The Importance of Nucleus Rotation in Determining the Largest Grains Ejected from Comets

Home , Comet Hyakutake

© Copyright 2010: Instituto de Astronomía, Universidad Nacional Autónoma de México Spain. Spain. Granada, Granada, de Universidad eit eiaad srnmı Astrof´ısica Astronom´ıa y de Mexicana Revista h ag riscnb pt e ee ndiam- in meter few a to up be nuclei. can cometary grains us large of of provide The composition can probe the meteoroids on a of information as characteristics knowledge Thus, the used of 1998). be study (Beech The can structure cometary streams stream. meteroid meteoroid Large a comet. of the produce of can tail dust grains leave the form and to pressure nucleus radiation the grains solar Small by Sun. dominated the are approach comets the as grains 2 1 si nw,tecmtr ulirlaedust release nuclei cometary the known, is As nttt eAto´sc eAdlcı,CI,Granada, CSIC, Andaluc´ıa, de Astrof´ısica de Instituto eatmnod ´sc piaa autdd Ciencias, de Facultad F´ısica Aplicada, de Departamento H MOTNEO ULU OAINI DETERMINING IN ROTATION NUCLEUS OF IMPORTANCE THE aoe aalsd´mto elsmyrsprćlsqepee epedredel desprenderse pueden part´ıculas que mayores cometa las cometa. el diámetros de analiza los También se para radar. valores los de con proponiendo medidas comparados 2014, alcanzará misión en de son que la ROSETTA Churyumov-Gerasimenko, obtenidos partir resultados a Los part´ıcula determinados la valores superficie. que la para de cometa rotación el expresión levantarse del de indicando sencilla pueda periodo una el muestra tener de Se principalmente debe m´ınimo inerciales, valor cometa. que rotación fuerzas del la las de a importancia debidas la las destaca Se gases los cometas. los de expansión clásicode radial de modelo del uso haciendo núcleos cometarios 04 sgigt eaaye n ag o h aiu imtro h dust the of diameter maximum the Words: for Key proposed. range is a Finally, lifted and be o analyzed can made. arrive that be to is grains to mission with measurements going ROSETTA comparison the is radar a of 2014, by and target comets obtained the different Churyumov-Gerasimenko, values of to comet value applied radius critical are this maximum can results for grain the expression Our rotation dust simple the given. larger A faster, is a value. is period certain Although rotation a the shown. than if radia is larger surface particularly by comet be nucleus and the the out from forces, of dragged lifted inertial rotation as be the the grain of to dust due importance of those The model gases. classical cometary expanding the using investigated is .INTRODUCTION 1. H AGS RISEETDFO COMETS FROM EJECTED GRAINS LARGEST THE edtriae ao ´xm e iaer elsprćlseetdsd los de part´ıculas eyectadas las diámetro máximo de del valor el determina Se h aiu imtro ag oleseetdfo h oeaynuclei cometary the from ejected boulders large of diameter maximum The oes eea oes niiul(aly itnn Hyakutake, Wirtanen, (Halley, individual comets: — general comets: nepaeaymdu meteoroids — medium Churyumov-Gerasimenko) interplanetary IRAS-Araki-Alcock, — LINEAR, A2 C/2001 eevd21 eray1;acpe 00Jn 16 June 2010 accepted 18; February 2010 Received , 46 ABSTRACT .Molina A. RESUMEN 2–3 (2010) 323–330 , cps si ye ta.(96 h sdfour used who 100 (1986) and 60 25, al. 12, et tele- at Sykes filters space-based broad-band in using as observed dust scopes, Cometary been me- largest have stream. the Leonid of trails diameter the the within for teoroids m 1.24 lower of a bound obtained produce (1998) to Beech conditions sounds, the electrophonic account into Taking eter. a aeegh sn h KCDcmr attached camera CCD opti- 2K ob- in the trail (2002) using dust wavelengths cometary al. cal a of et ground- evidence Ishiguro first by tained Thus, observed telescopes. been based have strems meteoroid oesdet mszdo agrprilsuigthe using particles larger 24 or mm-sized period to short & due 27 of comets Kelley, trails debris Reach, observed (2007) Sykes Satellite. Astronomical Infrared 1,2 µ aeao the on camera m pte pc Telescope Space Spitzer eidhsto has period rotation lly n µ nthe on m Also, . 323 © Copyright 2010: Instituto de Astronomía, Universidad Nacional Autónoma de México rm tahdt h ulu scniee.The follows: as written considered. be is can nucleus motion of the equation reference to a attached the because appear frame and Sun, which force the forces, drag inertial gas of the the grav- and force, the pressure nucleus radiation suffer the solar they of surface, forces nucleus itational particles the describing the left par- comet Once have those the 1997). of (Fulle around orbits Some orbiting pseudostable be comet. the can of ticles surface the from htcnb riigaon oeayncesare nucleus interest. cometary greatest a particles the around the of orbiting of be size can the that and of 1997) estimations Keller the & on therefore Knollenberg, landing Kuhrt, of see risks comet physical neigh- a (for the comet visiting a of spacecrafts the bourhood for consti- hazard This a orbits. tutes pseudostable in nuclei cometary diameter. in m 0.18–0.35 was 2002), meteoroid (Babadzhanov that streams then meteoroid known all eto otertto ftecmt apply ( I period with rotation comet. comet low a the very 1P/Halley, at- of comet a to special I rotation expressions with the our