19. New Evidence for Interplanetary Boulders?

ZDENEK SEKANINA Smithsonian Astrophysical Observatory Cambridge, Massachusetts

The present paper critically discusses the method of detection, the magnitude and the rate of occurrence of sudden disturbances in the motions of some short-period comets. The disturbances have recently been suggested as potential indicators of collisions be tween the comets and interplanetary boulders—minor objects whose existence was pre dicted by M. Harwit in 1967. The character of explosive phenomena, caused by an impact of such a boulder on a comet's nuclear surface, depends significantly on the surface texture of the target body. To advance our understanding of the impact mecha nism, a method is suggested which would supply a good deal of the missing information about the structure and optical properties of nuclear surfaces from precise photometric observations of cometary nuclei at large solar distances.

THE IMPACT HYPOTHESIS suggests that the observed disturbances can be generated by collisions of the boulders with low ECENT EXTENSIVE DYNAMICAL STUDIES of a density comet nuclei, if the comet-to-boulder R number of short-period comets by Marsden mass ratio is about 106. As a result of such an (1969, 1970), by Yeomans (1972), and by impact the comet would lose as much as 10 Marsden and Sekanina (1971) resulted in a percent of its mass. Repeated impacts can easily discovery of easily detectable disturbances in the result in a splitting of the nucleus, or its complete motions of the comets we call 'erratic': P/Biela, disintegration in a relatively short period of time. P/Brorsen, P/Giacobini-Zinner, P/Perrine-Mrkos, With Harwit's space mass density of boulders the P/Schaumasse, possibly also P/Forbes and proposed hypothesis predicts an average rate of P/Honda-Mrkos-Pajdu§akova. The disturbances some five impacts per 100 revolutions for a comet differ from the regular nongravitational effects 1 km in diameter. To produce an impulse of 1 m/s and seem to take form of sudden impulses of the average boulder should be 108 g in mass, or about 1 m/s, perhaps preferably at larger solar 3 to 10 m in diameter, depending on its mass distances. Their interpretations in terms of density; the comet would be 1014 g in mass, and processes stimulated by internal cometary sources 0.2 g/cm3 in density. Such a nucleus can be com of energy have been discarded on various grounds. posed of snows mixed with highly porous dust In contrast, hypervelocity impacts of small objects grains. Impacts of the same boulders would not seem to be consistent with empirical evidence. measurably affect motions of the comets with The existence of interplanetary boulders has been heavy compact cores like P/Encke. predicted by Harwit (1967), of spatial density as These have been some of the main conclusions high as 10~18 g/cm3. Application of the mechanism formulated by Marsden and Sekanina (1971) of crater formation at hypervelocity impacts from their extensive study of the motions of the 199

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'erratic' comets. In the present paper we discuss hand, from equation (2), numerical values of some of the fundamental constants of the problem in greater detail. We A (j £ dtj = -AJdffi-1'* (6) will refer to the above paper as to Paper 1. so that (A/x) = - (2 r)-U /fc/ a-3/2 (7) RADIAL AND TRANSVERSE COMPONENTS r 5 1 2 OF THE NONGRAVITATIONAL EFFECTS It is convenient to convert A/x of equation (4) IN THE DAILY MEAN MOTION to AJT2 and (A/x), of equation (7) to ATU the effective rates of delay (A7\>0) or advance An acceleration, the radial component of which (A!Ti<0) in the perihelion passage per revolution is Z\ (positive outward from the Sun) and trans due to, respectively, the transverse and radial verse component Zi (perpendicular to Z\ in the components of the acceleration of equation (2). orbit plane, positive in the direction of motion), Expressing AT, in days per revolution per revolu applied at a solar distance r generates an in tion we find stantaneous rate of change in the daily mean AT = 58A I fi3i2 (8) motion 1 1 i 7 5 2 A7 2=1096il2/lo / _3esinj, 3(l-e»)^v m The integrals h and 7 are of the same order of a(l—e2)1'2 r 2 magnitude. For a typical short-period comet ratio where v is the true anomaly, a and e are the semi- AT2/ATi is about 10, even when the radial com major axis and eccentricity of the orbit. We ponent is almost an order of magnitude larger accept that the nongravitational acceleration than the transverse component. varies with the solar distance r, DYNAMICAL DISTURBANCES Zi = A{f(r) /(1AU)=1 (2) The computer programs used by the authors, mentioned earlier for calculating the orbital • = 1,2,3 elements and nongravitational parameters from

