:5 log

zB

N G+2

+ p

1+

G

where z =G+2= b, and b = SB p for a particular

0

0

p oint in the coma p ,SB . By measuring mpversus p,

0 0

it is p ossible to t for  and B Meech et al., 1993.

N

Extensive narrowband photometry of comet P/Halley Mil-

lis and Schleicher, 1986 showed that by observing the varia-

tions in the column density of gaseous sp ecies, the signature

of the nucleus rotation could b e detected even in an ac-

tive comet where the nucleus scattered lightwas negligible.

Here, the coma brightness variations re ect the uctuations

in cometary activity as areas of greater volatility on the sur-

Fig. 3 | Directly measured comet nucleus and NEA face rotate into and out of .

rotation p erio d distributions.

Although it is unlikely that neither the nucleus shap es nor the rotation rates are primordial owing to mass

loss, it is interesting to compare these prop erties with those of the Near{Earth{Asteroids NEAs, manyof

whichmay b e inactive comets. Whipple 1982 originally found that the p erio d distribution of the comets

was signi cantly di erent than that of the NEAs, however, Fig. 3 shows that the distributions are similar

when using only the directly determined p erio ds. With rep eated p erihelion passages and mass loss, it is

exp ected that comets will acquire a mantle of non{volatile material which will result in reducing the active

fraction of the nucleus surface. Sustained activityover several orbits from sp eci c active areas should give

rise to torques which will result in rotational spin{up and will e ect the non{gravitational orbital motion of

the comet and is a p ossible cause for nucleus splitting. However, the rotational evolution of a comet will 5

Fig. 4 | Rotational lightcurves for well-observed bare comet nuclei.

The comets are arranged in order of increasing nucleus size see Table

1. All the y{axes are scaled the same for direct comparison of the

lightcurves. The t for the phases have b een selected to align all the

o

lightcurves; the p erio ds used are shown under each gure. [a] Wilson{

Harrington Osip et al., 1995, [b] Phaethon Meech et al., in prep., [c]

Kop Meech et al., in prep, [d] Schwassmann-Wachmann 2 Luu &

Jewitt, 1992, [e] Encke Jewitt & Meech, 1987; Luu & Jewitt, 1990,

[f ] Arend{Rigaux Millis et al., 1988, [g] Temp el 2 Mueller & Ferrin,

1996, [h] Levy P/1991 L3; Fitzsimmons & Williams, 1994; [i] Neu-

jmin 1 Jewitt & Meech, 1988a, [j] Chiron Bus et al., 1989; Marcialis

& Buratti, 1993. 6

dep end on the lo cation and numb er of active areas on the nucleus. As seen in Table 1, all comets for which

wehave observations have fractionally small active areas, which implies lo calized regions of activity. Belton

1991 and Samarasinha & Belton 1995 give excellent reviews on the sub ject. There is now evidence for

complex rotation for 3 comets: P/Halley Belton et al., 1991, P/Schwassmann{Wachmann 1 Meech et al.,

1993 and P/Temp el 2 Mueller & Ferrin, 1996, in which the authors have observed a change in p erio d.

Likewise, a change in rotation p erio d was rep orted for comet C/1990 K1 Levy; Feldman et al., 1992.

Samarasinha et al. 1996 use numerical simulations to show that the nucleus of 46/P Wirtanen is a likely

candidate for signi cantchanges in spin p erio d during one apparition. Finally, accurate knowledge of the

spin state can also provide information ab out the comet's internal prop erties.

Nucleus Colors

There are very few published measurements of the colors of bare comet nuclei. Extensivework by Hartmann

et al. 1982 has shown that observations of outer solar system ob jects may b e classi ed by their p osition

in a VJHK color diagram; this is correlated with alb edo and surface material comp osition. Hartmann and

Cruikshank 1984 applied this technique to active comets and found that the colors were correlated with r ,

with the redder colors found closer to the sun. This was interpreted as either a change in mean particle size

or comp osition as the icy material sublimated closer to the sun. Jewitt and Meech 1988b rep eated this

exp eriment on a similar set of active comets and did not nd a trend in color as a function of r . It is dicult

to interpret these results b ecause for active comets a change in the grain size distribution will e ect the

colors. More recently, Luu 1993 has obtained sp ectra of distant inactive comet nuclei and susp ected comet

nucleus candidates and has found a wide range in colors ranging from slightly blue to very red compared to

solar colors. Figures 5a and 5b show the distribution of colors for comets observed in a long{term program

to monitor cometary activity as a function of r Meech, unpublished . Not all of the measurements refer to

the bare nuclei, however, care was taken to only include measurements from comets far from the sun so that

gas contamination was not likely to b e a problem for the color measurements; i.e. that they either p ertain to

the nucleus or the nucleus plus dust. The colors are plotted as a function of r in Fig. 6. With the exception

of Chiron r = 10{11 AU, a trend of reddening with increasing r app ears to b e evident in these observations.