obtained. theory to be outgassing can tention classical particle a ejected use largest the of h ags jce atcefo h ulu fthe of nucleus the of from diameter in particle comet the ejected estimate largest I the mission, Rossetta the interest target the of the to 67P/Churyumov-Gerasimenko, ob- Due Comet nuclei the in measurements. of cometary radar size by several the tained from on particles results with ejected comparison a shows 6/itnn eyfs pnigcmt( comet spinning fast very a 46P/Wirtanen, ihtelws est aus 0 gm kg 400 values, density meteoroids lowest im- the are the brightest Leonids with the the kg that 9 produced Assuming to that kg pact. 1.3 meteoroid of the range meteor mass for Leonid a the derived of They meteoroids asso- shower. of were which flux the 1999, side November to night 18 ciated ana- the on (2000) Moon on the al. observed of et flashes Ortiz impact Moon. five the lyzed of impact surface they ob- the when the on occur of that flashes means the by of studied servations these be telescopes, can Obser- of meteoroids Kiso use large the direct the at from telescope Aside Schmidt vatory. cm 105 the to 324 .SZ FTELRETEETDGRAINS EJECTED LARGEST THE OF SIZE 2. d dt 2 ~ r oeaygso h ulu rg utparticles dust drags nucleus the of gas Cometary nti ae,Iso in show I paper, this In the around found be also can grains ejected Large 2 d + = µM § 3 16 r .Tecnlsosaepeetdin presented are conclusions The 6. C c 3 S πC D G m ˙ p g Q 3 v p ~ r g d r β c 2 · − ~ r c GM ~ r c − c § ~ r § d o h diameter the how 2 ~ r r d d 3 ) n ocomet to and 3), + βM S G − 3 § r ~ r fthe of , c 3 c 4). § § 7. MOLINA 5 h rgcecet ˙ coefficient, drag the qaino oin n,priual,o h values the the in of terms particularly, for rotation obtained and, I motion, the paper, of this of equation In importance located). the is show particle dust the where h comet, the oesrttn lwy Ω slowly, For rotating periods. comets rotational different of comets several for ae(loapaigas appearing (also rate aito rsuet rvttoa oc fteSun, the of force G gravitational to pressure radiation g where hnΩ than a velocity, gas g cteigecec ftegrain, the of efficiency scattering ocmtvector, comet to ino h oe and comet the of tion h enttlslrrdainand radiation solar total mean the sotie from obtained is to ftertto ftecmtand comet the of rotation the of t rsne,frshrclprils cuaeexpres- accurate for particles, (1976) sions spherical Henderson for conditions. presented, flow the and particle il sasmdadacntn au f2for 2 of value par- constant the a for and shape assumed spherical is a ticle paper, this In ditions. mlydfralcss h constant The cases. all for employed ay oe 99.Tevleo 1 of value The (Burns, 1979). Soter size & decreasing Lamy, radiation with the increases grains, force small pressure very Excluding particle. where rmtesrae(e,freapeMln,Moreno, Molina, example lifted Jiménez-Fernández for & be (see, can 2008): surface that the diameter from largest with particle this the in show Fulle. I of as work important the be paper. in can present they not cometary However, the are three of last rotation and the that the nucleus, to due for as are except nomenclature which terms, (1997) same Fulle the expres- by above used employed the have assume In also we 0. I is sion obliquity 1968). nucleus the Probstein that & Finson (see light eff eff stetime. the is stegaiainlconstant, gravitational the is β Here, h rgcecetdpnso h hp fthe of shape the on depends coefficient drag The rmeuto 1,Ioti nepeso for expression an obtain I (1), equation From = ≈ ymaso h expression the of means by Ω + g ρ g R 2 d − As . R stedniyand density the is C sterdu ftecmtr ulu and nucleus cometary the of radius the is Ω ~ r 2 cos D d ~ r M 2 d R d g stencest ri vector, grain to nucleus the is ayn vrawd ag fflwcon- flow of range wide a over varying d S C 2 − max ( cos max = p stems fteSun, the of mass the is φ ( µ o oeswith comets for ) Ω ~ C n ics h eut obtained results the discuss I and , 1 = 2 G 1 = = p φ · 4 ~ r πρ 3 = m ( d ρ . φ g 19 ) d − g Q n 2 + Ω ~ 1 stelttd ntesurface the on latitude the is g stegaiainlaccelera- gravitational the is R/ E β eff stegoa a asloss mass gas global the is · nteliterature), the in , s 2 10 d (8 ,i ilb uhlarger much be will it 3, R 3 steaglrvelocity angular the is Ω ~ h imtro h dust the of diameter the C ~v − 16 cGM cos d 3 D πR × m gm kg ˙ 2 β ~v M g Ω ~ φ S d 2 v β = ) . c . g 19 = − τ ≪ c stertoof ratio the is stems of mass the is 2 1 , − C · where , d~ r C ~ r h pe of speed the 2 10 p ≫ c , g p Q d − steSun the is Q /dt p srelated is n then and 3 3 ( v p ρ π/ρ gm kg g d where C sthe is C sthe is d E D ) D n s − (1) (2) − G 1 is is is 2 , , © Copyright 2010: Instituto de Astronomía, Universidad Nacional Autónoma de México rmeuto 2,Iobtain I (2), equation From h au of value the Thus, ieices in increase tive h oeayrtto nteotie ausof values obtained the in rotation cometary the 1. Figure in shown is densities nucleus of nrdc h parameter the introduce I ulu oainwhen rotation nucleus ρ n h oeayncesa teghesbody, strengthless a as nucleus g cometary the ing d agrta rtclperiod critical a than larger ods and where is curve the the of above density region versus the period Only permitted. rotation nucleus. Critical cometary 1. Fig. r osbe tews h oe ol