where At are the acceleration components at 1 AU comet observations, are designed to search for in units of the solar gravitational acceleration at smoothly, continuously varying deviations from 1 AU. Upon integrating over a revolution period, the gravitational law. If a disturbance is detected and writing by the program in a comet's motion, contradicting the above assumption, the integration procedure does not necessarily fail. What does happen Ii= (' f(r)r*dv (3) depends much on the number of the comet's •'-*• apparitions linked. A solution may be found, we obtain the change in the daily mean motion which gives quite an acceptable distribution per revolution: of residuals, but the nongravitational parameters A/x = -ZAzkharU2 (4) are inconsistent with those computed from the comet's adjacent apparitions not including the There is no contribution from the periodic varia dynamical anomaly. Figure 1 shows an example tions in the radial component of the acceleration. of such a forced solution. The regular nongravita However, there is a secular effect from Z\ because tional effects shape the continuous background of its contribution to the "effective" gravitational SABEFZ. Between tB and tB a disturbance BCTDE constant. On the one hand we have is superposed on the quiescent phase BE. If an attempt is made to link apparitions between t^ A(/ ~idt) = 2^_1/2Afc = 2irp-1/2a3/i!(A/x), (5) and tz, and the nongravitational effects are allowed to vary exponentially with time, where p = a(l — e2) and (A/x), is the change, per A~exv(-Bt) (9) revolution, in the daily mean motion due to the change in the Gaussian constant k. On the other the empirical fit yields the curve A'CDFZ' such

Jupiter, along the two orbits should be taken into g ' DYNAMICAL ANOMALY account in equation (10). In practice, the per P H| S (DISTURBANCE) turbations are very small unless the comet makes a close approach to Jupiter during the critical « A' HH EMPIRICAL FIT period of time. Unfortunately, these encounters to* Vv\ (FORCED SOLUTION) are fairly frequent and often limit our results in 5J CONTINUOUS ^^Jy///\ / g BACKGROUND W&gHC^&P / Z accuracy. P (QUIESCENT [&»«/ ^^&fe<^ *^rrr777Zffl>, 5 PHASE) f||g87 ^-^ZZZ^Z^ , SUDDEN IMPULSES We do not—and practically cannot—have direct 8 ! ! ! 1 ! _J I I i i evidence of the character of the dynamical dis •s 'A 'a 'E 'z turbances affecting the 'erratic' comets. We guess TIME that they take form of discrete discontinuities FIGURE 1.—Sudden dynamical anomaly, or disturbance, (see Paper 1), because so far it has always been interferes with continuous, quiescent-phase nongravitational effects in a comet's motion. The disturbance found that observations from only the minimum can be detected by means of a 'forced' solution: the number of apparitions, necessary for the least- cross-shaded areas compensate the one-way shaded squares procedure to work, can satisfactorily be areas. fitted whenever a disturbance is involved. Outside that span the forced solution completely fails. that Typically, there are long intervals of quiescent phase before such a disturbance (P/Giacobini- area(AA'CBA) + area(DFED) Zinner), or after it (P/Biela), or both before and after (P/Schaumasse). = area(CTDC) + area(FZZ'F) (10) If we take the disturbance in the form of a The coefficient B of the secular variations— sudden impulse (tB-^tE in fig. 1) and are able to negative in the quiescent phase in figure 1— estimate the quiescent-phase background, we can suddenly becomes positive due to the disturbance. determine the impulsive increment in the orbital Thus, figure 1 is a very obvious demonstration velocity, AVV, associated with the discontinuity, that whenever a disturbance is involved, B comes from the difference between the disturbed and out fictitious. It is easy to understand that the quiescent nongravitational parameters. The im sign and magnitude of B depends not only on the pulse corresponds to the area BCTDEB in disturbance-to-background ratio, but also on the figure 1. selected span of time. For example, B would be The component of the nongravitational accelera strongly negative, if we tried to link apparitions tion along the orbital velocity vector, Zv, is given by between ts and tE. Moreover, the forces generating the quiescent-phase and disturbance effects may Z^iZJTx+ZiVdV-i (11) work in opposite directions, and we may fail to find a satisfactory solution of the form of equation where Z\, Z2 are identical with those of equation (9) and must accept another empirical form. If (2), V is the orbital velocity, Vx and F2 its radial only three apparitions are linked it is always and transverse components respectively. In possible to find a satisfactory solution with tegrating over the revolution period, we have constant A. Figure 1 corresponding to this case from equation (11) would have a staircase shape, and the general ip ir (2 ll_1/2 rule, equation (10), would again be in power. In i>= J Zvdt=KA2J f(r)r<---\ dv (12) practice, however, the validity of equation (10) is only approximate. The reason comes from the where v is the true anomaly; K = 29.8X103, if yp is difference between the real orbit (with the un to be given in meters per second. The expression, known profile of the disturbance) and the fictitious equation (12), is independent of Zi for the reasons orbit found by the forced continuous solution. The discussed above.