The colors of the Sun and some representative Centaurs are shown for comparison in Fig 5 which show

that comet nuclei / comae are generally redder than the sun | exhibiting a wide range in colors. With

the discovery that Pholus and 1993 HA Centaurs were extremely red came the suggestion that the red

2

surfaces indicative of organic solids are the result of cosmic{ray irradiation Owen et al., 1995; Cruikshank

et al., 1996. The authors suggest that exp osure to UV radiation as the ob jects approach the sun causes

a loss of which results in a attening of the sp ectra to the more neutral sp ectra typical of dark

ob jects. In this case, it might b e exp ected that ob jects in the Kuip er Belt should exhibit very red surfaces.

The actual color distribution, while not known, app ears to b e similar to those of the comets in Fig. 5, and

the diversity in colors may re ect a combinaation of irradiation pro cesses and surface impacts Luu, 1996.

Fig. 5a | V{R colors for bare comet nuclei and coma Fig. 5b | R{I colors for bare comet nuclei and coma

plus nucleus Meech, unpublish ed. The V{R colors of plus nucleus Meech, unpublish ed. The R{I colors of the

the sun and 2 Centaurs are also shown for comparison. sun and 2 Centaurs are also shown for comparison. 7

Fig. 6a | V{R color trends with distance. Filled circles Fig. 6b | R{I color trends with distance. Filled circles

are for bare nucleus measurements, op en squares for mea- are for bare nucleus measurements, op en squares for mea-

surements of coma plus nucleus. Data are from Meech surements of coma plus nucleus. Data are from Meech

unpublished . unpublished .

Internal Prop erties

The internal prop erties of comet nuclei are not well understo o d, and all estimates to date rely on indirect

observations combined with mo delling. Table 2 summarizes the evolution of density measurements, b e-

ginning with the analysis of the non{gravitational motions of P/Halley, which didn't lead to particularly

constraining results. The close jovian passage and subsequent break{up of comet Sho emaker{Levy 9 has

probably given us the rmest estimate of a comet nucleus density. All of the tidal mo dels shown in Table

2 give consistent results. In the most recent pap er Asphaug and Benz 1996 mo del the tidal elongation of

the and the subsequent gravitational clumping using an N{b o dy co de arriving at a bulk density

2

of  =0:6gcm and a radius of 0.75 km for the progenitor. They were able to reconcile their small

nucleus size with the mo delling done by Sekanina 1995 who examined an ep o ch when the comet fragments

had b egun to elongate after disruption. From these mo dels, it was shown that the b est representation of

the nucleus was as a strengthless aggregate of cometesimals whichwere held together gravitationally. The

original idea of cometary rubble piles was prop osed byWeissman 1986 and Donn and Hughes 1986,

and is now considered to b e the likely result of comet accretion mo dels Weidenschilli ng, 1994. In this

scenario, grains continue to accrete collisionall y until they are  10's of m in size. They don't clump into

gravitationally b ound condensations until this size b ecause of nebula turbulence. This creates a b o dy with

strength in the sub{units but little strength against splitting, and b ecause of packing ineciencies should

give rise to low bulk densities.

A di erent technique can b e used to place constraints on the nucleus density from the rotation by assuming

that comets will not b e rotating faster than the centripital limit for break{up. By setting the centripital

2

acceleration [a =2=P  a], where P is the rotational p erio d, and a is the long axis of the comet, equal to

c

the gravitational acceleration, a at the ap ex of a prolate spheroid, one can place lower limits on the nucleus

g

density. The gravity for the ap ex of the nucleus is given by Luu & Jewitt, 1992:

a = 2 G a F f  [4]

g

where G is the gravitational constant,  the nucleus density, f is the axis ratio b=a and F f  is given by:

p p

2 2 2 2 2

2 2

1f +f lnf + f ln2+2 1f f  2f

[5] F f =

2 1:5

1f  8

The axis ratios versus rotation p erio ds for the comets in Table 1

are plotted in Fig. 7, in addition to those of the NEAs for com-

parison. Lines of critical rotation are shown for several densities

3

ranging from 0.1 to 3.0 gm cm . Many of the NEAs require den-

3

sities greater than 1.0 gm cm , in contrast to the comets. The

gure shows that densitylower limits for comets allow densities

3

less than that of solid {ice,  = 1.0 gm cm , which is con-

sistent with the exp ected bulk density from the rubble pile mo del

describ ed ab ove.