yapart. fly would comet the Thus, otherwise possible, are ρ erto vrteilmntdhmshr,Iobtain in- I After hemisphere, illuminated comet. the the over on tegration depends which constant fit l,adi cos( if and gle, cos( nFgr show I 2 Figure In where oad h u.FloigFle(97,˙ anisotropy (1997), nu- Fulle strong Following cometary a Sun. suggest the the towards and from anisotropic grains is assume of cleus I emission grains). when the the on is that acting (that forces other it greater the is of than force values gravitational lift cometary low not attractive for the would surface grains the the from because crucial, is motion o luiae eipee ˙ write, can I hemisphere, Then, angle. illuminated zenith for the of cosine the of eff n n . si gm kg in is nodrt lutaeterltv motneof importance relative the illustrate to order In h uniy˙ quantity The Z utb oiieadte nyrtto peri- rotation only then and positive be must ρ ) n α τ P τ < crit nk m kg in 100 = stertto eid For period. rotation the is dr eipee where hemisphere) (dark 0 stenraiaincntn,and constant, normalization the is 3 = − d Z max 3 . · 76 uv of curve A . − ) d ( 3 m d max ≥ , · max hntecmti o rotating. not is comet the when g 10 d ,˙ 0, α v max AGS ATCE JCE RMRTTN OES325 COMETS ROTATING FROM EJECTED PARTICLES LARGEST g 5 u otecmtr rotation. cometary the to due versus m − √ ntedffrnileuto of equation differential the in τ g 1 ρ 2 d v ilb needn fthe of independent be will n max 0 g ≫ α with aisa h hr power third the as varies α τ τ stepretg rela- percentage the as /d 1 crit 100 = m . o ieetvle of values different for 4 max 0 g τ · o ieetvalues different for v τ 10 g si eod and seconds in is crit where , ) Z · 11 = ( h eihan- zenith the ρ ρ τ = n n 3 Gτ m − P π nseconds in p 1 g 2 − Asum- . v 3 − g cos d π/ρ γ max 0 r if 0 = d 1) γ 3 max ( sa is − Z n G 1 ) is , . , ftencesi naiorpcgseisni con- in emissin gas anisotropic an point sidered. sub-solar if the nucleus at the valid only of is (2) equation that oeuedensity molecule etne l 91 n eeecsteen.I any In consider (see to therein). enough g days slow references is 7.1 rotation spin and observed of the of 1991, case, period component al. a the et has Belton and with long-axis days, the vector 3.69 around rotates momentum of long-axis angular period The a total rotation. the complex a around the nucleus in Halley’s of consider be explanation to to An is periods works. observed many two of subject the i.2 ecnaerltv nraein increase relative Percentage 2. Fig. oeayrtto o ieetvle ftencesden- nucleus the of sity. values different for rotation cometary yvlm n ic h ouemxn ais(rela- ratios H mixing volume to the tive since was and 80% comet was volume abundance by the water derived of the distance Since AU. heliocentric 0.89 The the uncertainty 50%. an by of estimated neu- carried they and the experiment spacecraft from Giotto spectrometer nucleus mass cometary the tral from km 1000 m o NH for m rse ytenme fmlclscm molecules of number the by pressed Z lsrta 000k)o (900 of distances km) (at 10,000 velocity than expansion closer gas a obtained al. et v an˙ tain ˙ ˙ .GANEETO RMACMTWITH COMET A FROM EJECTION GRAIN 3. eff g n g g si ms cm in is v v 1 = rnosye l 18)drvdawater a derived (1986) al. et Krankowsky h tt frtto fHle’ oe a been has comet Halley’s of rotation of state The ≈ g g m o niorpceiso.I hudb noted be should It emission. isotropic an for g (˙ 8( = IHRTTO EID COMET PERIOD. ROTATION HIGH A g 3 . . 25 from n %(pe ii)frteCH the for limit) (upper 7% and 2 n )wr 3 were O) H m − 2 g 0 Z 1 v v o niorpceiso,Icnob- can I emission, isotropic an For . n g g ) where , n utpyn y4 by multiplying 0 H hr ˙ ( where , 2 . %frCO for 5% 1P/HALLEY O 4 = Z n . 7 m stegsms u ex- flux mass gas the is · 10 ± g v 2 0)ms m 200) 7 0 uprlimit) (upper 10% , g ) oeue cm molecules πR 0 stequantity the is 2 Krankowsky . d − − max 2 4 1 obtain I , Putting . s − u to due 1 and , − 3 at © Copyright 2010: Instituto de Astronomía, Universidad Nacional Autónoma de México htdslydi h rudbsdosrain by observations authors. latter ground-based the the in than displayed observation HST that the be- in contrast coma higher con- and much radius nucleus tween authors the nucleus to former the owing realistic for The more values Rodionov obtained km. & their 1.4 sidered Crifo is by which reported (1997) that than radius smaller This is measurements. Telescope Space Hubble 0 ainlpro Lm ta.1998). al. rotators et fastest (Lamy the ro- period well-determined one tational a it having nuclei makes cometary hours among rotation 6 its because of comet period this Further- choosen have therein). I references more, and radio Schulz 1999, to (see Schwehm ultraviolet space & comets from the and period from ground short from studied mis- wavelengths Rosetta) observed been space of best has any target the and a of among as target is chosen a it initially Although was now (it not astrograph. sion is Carnegie comet f/7.4 this inch with Observatory 20 Lick the the at obtained mo- plates proper on its tion A. studying by C. 1948 comet by January in as discovered Wirtanen such was comet period, This rotation of short case 46P/Wirtanen. the a to with equations comet previous a the apply I reason, h oainpro f6hus(aye l 98,I 1998), al. et (Lamy factor hours a 6 obtain