differential perturbations, predominantly due to Let V'quiesc and ^distrb be yp for the quiescent phase

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and the disturbed period, respectively. The comet's motion: impulsive increment in the orbital velocity associated with the disturbance is then w»=(ty72)1/2 = KO-1/2 1+U-e2)1'2- -(1-e) 1/2 IT

AVV = Odistrb — tqmesjv 1/2 + (effect of differential perturbations) (13) •K{(2e)1'2(l+e)-1'2} (15) where v is the number of revolutions covered by Relating the direction of the impulsive velocity the forced fit. The positive AV means the comet is V to that of the relative collision velocity we now effectively decelerated, the negative means accel can find AV averaged over a revolution period: erated. If Ai has been allowed to be subject to secular variations, its effective value during the AF=AF„ period of time covered by the forced fit must be used in equation (12). l-(l-e' .2^ 1/2 The total impulsive velocity, AV, associated X with the disturbance cannot be derived from its 2- - (l-e)"2Z{(2e)1/2(l-|-e)-1/2} component along the orbital velocity vector, because the angle between the impulse and the orbit tangent is not known. Assuming that the (16) discontinuity in motion is due to a collision with The ratio AF/AF„ is listed in table 1 as a func a small object moving in a circular orbit around tion of the eccentricity. the Sun in the comet's orbital plane, we have derived in Paper 1 the following formula for the mean quadratic relative velocity between the two IMPULSIVE VELOCITIES ASSOCIATED colliding bodies, averaged by integration over a WITH THE DISTURBANCES OBSERVED IN revolution period: MOTIONS OF THE 'ERRATIC COMETS w= (w2) 1/2 The method described in the preceding section 1/2 can give a reasonable estimate of the impulsive = Ka-U2 2- - (l-e)1'2X{(2e)1/2(l-|-e)-1/2} velocity, particularly if there is no close approach IT to Jupiter involved. Table 2 lists AVV and AV (14) obtained in this way for the 'erratic' comets and compares them with the values derived by where K{m\ is the complete elliptic integral of Marsden for P/Schaumasse, P/Perrine-Mrkos the first kind with modulus m. Similarly we can and P/Biela, and by Yeomans for P/Giacobini- calculate the mean quadratic component of the Zinner, who have used a different approach. relative collision velocity in the direction of the These authors have computed what we call AVV from the difference between the observed time of TABLE 1.—Ratio AF/AV„ VS Eccentricity, e perihelion passage and that extrapolated from a quiescent phase. e AV/AVV The fundamental difference between the two methods is that the one we suggest tends to smooth the disturbance out and represents there 0.1 2.24 0.2 2.22 fore a lower limit of the most probable impulsive 0.3 2.19 velocity. On the other hand, the method applied 0.4 2.15 by Marsden and by Yeomans extrapolates, and 0.5 2.10 therefore tends to exaggerate the effect of the 0.6 2.04 disturbance. Indeed, table 2 clearly shows that 0.7 1.96 0.8 1.87 our values of the impulsive velocity are system 0.9 1.75 atically smaller. In any case, the table suggests that 1 m/s, which was accepted in Paper 1 for the

TABLE 2.—'Erratic' Comets: Impulsive Velocities Associated With Dynamical Disturbances

Comet's mean motion A7„ effectively0

Comet" Disturbance AVV AV derived between— from eq. from eq. otherwise11 (13) (m/s) (16) (m/s) (m/s) In quiescent By phase disturbance

P/Biela 1772/1805 0.8 1.5 A D d 1842/43 0.1 0.2 "1 M2 A D P/Brorsen 11846/73 (0.3) (0.5) A ? 1873/79 1.6 3.0 A D P/Schaumasse 1927/43 0.2 0.5 1.9 Mi A A

P/Perrine-Mrkos 1955/68 1.5 3.0 3.5 Ux A A P/Giacobini-Zinner 1959/65 0.6 1.1 1.4 Y D D

a Data on P/Honda-Mrkos-Pajdulakova and P/Forbes are inconclusive. b Afi = Marsden (1970); M2 = Marsden (1971) [also in Marsden, Sekanina (1971)]; F = Yeomans (1971). " A = accelerated; D = decelerated. d Satellite nucleus at splitting. e Velocity of separation essentially in sunward direction. £ Impulsive velocity rather uncertain.