Finally,Table 3 shows the evolution of the attempts to determine

the tensile strength for various comet analogue materials. Most of

the measurements which rely on tidal stress mo dels have tensile

2 4 2 3

strengths in a range b etween 10 {10 Nt m  10 , whichis

Fig. 7 | Rotation p erio ds versus axis ratio, similar to the estimated strengths for the interplanetary dust pari-

a:b from Table 1 and McFadden et al., 1989, cles IDPs, many of whichhave cometary origins. Likewise, mea-

and Lagerkvist et al., 1989, for NEAs circles surements from arti cial nuclei created in the lab have strengths

and the comets in Table 1 squares. The solid which are in the same range. Although there is not yet a clear

lines show curves of critical rotation for densi- consensus on the tensile strength of cometary material, the results

3

ties of 0.1, 0.3, 1.0 and 3.0 gm cm from to in Table 3 suggest that the value is low | probably lower than

to b ottom. that of terrestrial snows.

Table 2. EVOLUTION OF COMETARY NUCLEUS DENSITY ESTIMATES

y z x

Density Technique Reference

0.28 { 0.65 H O and non-grav analysis on P/Halley 1

2

0.03 { 4.9 H O outgassing and non-grav analysis on P/Halley 2

2

0.6 +0.9/-0.4 H O outgassing and non-grav analysis on P/Halley 3

2

<0.7 { 1.5 P/SL9 theoretical mo dels of tidal disruption 4

0.5 P/SL9 mo dels of tidal break-up of primordial rubble pile 5

0.55 P/SL9 breakup mo dels 6

0.6 P/SL9 breakup gravitational clumping mo dels 7

<0.4 Numerical simulation of comet rotational state evolution 8

>0.3 Rotational analysis 9

>0.2 Rotational analysis 10

0.5 Mo del of 14.3 AU outburst of P/Halley 11

<1.0 HST obs of Coma of Chiron and b ound mo del 12

y 3 3 z x

Notes: Nucleus densityingmcm 10 ; Technique used to determine the nucleus density estimate; References:

[1] Rickman, 1989, [2] Peale, 1989, [3] Sagdeev, et al., 1988, [4] Boss, 1994, [5] Asphaug & Benz, 1994, [6] Solem, 1995,

[7] Asphaug & Benz, 1996, [8] Samarasinha & Belton, 1995, [9] Jewitt & Luu, 1989, [10] Fitzsimmons & Williams,

1994, [11] Prialnik & Bar-Nun, 1992, [12] Meech, et al., 1996.

CONCLUSIONS

Whereas there have b een tremendous technological innovations whichhave facilitated a recent rapid growth

in our understanding of the physical prop erties of cometary nuclei, we still have knowledge of only a small

sample of nuclei | not enough for statistically meaningful comparisons with small asteroids, or with the

Trans{Neptunian Ob ject p opulation. The observed nuclei are generally small, with sizes ranging from 

1 { 83 km, with the average size estimates decreasing with detectors b etter able to detect activity. The

measured alb edos are uniformly low, b etween 0.02{0.04. The Jupiter family comet sizes are similar to the

NEA small asteroid p opulation, however, we see evidence that the comet size distribution changes in the

outer solar system where much larger b o dies are observed. However, it should b e noted that these trends

are still plagued by selection e ects. Comet nuclei can b e describ ed as prolate ellipsoids with axis ratios

varying b etween 1.1{2.6, and rotation p erio ds ranging from 5 hours to several days. The rotation rates of

the comets have b een found to b e similar to the NEA rotation rates, however, there is evidence for complex 9