of period for value rotation a the considering and Wirtanen 46/P Comet for etwt rusn&Lm 20) h pointed who (2003), agree- Lamy in & is result Groussin This with comet ment case. of non-rotating larger rotation percent the 40 fast than than more the diameter a to has due Wirtanen nucleus the from ainfrtevle bandfor ro- obtained nucleus values of importance the the for show tation to is paper this r qa o10 gm kg 1000 densities nucleus to and equal dust are if m 1.06 and 0.17 between msina eotdb ul 19) ocuethat conclude I (1997), m Fulle by reported anisotropic as strong emission a considering and together, all this 326 i hscs fcmtHle) banvle of values obtain I Halley), comet of case this (in qain() n osdrn that considering and (3), equation ˙ .GANEETO RMACMTWITH COMET A FROM EJECTION GRAIN 4. . 2k aisa eie yLm ta.(98 from (1998) al. et Lamy by derived as radius km 02 g v suigancesms est f10 gm kg 1000 of density mass nucleus a Assuming oe 6/itnni ml oe f0 of comet small a is 46P/Wirtanen Comet smnindi h nrdcin ups of purpose a introduction, the in mentioned As qain()cnb erte as rewritten be can (2) Equation sn ˙ Using g agsfo 5 from ranges d O OAINPRO.COMET PERIOD. ROTATION LOW max m g = v g ρ 1 α d 5 = 9 f4.Telretpril ejected particle largest The 43. of 46P/WIRTANEN 64 C . . 0 D 0 π · m 2 · ˙ − 10 R 10 g 3 v 3 7 . 7 g o3 to − Gρ 3 n . . 1 1 − · · 10 3 τ 10 1 3 τ d π 2 π 2 8 max 8 cos cos gms m kg gms m kg o that For . 2 2 φ φ . ≪ − − . 2 d 60 . Gρ 2 max (3) − in ± MOLINA n 3 atro bu . ftertto ftecmtis comet val- the absolute obtain of to for rotation order a ues the In by if account. enlarged into 1.4 be taken about must of size maximum factor the that out fhloeti itneat distance heliocentric function a of as investigated was 46P/Wirtanen Comet Jra&Rcmn19)ada ml s1 as small as and 1995) Rickman & (Jorda AHane l 95 loapa nteliterature. the in appear also 1995) al. et (A’Hearn h Ootasn aebsdo oe eut fless of results 10 model for on than limit based pro- upper rate outgassing an gas CO gives the the (1999) essentially Enzian is rate. wa- second per- duction of per 99 number molecules than the ter Therefore, (more the perihelion. water of near mainly cent) composition was The gas emitted 1999). Schwehm & Schulz v l h xrsinfrtetemlvelocity thermal the for expression the ply faot(2 about of CO and CO of dance ob 04 lhuhvle slrea 4 as large as values (Fink although 46P/Wirtanen value of 2004) reasonable Combi rate a & production be gas to the seems for perihelion near ond d for 0 msin hn fe osdrn qain() us- (3), equation considering ing after Then, emission. h pe ii o h imtro h ole could boulder the of diameter assumed the If is for emission limit case. upper gas Halley the anisotropic the of strongly in cosine a indicated the such as of angle, power zenith third the the as varying ejection hw bv siaeavlefr˙ for value a estimate I above shown 7 s m 170 rmrdrmaueet) suigavlefor 200 com- value al. about a I et of Assuming Nolan section by measurements). next obtained radar the those from (In with results (2006) used our velocity pare al. expansion et velocity, thermal gas Nolan the same by for the expression is above which the interactions. here grain of individual use theory for I kinetic used the be tail, on must based gases gas approach cometary an the that the of but many with describing that associated for made argued adequate phenomena who is is (2002), gas model Chen fluid the a & of Williams, speed Ma, outflow by the detailed A of discussion flows. hydrodynamical produce tionably nv(97 eotta oa a rdcinrates production gas total 4 that of report (1997) onov and nuprlmto 0 s m 300 of limit upper an where g . max 8 (1 = · nodrt eemn h au for value the determine to order In ul 19)as osdrdfr4PWrae an 46P/Wirtanen for considered also (1997) Fulle d R × 10 M max ol nyb ffce yaot2.Avalue A 2%. about by affected be only would 0 and m 600 = 10 R 5 / 26 d h ae oeua egt rf Rodi- & Crifo weight. molecular water the − n 21 and 2) ewe .2ad61m. 6.1 and 0.22 between 28 max h da a constant, gas ideal the 1 aigit con h considerations the account into Taking . oeue s molecules v . oeue e eodo rae unques- greater or second per molecules th 0 ± utko ˙ know must I ± Wli 92 n then, and 1982) (Wallis 0 ,Iobtain I K, 100 . 5 0 . · 4) 10 ρ · d 5 2 10 − 10 = gms m kg oeue f1,tevleof value the 1%, of molecules 1 28 vnasmn nabun- an assuming Even . ae oeue e sec- per molecules water 3 m − r h 1 gm kg g − v ≤ 2 n oe ii of limit lower a and v g g h vlto of evolution The . o niorpcgas isotropic an for T 4 − 4 s m 240 = . 3 h temperature the U(e,e.g., (see, AU 6 banvalues obtain I m v g g v g = v g between − v ap- I , q th 1 · · 2 with πM 10 10 and RT 28 28 T , © Copyright 2010: Instituto de Astronomía, Universidad Nacional Autónoma de México esvrltn fmtr.Arpeettv au for value representative A meters. d of tens several be oa a rdcinrt f2 of rate production gas total a C e eodwe h oe a at was comet the when second per hsmdllast nepeso o h terminal the particle: spherical for a expression of nucleus. an velocity cometary to ejection the leads of model surface This sub- the by from released gases limation outflowing drag- by pro- the particles of postulates first ging which model, (1951) gas-drag Whipple a by the used posed within They grains beam. of terminal ensemble radar the entire of the of components Doppler velocities radial the the computed from not They spectra was ratio. a comet presented signal-noise observations last low radar the the because although modeled O6, was A2 C/2002 coma C/2001 and Hyakutake, grain are: IRAS-Araki-Alcock, comets a Halley, These (LINEAR), which radar. for by comets showeddetectable all al. they for et when Nolan results A2 comet, (2006), this C/2001 Besides Comet (LINEAR). al. of detec- was measurements et firm measurements radar Nolan analyzed A radar in from et published grains therein). Harmon first large references (see of and comets tion 2004, several in al. grains large of (as angle zenith 1997). the Rodionov of & Crifo cosine by ejec- the assumed the with if varies obtained be tion could value intermediate An IER hyassumed They LINEAR. ini sue a h hr oe ftecsn of be cosine would the value of our power angle) third zenith the the (as assumed emis- anisotropic is strongly sion a If emission. gas isotropic ρ distance, liocentric a gravity, of sence seHro ta.18,adrfrne therein). references and 1989, al. Also, et Harmon (see a/a bandvle o h factor they the measurements for Doppler values radar obtained the to model the where C in()b oa ta.(2006), equa- al. the et to Nolan leads by also (4) model tion the surface; the at flux d max m v v 10 = .CMAIO IHOHRCOMETS OTHER WITH COMPARISON 5. sterdu ftelretganta a elifted be can that grain largest the of radius the is oa ta.gtago tt h pcr with spectra the to fit good a get al. et Nolan aa bevtoshv niae h presence the indicated have observations Radar m (3 = 6cm 36 = ) hudbe should V 1 C / t 3 2 v C sepesdby expressed is where , gm kg a = D m v V g = 1 0 ZR/ BEVDB RADAR BY OBSERVED / a − 2 1 d 32 3 V / a max s m 2 9 0 n orpro,asmn an assuming period, hour 6 a and 4 πGRρ savlct cl atr Fitting factor. scale velocity a is ) C sterdu ftepril,and particle, the of radius the is ρ stetria eoiyi h ab- the in velocity terminal the is v d D AGS ATCE JCE RMRTTN OES327 COMETS ROTATING FROM EJECTED PARTICLES LARGEST g 0 = − ) v 1 1 g 4 s m 240 = / Z n 2 V . o h oe /01A2 C/2001 comet the for where , ρ ,wihi bandfor obtained is which m, 4 t ρ d n = = 00k m kg 1000 = C · C 8 10 v v πGR a rmti model this From . 3 28 Z − − C 1 ∼ / 1 ae molecules water stems gas mass the is v 2 , 2 2 d (1 1 ρ max R . n Uo he- of AU 1 V − t . 0 m, 600 = − = a/a 3 = 3 , V m 0 . ρ m. 2 (1 d ) (4) 1 / = − 2 scnb eni iue1 n o htvleo the of value ( that density for nucleus and high 1, Figure a in period, seen be can as .3(si h aeo oe 6/itnn.There- 46P/Wirtanen). comet the of of fore, factor case a the by in (as particles inclusion 1.43 lifted the the estimated of the then radius enlarge considered, maximum should effects is rotational period the of hour G. 6 (D. a 2009). solution 19, If unique May a they communication, obtain but personal to Schleicher, possible, data was few period too rotational had a hour that 6 concluded and or arcs 3 the CN studied the They of motion telescope. outward Hall m Lowell the 1.1 at Observatory obtained (LINEAR) A2 of C/2001 imaging Comet band narrow and photometry from discrepancy. results such of reason the know not do I ment rtclpro o ulu est f10 gm kg 1000 the than of less density pos- nucleus be the would a here it for consider because period not h critical do 3 of I period m. sible 14 than more be or eg,Meh1996). than Meech larger (e.g., hours periods 5 rotational have ro- cometary observed fastest tators the Besides, assumed. be should oee,if However, e.Tu,Itk h vrg ausfrteJuly 2008): the for al. Hal- values et comet average Magee-Sauer [402(H for the in 4 as take I (Table way I observations abundance), similar Thus, molecular a ley. total in not for proceed the is account must of composition molecules the 90% us- water As nearly 2001 (although tele- water Keck-2 July Kea. only the 10 Mauna on at on instrument scope (2008) NIRSPEC by the obtained ing al. abundances techniques et molecular other Magee-Sauer the with consider measurements I radar from Z surface 0 gm kg 500 hi qain() te aus nfc,aeobtained: are fact, Z in values, other (4), equation their oeue e eoda eicnrcdsac of distance heliocentric a at 1 second per molecules 5.5(CH oa ta.(06 suigiorpcganejec- grain by isotropic reported assuming 1 that (2006) with tion: al. agreement et in Nolan is value This ie naiorpceeto ihtidpwro the of power third with ejection anisotropic an sider neuto 2 n mtigtertto em I term, rotation the omitting and obtain (2) equation in 5 ,Ioti au f20ms m 270 of value a obtain I of K, temperature gas 250 a completely Assuming using techniques. obtained different were values both because netn ˙ inserting . 160 1 = f7 of ode,Shece,&Ger(01 presented (2001) Greer & Schleicher, Woodney, nodrt opr the compare to order In − . 6 2 · d 4 1 ) 6.3(C O), T 10 − · ,1.6(C ), max . a 10 7 U h euti ˙ is result The AU. 173 m − 5 .Tu,te bandavlefor value a obtained they Thus, K. 250 = m − 3 3 g − 4 , 0 = siae yNlne l 20)should (2006) al. et Nolan by estimated · C 3 1 = cm g R 10 v cm g . 3 m n eprtr tthe at temperature a and km, 1 = 2mfriorpceeto.I con- I If ejection. isotropic for m 32 . 2 6cm 36 = 4 H gs kg 2 2 · 2 2 H s 10 ,2HN,0.2(H 2(HCN), ), − s 6 − 1 − 3 ,1.