Table 3. COMETARYMATERIAL STRENGTH ESTIMATES

y z x

Tensile Strength Material Technique Reference

3

10 tidal stress; sungrazer Ikeya-Seki =1.0 1

3

4.3  10 tidal stresses on Bro oks 2 at p erijove=1.0 1

3

10 mantle icy dirtball nucleus mo dels 2

2 3

10 {10 electrostatic fragmentation of P/Halley dust  3

3

2.7  10 P/SL9 tidal breakup mo dels 4

2 4

10 {10 analysis of cometary spin & size characteristics 5

4

10 ram pressure from outgassing from nucleus 6

3 5

10 {10 lab oratory measurements of arti cial nuclei 1

8

10 sho ck strength during Tunguska breakup 1,7

8

10 survival of sungrazers { for non{p orous ice 8

2 3

2  10 {10 dry snow icy dirtball nucleus mo dels 2

5

10 snow 50 p orous snow 8

5

3.5  10 p orous ice icy dirtball nucleus mo dels 2

3

1{5  10 fragmentation ram pressure, Draconids 9

3

1{5  10 IDPs analysis of interplanetary dust particles 10

6 8

6  10 {410 chondrites measurements of chondrites 11

8

4  10 iron measurements of iron meteorites 11

y 2 3 z x

Notes: Tensile Strength in Nt m  10 ; Technique used to determine the tensile strength estimate; References:

[1] Mendis et al. 1985; [2] Mohlmann, 1995; [3] Bo ehnhardt & Fechtig 1987; [4] Greenb erg et al. 1995; [5]

Hughes 1991; [6] Sekanina 1982; [7] Sekanina 1983; [8] Green 1989; [9] Sekanina 1985; [10] Bradley & Brownlee

1986; [11] Wasson 1974.

rotational states for 3 comets: P/Halley, P/SW1 and P/Temp el 2. The colors of the nuclei suggest a very

diverse p opulation with a wide range in colors which are generally redder than solar. The colors of the short

{p erio d comet nuclei are similar to the C and D class asteroids, and show the same spread in colors that

are seen in the Trans{Neptunian Ob jects.

In contrast to the external physical prop erties, there are no direct measurements of the internal prop er-

ties. The indirect techniques used to infer the bulk internal prop erties suggest a wide range in values.

3

Bulk nucleus densities fall b etween 0.3{1.0 gm cm , implying a relatively large p orosity, and the tensile

strengths are estimated to b e low | similar to the strengths found for interplanetary dust particles, but

less than that of snow. If we are to ever b etter constrain the solar mo dels, and close the gap b etween theory

and observation, in particular in the realm of the evolution from m{sized to km{sized planetesimals, we

need b etter observational constraints. For the rst time wehave the ability to b egin to determine the size

distribution of bare comet nuclei; however, as our estimates are getting revised to smaller sizes, and given

our knowledge of the low alb edos, we require larger and larger telescop e ap erture to make these observations.

ACKNOWLEDGEMENTS

This work was supp orted in part by grants from the NASA Planetary Astronomy Program NAGW-1897

and NAGW-5015, the National Science Foundation AST-92-21318, and the Space Telescop e Science In-

stitute GO-03769.01-91A and GO-05834.01-94A. I would esp ecially like to thank O. Hainaut for help with

formatting the latex for this pap er and our librarian, K. Rob ertson, for all her help with database searching

for references for this pap er.

REFERENCES

A'Hearn, M. F. 1988. \Observations of Cometary Nuclei", Ann. Rev. Earth Planet. Sci. 16, 273-293.

A'Hearn, M. F., H. Campins, D. G. Schleicher and R. L. Millis 1989. \The Nucleus of Comet P/Temp el

2", Astrophys. J. 327, 1155-1166.

Allen, D. A. 1970. \Infrared Diameter of Vesta, Nature 227, 158-159. 10

Altenho , W. J. and P. Stump 1995. \Size Estimate of \Asteroid" from 250 GHz Measure-

ments", . Astrophys. 293, L41-L42.

Asphaug, E. and W. Benz 1996. \Size, Density, and Structure of Comet Sho emaker{Levy 9 Inferred from

the Physics of Tidal Breakup", Icarus 121, 225-248.

Asphaug, E. and W. Benz 1994. \Density of Comet Sho emaker{Levy 9 Deduced by Mo delling Breakup

of the Parent \Rubble Pile" ", Nature 370, 120-124.

Bauer, J., K. J. Meech and O. R. Hainaut 1996. \Rotation of the Nucleus of Comet 46P/Wirtanen",

BAAS, submitted.

Beckwith, S. V. and A. I. Sargent 1993. \The Occurrence and Prop erties of Disks Around Young Stars",

in Protostars and Planets III, ed. E. H. Levy and J. I. Lunine, Univ. AZ Press, 521-541.

Belton, M. J. S. 1990. \Rationalization of Comet Halley's Perio ds", Icarus 86, 30-51.