(O,13(CH 16.6(CO), ), 1 1 n au for value a and gs kg , ti necletresult excellent an is It . a 1 m / 2 − 23 = 1 d s m m max and ρ g n . − 1 = .Frtemo- the For m. 2 − > 1 ausobtained values v 1 g 20k m kg 1200 . sisre in inserted is for 4 7 s m 270 = 2 · a CO)] 10 m v g 3 0m. 10 = Then, . gs kg 3 OH), · 10 − − − − 26 3 1 3 1 ) . © Copyright 2010: Instituto de Astronomía, Universidad Nacional Autónoma de México hsppradteasmto fa msinas emission an of assumption the cos and paper this mea- radar from derived surements. result the with consistent is ta.19)adavleo bu . mo radius of km comet 2.4 the of about radius of the value for Taking a representative. and is 1997) Harmon in al. references contin-et cited radio (see on measurements comet and uum this observations of infrared size on nucleus based the of estimations several ieto fganeeto,adasmdta the 90 that a assumed in the and ejected in were ejection, anisotropy grains grain an proposed of implied they direction comet. asymmetric, asymmetry was the the echo of that coma coma the the As in grains centimeter-sized used yrdro ac 96b amne l 19)at (1997) of al. et distance Harmon heliocentric by 1996 a March on radar by (1989). al. et Harmon o niorpceiso nteilmntdhemi- illuminated of the value a on Thus emission sphere. isotropic an for R etwt h value the with tent hs ausaetoeas sdb amne al. et of value Harmon the by insert used I also If All those AU. (1989). 1.024 are at values (1984) these al. et Feldman by measured ssonb oa ta.(06 ntereuto (4) of equation value their in a (2006) obtain al. I et Nolan by shown as hti oelkl htol %o h oa sur- must total 50 value the of the factor of to a 1% applied therefore and be only active, that is (1985) area likely al. face measure- et more Hanner radar is like the that argued they from Then, obtained ments. result the with amne l 18)etmtdvle o h maxi- the (3). for equation values radius estimated of mum (1989) term al. rotation et the Harmon by unaffected is a-rgmdlasmn niorpceeto and ejection isotropic an obtained assuming model applied gas-drag also a They measurements. polarization radar eie ulu oainpro f23dfo radar from d Then, 2–3 of measurements. period rotation nucleus a derived fteCmtC20 2(i or eid obtain I period) hours value (six rotation fast A2 a the C/2001 and Comet angle the zenith of solar the of cosine 328 msin rmcmtIAadsoe httero- Feldman, the be that must ultraviolet showed period and rotator. the tation IAA observed slow comet from (1984) very emissions Millis a & is A’Hearn, IRAS-Araki-Alcock IAA) period. (comet rotation different very uhsalrta htteoerpre yNolan by reported using (2006) one the al. et that than smaller much m n h a asls aeo 6 of rate mass-loss gas the and km, 5 = 3 nteohrhn,Ihv sdeuto 2 of (2) equation used have I hand, other the On oe yktk C19 2 a loobserved also was B2) (C/1996 Hyakutake Comet h te w oesmnindaoehv a have above mentioned comets two other The ( Z ρ n obtained I and ) n d = max a m ρ a d 6 = m 3 = fteeetdprilso mfrom cm 3 of particles ejected the of 10 = . × ,wihi ag au but value large a is which m, 6 C a a v m 10 3 m g ≥ 6cm 36 = 0 = − eff gm kg a d a 6 = 4 7h amne l (1989) al. et Harmon h. 27 m max m = ≃ ,wihi inconsistent is which m, . 0 = 6m hc sinconsis- is which m, 06 ◦ 6 = g wd oe hr are There cone. -wide × − 5 = U hyobserved They AU. 1 n h au of value the and 3 . 1 C 3mi on,which found, is m 03 10 , / × 2 v v − × s m g cm 8 = 10 4 10 8 s m 280 = − eotdby reported m − 4 − 1 3 obtained m . · .Ihave I m. 1 10 / 2 5 s m s g d max − − − MOLINA 1 1 1 , dp au f2k o h aiso h ulu of nucleus the of radius the for km 2 of value a adopt I rmeuto (2) equation from R v ffcierdu f2 of radius effective tte82mVr ag eecp T n deter- and 12 UT1 of Telescope period Large rotation Very a mined m 8.2 the at C pc eecp bandama ffcierdu of radius effective mean 1 a obtained Telescope Space hi qain() then (4), equation their an cos of grains as assumption the emission our maintained that have stronger I 1997) a asymmetry. with although al. asymmetrically, ejected et are Harmon (as assumed tain eido 6 of rotational Hyakutake’s period defini- Comet a of presented determination (1998) tive al. from et from Telescope. h Schleicher Space However, 12.5 period Hubble of the min period with rotation made 14 a observations derived h (1996) Larson 6 al. and et a photometry obtained photoelectric Schleicher (1996) narrow-band B2). were al. periods (C/1996 et possible Hyakutake two to first, At attributed assumed. is tion ihCDiae.Te,adatraotn this adopting factor after rotation and the Then, value, last images. CCD with ulrnewt oaco w 2K two of mosaic a with vi- range the sual in 67P/Churyumov-Gerasimenko broad-band performed of (2008) imaging al. et Tubiana (2005). e sHro ta.(1997), al. et Harmon as ues 0 gm kg 500 f1.