Belton, M. J. S. 1991. \Characterization of the Rotation of Cometary Nuclei", in Comets in the Post-

Hal ley Era, Ed. R. L. Newburn, M. Neugebauer, and J. Rahe, Kluwer, Dordrecht, 691-712.

Belton, M. J. S., W. H. Julian, A. J. Anderson and B. E. A. Mueller 1991. \The Spin State and Homo-

geneity of Comet Halley's Nucleus", Icarus 93, 183-193.

Bo ehnhardt, H. and H. Fechtig 1987. \Electrostatic Charging and Fragmentation of Dust Near P/Giacobini{

zinner and P/Halley", Astron. Astrophys. 187, 824-828.

Bo ehnhardt, H., H. Rauer, S. Mottola and A. Nathues 1996. IAUC Circ. 6392.

Boss, A. P. 1994. \Tidal Disruption of Perio dic Comet Sho emaker{Levy 9 and a Constraint on Its Mean

Density", Icarus 107, 422-426.

Bradley,J.P. and D. E. Brownlee 1986. \Cometary Particles | Thin Sectioning and Beam

Analysis", Science 231, 1542-1544.

Bus, S. J., E. Bowell, A. W. Harris and J. V. Hewitt 1989. \2060 Chiron: CCD and Electronographic

Photometry", Icarus 77, 223-238.

Bus, S. J., M. W. Buie, D. G. Schleicher, W. B. Hubbard, R. L. Marcialis, R. Hill, L. H. Wasserman, J. R.

Sp encer, R. L. Millis, E. W. Dunham, C. H. Ford, E. W. Young, J. L. Elliot, R. Meserole, C. B. Olkin,

S. W. McDonald, J. A. Foust, L. M. Sopata, and R. M. Bandyopadhyay 1996. \Stellar Occultation

by 2060 Chiron", Icarus, submitted.

Campins, H., M. F. A'Hearn and L.-A. McFadden 1987. \The Bare Nucleus of Comet Neujmin 1", Astron.

Astrophys. 316, 847-857.

Chamb erlain, A. B, L.-A. McFadden, R. Schulz, D. G. Schleicher and C. J. Bus 1996. \4015 Wilson{

Harrington, 2201 Oljato, and 3200 Phaethon : Search for CN Emission", Icaurs 119, 173-181.

Cruikshank, D. P. 1983. \The Nucleus of Comet P/Schwassmann{Wachmann 1", Icarus 56, 377-380.

Cruikshank, D. P., T. L. Roush, M. J. Bartholomew, L. V. Moroz, T. R. Geballe, S. M. White, J. F. Bell I I I,

Y. J. Pendleton, J. K. Davies, T. C. Owen, C. deBergh, D. J. Tholen, M. P. Bernstein, R. H. Brown,

K. A. Tryka 1996. \The Comp osition of Planetesimal 5145 Pholus", Icarus, submitted.

Donn, B. and D. Hughes 1986. \A Fractal Mo del of a Cometary Nucleus Formed by Random Accretion",

in Proc 20th ESLAB Symposium on the Exploration of Hal ley's Comet, Eds. B. Battrick, E. J. Rolfe

and R. Reinhard, Vol I I I, 523-524.

Duncan, M. J, H. F. Levison, and S. M. Budd 1996. \The Dynamical Structure of the Kuip er Belt",

Astron. J., in press.

Fay, T. D. and W. Wisniewski 1978. \The Light Curve of the Nucleus of Comet d'Arrest", Icarus 34, 1-9.

Feldman, P. D., S. A. Budzien, M. C. Festou, M. F. A'Hearn, and G. P.Tozzi 1992, \ and

Visible Variability of the Coma of Comet Levy 1990c", Icarus 95, 65-72.

Fitzsimmons, A. and I. P. Williams 1994. \The Nucleus of Comet P/Levy 1991 XI", Astron. Astrophys.

289, 304-310.

Green, J. R. 1989. \The Thermo{Mechanical Behavior of Cometary Nuclei", Ph.D. Dissertation, Univer- 11

sityofTexas, Austin.

Greenb erg, J. M, H. Mizutani and T. Yamamoto 1995. \A New Derivation of the Tensile Strength of

Cometary Nuclei: Application to Comet Sho emaker{Levy 9", Astron. Astrophys. 295, L35-L38.

Hainaut, O., R. M. West, A. Smette and B. G. Marsden 1994. \Imaging of Very Distant Comets: Current

and Future Limits", Astron. Astrophys. 289, 311-324.