–27hus hyetmtdancerden- period m nuclear kg a a 370 with estimated of They axis it sity that principal hours. found 12.4–12.7 a they of around an and with rotating km, this body 1.72 is irregular con- of deter- of an They nucleus (2007) radius is effective comet the curves. the al. light of that visual et cluded shape several Lamy and from ra- comet size a km. indicate the 2 studies mined about precise more of radius km, dius a 3 favored about estimations of first Although model. eaiek nlt 04 hti h ti impor- is it Churyumov- why the comet is consider That to of tant 2014. rendezvous surface late will the in Gerasimenko spacecraft upon land Rosetta and The mission. CHURYUMOV-GERASIMENKO 67P/ COMET 6. al. et Harmon by results the (1997). with consistent not is n elye l 20)uigteMliadImag- Multiband the 24 using (MIPS) (2009) Photometry ing al. et Kelley and g . v 93 2 = 9 s m 290 = hscmti h urn agtfrteRosetta the for target current the is comet This 0gvnb oa la.(06 sisre in inserted is (2006) al. el Nolan by given 40 = − d max 2 . km, 4 . 3k n 2 and km 03 − 1 = 3 . 23 eerpre yDvdsn&Gutiérrez & Davidsson by reported were − ρ . ± .O h te ad ftevalue the if hand, other the On m. 7 n 1 3 n ˙ and , ( 0 00k m kg 1000 = Z − . 3hcmiigpooercdata photometric combining h 03 3 ,frcmaio,adte ob- I then and comparison, for ), . d 38 . max 04 n este ewe 0 and 100 between densities and d max ± m ± a 0 g 0 0 = . m . 4k.Lm ta.(2008) al. et Lamy km. 04 5 = bandwt h present the with obtained 1k,rsetvl.Here, respectively. km, 11 µ er5mi on,which found, is m 5 near hne fteSpitzer the of channel m . . 5mi stoi ejec- isotropic if m 15 7407 − · α 3 10 n h aeval- same the and , ρ d s3.Ihv also have I 39. is 3 ± × gs kg 0 gm kg 300 = 0 KMTCCDs MIT 4K . 01hadan and h 0011 − 1 obtain I , − 3 , © Copyright 2010: Instituto de Astronomía, Universidad Nacional Autónoma de México e eesprscn o etmtrprils Here particles. assume centimeter for I second a per to meters particles submicrometer few for second per meters of fds atce sfntoso iea perihelion at size of functions as ( particles Agar- dust AU. of 1.34 of speeds terminal distance Müller, Grün obtained corre- wal, & (2007) heliocentric it a paper that to of perihelion sponds (4) near equation curve to value according fitted and, maximum mentioned the above is the which of second, per molecules suetema au fteitra etoe by for Gutiérrez mentioned (2005) interval & the Davidsson comparison. of value Nolan for mean by therein) the used assume references I that and as (2006, order al. same et kinetic the the using of K and 250 theory of temperature a to sponding uvs osdragspouto aeo 0 of rate production gas a consider and I apparition, analytical curves. 1996 fitted the least-squares and approximate obtained 1982 the measurements both rate production during out carried et (2007) Lamy al. 67P/Churyumov-Gerasimenko. comet the tttsa sflwyt siaetemxmmsize maximum the estimate to way useful an stitutes erdt atclrcmtt-u itne because m distance, comet-to-Sun particular a to ferred etiua oc u ote1.47hrtto pe- The rotation h of value considered. 12.7407 the is the increases to angle riod due zenith force the centrifugal of cosine the ρ ρ d opitotta h ausotie for obtained values like the would that I out point comparison. to 2006, for therein) al. references et (Nolan and measurements radar from tained nTbe1our 1 Table in ˙ ≃ d d max g and , = v 1 h tnadmdlo lntr ugsigcon- outgassing planetary of model standard The g . 9A) hi ausg rmsvrlhundreds several from go values Their AU). 29 ρ 0 = eed on depends n nteasneo ulse nomto for information published of absence the in τ . v ,i neeto stetidpwrof power third the as ejection an if m, 3 g 12 = 7 s m 270 = d . oain(e text). (see rotation a d .CONCLUSIONS 7. max 47h hn banavleof value a obtain I Then, h. 7407 h atclm hw h ecnaerltv nraein increase relative percentage the shows column last The oa ta.(2006). al. et Nolan yktk 10 Hyakutake A 0.06 IAA /01A 20 A2 C/2001 67P/C-G Wirtanen Halley ~ r c oe aa esrmnsTi work This measurements Radar Comet AUSOF VALUES . eut oehrwt hs ob- those with together results AGS ATCE JCE RMRTTN OES329 COMETS ROTATING FROM EJECTED PARTICLES LARGEST − 1 hc stevlecorre- value the is which , d max as d d ≥ ρ max b max α n apel amn hpr (1989). Shapiro & Harmon, Campbell, IHTOEFO HSWORK THIS FROM THOSE WITH 0 e . 0 gm kg 300 = 28 = amne l (1989). al. et Harmon 04 (m) d c RMRDRMAUEET COMPARED MEASUREMENTS RADAR FROM e b d max . .Ishow I 8. . .914 .710 0.89 0.17–1.06 1.59–1.47 7 r r re- are ≃ ≃ ≃ c · (AU) 10 1 0.005 1 1.7 1 − . 43.6 14 AL 1 TABLE 28 3 , naiorp oadteSna h oieo the of cosine the as Sun the considering toward assumption anisotropy isotropic moderate assuming an more of about A instead of area, area ejection. total active the an equivalent of by is 12% emission This an (1997). assuming Fulle an- to by zenith the proposed of cosine as the gle) of power third the (as Sun einrd nestecmti oaigwt oga long with rotating is cannot ( comet ejection, period the dust unless cometary ignored, the be of in Therefore, terms equation rotation h. the introduce rotation 6 which around to forces, inertial periods due the with percent comets 40 fast than for more by increases etteetmtdvle of af- values considerably estimated can (3) the equation fect of quantities the in uncertainties The 67P/Churyumov-Gerasimenko. hs eotdb oa ta.(06 n refer- and val- estimated (2006, than have of I smaller al. ues Additionally, are et therein). results Nolan ences by our reported general, those In Halley, IRAS-Araki- obtained Alcock. and comets: those (LINEAR) four A2 with C/2001 for Hyakutake, results measurements radar our from compared have I d and cleus rae u ortto ftences Thus, nucleus. the of rotation to due creased lyntwl nw.Tedsrpnybtenthe between discrepancy The of values known. well not ally eednl fteeuncertainties, these of In- dependently of Churyumov-Gerasimenko. comet velocity from grains the the measures Dust and experiment Analyser Accumulator) Impact (Grain GIADA resolved the be when will models hydrodynamic the from those ˙ quantity the hand, other the on and, d max max . .429 43 1.34 1.1 0.3 3.2 aecniee togaiorp oadthe toward anisotropy strong a considered have I R (m) fteds itdfo h ufc facomet. a of surface the from lifted dust the of R d utb elkon h aiso h nu- the of radius The known. well be must max ≥ per stetidpwri qain(3) equation in power third the as appears v 5hours, 15 g r o oe 6/itnnadfrcomet for and 46P/Wirtanen comet for ≃ ≃ ≃ c bandb sn iei hoyand theory kinetic using by obtained c (AU) d 1 amne l (1997). al. et Harmon 1 39 1 a max . 643 16 u ocometary to due α ≤ for 5 ≃ ≃ α 0 0 ρ d n max 10 = any ˙ Mainly, . d max 3 m gm kg g ilb in- be will v g − susu- is 3 m ). d max g v g © Copyright 2010: Instituto de Astronomía, Universidad Nacional Autónoma de México eihagewudla ovle of values to lead would angle zenith 330 .Mln:Dpraet eFıiaAlcd,Uiesddd rnd,Facultad Granada, de Universidad F´ısica Aplicada, de Departamento Molina: A. 1921 278, Science, 1997, al. et K., J. Harmon, Campbell, & J., S. Ostro, C., M. Shapiro, Nolan, A., K., A. J. Hine, Harmon, B., D. Cambpell, K., J. Harmon, S., McCorckle, R., Knacke, K., 879 D. 412, Aitken, A&A, S., 2003, M. P. Hanner, Lamy, 327 & 154, 1237 O., AJ, 325, Groussin, 1968, A&A, F. 1997, R. M. 52, Probstein, Fulle, Sci., & L., Space M. Planet. Finson, 2004, R. 1984, M. L. Combi, R. & Millis, U., & Fink, F., M. 131 A’Hearn, 90, D., Rev., P. Sci. Feldman, Space 1999, A. Enzian, 176, 319 Icarus, 127, 2005, Icarus, Gutiérrez, J. P. 1997, & R., V. J. A. 1989, B. Rodionov, Davidsson, I. & I. F., Shapiro, J. Crifo, & 1 40, K., Icarus, J. & 1979, Harmon, S. H., B., Soter, W. & D. L., Julian, Campbell, P. Lamy, A., A., E. J. Burns, B. Mueller, S., J. M. 499 2007, 116, Belton, AJ, 317 1998, 384, M. E. A&A, Beech, 2002, G¨run, B. J., P. D. Babadzhanov, Osip, G., & D. Schleicher, L., R. M., Millis, M., A’Hearn, Müller, J., Agarwal, sup- was work ESP2006-02934, AYA2009-08190. This im- AY2007-6370, and contracts an paper. by in this ported resulted of which version referee proved anonymous an of the in studied be will lifted, is future. the grain the of the of longitude where and place orbit obliquity anomaly, the he- true of the comet, eccentricity on dependence distance, The liocentric here. estimated those of .B 04 nCmt I d .C etu .U. H. Ari- Festou, of C. University M. (Tucson: 265 Weaver ed. Press), A. zona II, H. Comets & in Keller, 2004, 1071 B. 338, D. ApJ, 1989, G. B. Marsden, & 97 I., 62, I. Icarus, 1985, T. A. Tokunaga, & F., P. Roche, 573 799 282, AJ, 453 1094 338, ApJ, 183 93, Icarus, 1991, J. A. Anderson, 223 118, Icarus, 1995, V. P. Birch, & 79 128, Rev., Sci. Space 0 80,Gaaa pi ([email protected]). Spain Andaluc´ıa, Astrof´ısica Granada, de de Instituto 18008, and 50, Spain Granada, 18071, s/n, Ochoa h uhrakolde h epu comments helpful the acknowledges author The REFERENCES d max uthalf just MOLINA ec,K .1996, J. K. Meech, Dello A., M. Disanti, J., M. Mumma, 337, K., MNRAS, Magee-Sauer, 2002, W. Chen, & P., I. Williams, 1996, Y., M. Ma, Niedner, & 433 C., 128, Randall, Rev., J., Brandt, Sci. S., Space Larson, 2007, al. et P., A’Hearn, Lamy, & A., H. Kelley, Weaver, L., L., 1997, Jorda, Jorda, I., Toth, U. P., O., Lamy, Groussin, H. I., Toth, Keller, L., & P. Lamy, J., Knollenberg, 326 E., 321, Nature, 1986, Kuhrt, al. et D., Krankowsky, Boehnhardt, C., Tubiana, H., 43, D. Wooden, Sci., S., Space M. Planet. Kelley, 1995, H. Rickman, L117 & 572, ApJ, L., 2002, Jorda, 707 al. 14, et J., M., AIAA Ishiguro, 1976, B. C. Henderson, clihr .G,Mli,R . sp .J,&Lederer, & J., D. Osip, L., R. Millis, G., Icarus, D. 2007, Schleicher, V. M. Sykes, & S., M. Kelley, T., W. Reach, Aceituno, R., L. Bellot-Rubio, Campbell, V., P. E., Sada, Howell, L., J. K., Ortiz, J. Harmon, C., M. Jiménez-Fernández, J. Nolan, & F. F., Moreno., A., Molina, ode,L . clihr .G,&Ger .2001, R. Greer, & G., D. Schleicher, 464 M., 113, L. ApJ, Woodney, 1951, L. F. (Tuc-Whipple, Wilkening L. L. ed. Comets, in 1982, K., M. Wallis, H. Boehnhardt, & M., Drahus, L., F. Barrera, Low, C., & Tubiana, M., D. Hunten, A., 321 L. 90, Lebofsky, Rev., V., Sci. Space M. 1999, Sykes, G. Schwehm, & R., Schulz, us,N,Gb,E,Bnv .P,&Vlauv,G L. 347 G. 194, Villanueva, & Icarus, P., B. 2008, Bonev, E., Gibb, N., Russo, 1081 1088 28, BAAS, 25 335, A&A, 777 1998, 489, M. A&A, 2008, A. J. Stansberry, & S., H. 665 45, Sci., Space Planet. 137, AJ, 2009, E. D. Harker, 4633 & E., C. Woodward, H., 575 .M 96 AS 8 1089 28, BAAS, 1996, M. S. 298 191, 921 2000, 405, U. Thiele, Nature, & Gutiérrez, J., J., P. Aceituno, 432 J., F. 181, Icarus, 2006, J.-L. Margot, & B., D. 521 102, Planets, & Moon Earth, 2008, ~meech/papers/acm96.ps AS 3 1121 33, BAAS, 357 Press), Arizona Univ. son: 377 490, A&A, 2008, 1115 232, Science, 1986, 98 crs 3,233 131, Icarus, 1998, . SC aioBj eHuétor de Bajo Camino CSIC, eCeca,AeiaSevero Avenida Ciencias, de http://www.ifa.hawaii.edu/