Hanner, M. S., D. K. Aitken, R. Knacke, S. McCorkle, P.F.Roche, and A. T. Tokunaga 1985. \Infrared

Sp ectrophotometry of Comet IRAS-Araki-Alco ck 1983d: a Bare Nucleus Revealed?", Icarus 62, 97-

109.

Hartmann, W. K. and D. P. Cruikshank 1984. \Comet Color Changes with Solar Distance", Icarus 57,

55-62.

Hartmann, W. K., D. P. Cruikshank and J. Degewij 1982. \Remote Comets and Related Bo dies: VJHK

Colorimetry and Surface Materials", Icarus 52, 377-408.

Holman, M. J. and J. Wisdom 1993. \Dynamical Stability in the Outer Solar System and the Delivery of

Short Perio d Comets", Astron. J. 105, 1987-1999.

Hughes, D. W. 1991. \Possible Mechanisms for Cometary Outbursts", in Comets in the Post{Hal ley Era,

R. L. Newburn, Jr., ed., Kluwer Academic Pub., Netherlands, 825-851.

Jewitt, D. C. and G. E. Danielson 1984. \Charge Coupled Device Photometry of Comet P/Halley", Icarus

60, 435-444.

Jewitt, D. C. and J. Luu 1989. \A CCD Portrait of Comet P/Temp el 2", Astron. J. 97, 1766-1790.

Jewitt, D. C. and J. X. Luu 1995. \The Solar System Beyond Neptune", Astron. J. 109, 1867-1876.

Jewitt, D. and K. J. Meech 1985. \Rotation of the Nucleus of P/Arend{Rigaux", Icarus 64, 329-335.

Jewitt, D. and K. Meech 1987. \CCD Photometry of Comet P/Encke", Astron. J. 93, 1542-1548.

Jewitt, D. C. and K. J. Meech 1988a. \Optical Prop erties of Cometary Nuclei and a Preliminary Com-

parison with Asteroids", Astrophys. J. 328, 974-986.

Jewitt, D. and K. J. Meech 1988b. \The Absence of a Color{Distance Trend in Comets", Astron. J. 96,

1723-1730.

Jorda, L. and H. Rickman 1995. \Comet P/Wirtanen, Summary of Observational Data", Planetary Space.

Sci. 43, 575-9.

Kam el, L. 1992. \The Comet Light CurveAtlas", Astron. Astrophys. Supp. 92, 85-149.

Keller, H. U., W. A. Delamere, H. J. Reitsema, W. F. Huebner, and H. U. Schmidt 1987. \Comet

P/Halley's Nucleus and its Activity", Astron. Astrophys. 187, 807-823.

Lagerkvist, C..-I, A. Harris, and V. Zappal a 1989. \Asteroid LightcurveParameters", in Asteroids II, eds.

R. P. Binzel, T. Gehrels, and M. S. Matthews, Univ. AZ Press, Tucson, 1162-1179.

Lamy,P. 1995. IAU Circular 6204.

Lamy,P. L., M. F. A'Hearn, I. Toth and H. A. Weaver 1996. \HST Observations of the Nuclei of Comets

45P/Honda-Mrkos-Pa jdusakova, 22P/Kop , and 46P/Wirtanen", BAAS, in press.

Lamy,P. L., and I. Toth 1995. \Direct Detection of a Cometary Nucleus with the Hubble Space Telescop e",

Astron. Astrophys. 293, L43-45.

Levison, H. F. and M. J. Duncan 1993. \The Gravitational Sculpting of the Kuip er Belt.", Astrophys. J.

406, L35-L38.

Lissauer, J. J. 1987. \Time Scales for Planetary Accretion and the Structure of the Protoplanetary Disk".

Icarus 69, 249-265.

Lissauer, J. J. and G. R. Stewart 1993. \Growth of Planets from Planetesimals", in Protostars and Planets

III, ed. E. H. Levy and J. I. Lunine, Univ. AZ Press, 1061-1088.

Lunine, J. I., S. Engel, B. Rizk and M. Horanyi 1991. \Sublimation and Reformation of Icy Grains in the

Primitive Solar Nebula", Icarus 94, 333-344. 12

Luu, J. X. 1996. \Colors of Kuip er Belt and Centaur Ob jects", in Asteroids, Comets, Meteors 1996,

COSPAR Collo q. 10.

Luu, J. X. 1993. \Sp ectral Diversity Among the Nuclei of Comets", Icarus 104, 138-148.

Luu, J. X. and D. Jewitt 1990. \The Nucleus of Comet P/Encke", Icarus 86, 69-81.

Luu, J. X. and D. C. Jewitt 1992. \Near{Aphelion CCD Photometry of Comet P/Schwassmann{Wachmann

2", Astron. J. 104, 2243-2249.

Malhotra, R. 1995. \The Origin of Pluto's Orbit: Implications for the Solar System Beyond Neptune",

Astron. J. 110, 420-429.

Marciales, R. L. and B. J. Buratti 1993. \CCD Photometry of 2060 Chiron in 1985 and 1991", Icarus

104, 234-243.

McFadden, L.-A., D. J. Tholen and G. J. Veeder 1989. \Physical Prop erties of Aten, Ap ollo and Amor

Asteroids", in Asteroids II, eds. R. P. Binzel, T. Gehrels, and M. S. Matthews, Univ. AZ Press, Tucson,

442-467.

Meech, K. J. 1987. \Optical Investigation of Cometary Nuclei, Ph.D. Dissertation, Massachusetts Institute

of Technology.

Meech, K. J. 1994. \Distant Comet Observations: Unlo cking the Early Solar System", Urey Prize Lecture.

Meech, K. J., M. W. Buie, M. J. S. Belton, B. E. A. Mueller and N. Samarasinha 1996, \Planetary Camera

Observations of Structures in the Inner Coma of Chiron", submitted Astron. J.

Meech, K. J., M. J. S. Belton, B. Mueller, M. Dicksion and H. Li 1993. \Nucleus Prop erties of P/Schwassmann-

Wachmann 1", Astron. J., 106, 1222-1236.

Meech, K. J. and M. J. S. Belton 1990. \The Atmosphere of 2060 Chiron". Astron. J. 100, 1323-1338.

Meech, K. J., D. C. Jewitt and G. R. Ricker 1986. \Early Photometry of Comet P/Halley: Development

of the Coma", Icarus 66, 561-574.

Meech, K. J., G. Knopp, T. L. Farnham, and D. Green 1995. \The Split Nucleus of Comet Wilson 1987

VI I", Icarus, 116, 46-76.

Mendis, D. A., H. L. F. Houpis and M. L. Marconi 1985. Fundamentals of Cosmic Physics 10, 1-380.

Millis, R. L., M. F. A'Hearn and H. Campins 1988. \An Investigation of the Nucleus and Coma of Comet

P/Arend{Rigaux", Astrophys. J. 324, 1194-1209.

Millis, R. L. and D. G. Schleicher 1986. \Rotational Perio d of Comet Halley", Nature 324, 646-649.

Mohlmann, D. 1995. \Cometary Activity and Nucleus Mo dels", Planet. Space Sci. 43, 327-332.

Mueller, B. E. A. and I. Ferrin 1996. \Change in the Rotational Perio d of Comet P/Temp el 2 Between

the 1988 and 1994 Apparitions", Icarus, in press.

OCeallaigh, D. P., A. Fitzsimmons, and I. P. Williams 1995. \CCD Photometry of Comet 109P/Swift{

Tuttle", Astron. Astrophys 297, L17-L20.

O'Dell, C. R. 1971. \Nature of Particulate Matter in Comets as Determined from Infrared Observations,

Astrophys. J. 166, 675-681.

Osip, D. J., H. Campins and D. G. Schleicher 1995. \The Rotation State of 4015 Wilson | Harrington:

Revisiting Origins for the Near{Earth Asteroids", Icarus 114, 423-426.

Osip, D. J., D. G. Schleicher and R. L. Millis 1992. \Comets: Ground{based Observations of Spacecraft

Mission Candidates", Icarus 98, 115-124.

Osip, D. J., D. G. Schleicher, R. L. Millis, and S. Lederer 1996. \Narrowband Photometry and Imaging

of 1996 B2", COSPAR Collo q. 10, 28.

Owen, T., D. Cruikshank, C. de Bergh and T. Geballe 1995. \Dark Matter in the Outer Solar System",

Adv. in SpaceRes. 16, No. 2, 41-49.

Peale, S. J. 1989. \On the Density of Halley's Comet", Icarus 82, 36-49.

Prialnik, D. and A. Bar-Nun 1992. \Crystallization of Amorphous Ice as the Cause of Comet P/Halley's 13

Outburst at 14 AU", Astron. Astrophys. 258, L9-L12.

Rickman, H. 1989. \The Nucleus of Comet Halley | Surface Structure, Mean Density, Gas and Dust

Pro duction", Adv. SpaceResearch 9, 59-71.

Ro emer, E. 1966. \The Dimensions of Cometary Nuclei", in Nature et Origine des Com etes, Pro c. Collo q.

Int. Univ. Li ege, 23-28.

Sagdeev, R. Z., P. E. Elyasb erg and V. I. Moroz 1988. \Is the Nucleus of Comet Halley a Low Density

Bo dy?", Nature 331, 240-242.

Samarasinha, N. H. and M. J. S. Belton 1995. \Long{Term Evolution of Rotational States and Nongrav-

itational E ects for Halley{Like Cometary Nuclei", Icarus 116, 340-358.

Samarasinha, N. H, B. E. A. Mueller and M. J. S. Belton 1996. \Comments on the Rotational State and

Non-Gravitational Forces of Comet 46P/Wirtanen", Planet Space Sci. 44, 275-281.

Scotti, J. V. 1994. \Comet Nuclear Magnitudes", BAAS 185, 43.06; and p ersonal communication.

Sekanina, Z. 1976. \A Continuing Controversey: Has the Bare Nucleus Been Resolved?", in The Study of

Comets, ed. B. Donn, M. Mumma, W. Jackson, M. A'Hearn, and R. Harrington, NASA SP-393, U.S.

Gov. Printing Oce, Washington, DC, 537-587.

Sekanina, Z. 1981. \Rotation and Precession of Cometary Nuclei", Ann. Rev. Earth Planet. Sci 9,

113-145.

Sekanina, Z. 1982. \The Path and Surviving Tail of a Comet that Fell Into the Sun", Astron. J. 87,

1059-1072..

Sekanina, Z. 1983. \The TunguskaEvent: No Cometary Signature in Evidence", Astron. J. 88, 1382-1414.

Sekanina, Z. 1985. \Precession Mo del for the Nucleus of Perio dic Comet Giacobini{Zinner", Astron. J.

90, 827-845.

Sekanina, Z. 1987. \Nucleus of Comet IRAS-Araki-Alco ck 1983 VI I", Astron. J. 95, 1876-1894.

Sekanina, Z. 1990. \Perio dic and its Idio cyncrasies", Astron. J. 99, 1268-1278.

Sekanina, Z. 1995. \Evidence on Sizes and Fragmentation of the Nuclei of Comet Sho emaker{Levy 9 from

Hubble Space Telescop e Images", Astron. Astrophys. 304, 296-316.

Solem, J. C. 1995. \Cometary Breakup Calculations Based on a Gravitationally{Bound Agglomeration

Mo del: the Density and Size of Sho emaker{Levy 9", Astron. Astrophys. 302, 596-608.

Wasson, J. T. 1974. Meteorites, Springer-Verlag.

Weidenschilli ng, S. J. 1988. \Comparisons of Solar Nebula Mo dels", in Workshop on the Origins of Solar

Systems, eds. J. Nuth and P. Sylvester, LPI Tech Rept. 88-04, 31-37.

Weidenschilli ng, S. J. 1994. \Origin of Cometary Nuclei as 'Rubble Piles' ", Nature 368, 721-723.

Weidenschilli ng, S. J. and J. N. Cuzzi 1993. \Formation of Planetesimals in the Solar Nebula", in Proto-

stars and Planets III, ed. E. H. Levy and J. I. Lunine, Univ. AZ Press, 1031-1060.

Weissman, P. 1995. \The Kuip er Belt", in Ann. Rev. Astron. Astrophys. 33, 327-357.

Weissman, P. 1986. \Are Cometary Nuclei Primordial Rubble Piles?", Nature 368, 721-723.

Whipple, F. L. 1982. \Rotation of Comet Nuclei", in Comets, ed. L. L. Wilkening, Univ. AZ Press,

227-50.

Wisniewski, W. Z., T. Fay and T. Gehrels 1986. \LightVariations of Comets", in Asteroids, Comets,

Meteors II, Ed. C.-I. Lagerkvist, B. A. Lindblad, H. Lundstedt and H. Rickman, Uppsala Univ.,

337-339.

Yamamoto, T. 1985. \Formation Environment of Cometary Nuclei in the Primordial Solar Nebula",

Astron. Astrophys. 142, 31-36.

Yoshida, S., T. Aoki, T. Soyano, K.-I. Tarusawa, W. Van Driel, M. Hamab e, T. Ichikawa, J.-I. Watanab e

and K.-I. Wakamatsu 1993. \Spiral Dust{Jet Structures of Comet P/Swift{Tuttle 1992t", Pub. Ast.

Soc. Japan 45, L33-L37. 14