typical impulsive velocity, seems indeed to be a 91 should depend linearly on I in figure 2. However, representative value for the 'erratic' comets. since we deal with observed lengths of trajectories that are very short compared to the rate of pre sumed impacts, statistical dispersion is significant RATE OF DISTURBANCES and the observed disturbance rates for individual The rate of dynamical disturbances is another comets differ widely from each other. We identify critical quantity for the impact hypothesis. only the best observed 'erratic' comets. It is Table 3 lists the number of observed disturbances, therefore logical that the upper left corner of 91, for the 'erratic' comets; the length, I, of their figure 2, the area of the highest disturbance rates, trajectories swept out between the first and last is populated most, whereas the strongest bias observed apparitions of each of the comets; and takes place along 31 = 0. Observational selection is the disturbance rate, T, denned as the number of also responsible for a factor of three between the disturbances per 100 AU: mean least-square rate 91// (dot-and-dashed line) and the differential rate d'Sl/dl (dashed line). It is T= 10091// (17) the latter that should more properly match the For the known 'erratic' comets the average unbiased disturbance rate. Indeed, the rate pre observed rate is about one disturbance per 100 AU dicted from the impact hypothesis (solid line) (see column 6 of table 3), a value about four agrees with the slope dyi/dl. times as high as the one predicted from the impact For the above reasons it is convenient to write hypothesis in Paper 1. However, it is easy to show the number of the 'erratic' comets with dis that the data of table 3 are strongly affected by turbance rates between T and T+dr in the form observational selection. The number of boulder impacts on a cometary dN.(T)=NMT) dr, r*(r) dr=i (18) nucleus is statistically proportional to the volume •'o of space swept out by the comet. The volume is given as a product of the comet's collisional cross- and to see how the total number, Nc, of the 'erratic' section and the length of its trajectory. Ideally, comets among known short-period comets and

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TABLE 3.—'Erratic' Comets: Observed Rates of Dynamical Disturbances

First/last Number of Length of Number of Disturbance Comet apparition revolutions swept-out detected rate covered trajectory disturbances (per 100 AU) (AU)

P/Biela 1772/1852 12 226 2 0.88 P/Brorsen 1846/79 6 95 2 2.10 P/Schaumasse 1911/60 6 131 1 0.76 P/Perrine-Mrkos 1896/1968 11 210 1 0.48 P/Giacobini-Zinner 1900/66 10 187 1 0.53 P/Honda-Mrkos-Pajdusdkovd 1948/69 4 61 1? '1.23 P/Forbes 1929/61 5 100 1? "0.75

" The disturbance rate of this comet is weighted by a factor of % to allow for the uncertainty as to whether the dis turbance indeed occurred.

velocity distribution function, with Ym being the most frequent r, 1 2 2 3 2 4>(r) dr=47r- / r rm- exP[- (r/rm) ] dv (21) we find

2 Xexp[-(r/rm) ]+erfc(r/rm)} (22) 100 200 300 400 where TRAJECTORY SWEPT, jl(AU ) FIGURE 2.—Observed dynamical disturbances. Solid cir erfc(z)=l-27r-1/2 f exp(-a;2) dx (23) cles: definite 'erratic' comets. Open circles: probable 'erratic' comets. Solid line: disturbance rate predicted from the impact hypothesis (see Paper 1). Dot-and- The characteristic rate is dashed line: least-square solution to the mean ob (24) served disturbance rate, 91/£ Dashed line: least- r.=i.087r. square solution to the mean-differential disturbance The fit to the empirical data is, however, un rate, d3l/d(. satisfactory. Alternatively, we can assume that (T) has the characteristic disturbance rate, Tc, given by the form of a two-dimensional Maxwellian velocity distribution. This assumption seems to be more C [ (T)dT= r(T)dV (19) plausible in view of presumably low obliquities between orbital planes of the short-period comets depend on the choice of the distribution function and interplanetary boulders. Then <£(r). The number of comets with disturbance <*>(r) dr=rr -2 ex [- r2/2r 2] dv (25) rates higher than r, m P m N+ (T)=NC exp[- F/2IV] (26) N+(T)=N r(y)dy (20) C and 1 (27) proves the most useful quantity for practical re=r„.(log.4) '» trials, because our statistics of disturbances is There is an improvement upon equation (22) in relatively complete for very high values of T. matching the data of table 3, but the fit is still Approximating (T) first by the Maxwellian poor for iVc+<3.

Let us next accept an exponentially decreasing PHASE EFFECT AND ALBEDO OF distribution COMETARY NUCLEI 1 <*>(r) dr=i3- exp[-r/^]dr (28) The dimensions and mass of an average 'erratic' comet are important for the impact hypothesis so that for two reasons: (29) N+(T)=Ncexp£~r/fl (1) The impact rate is proportional to the and collisional cross-section of the comet's nucleus. rc = /3-loge2 (30) (2) If the impulsive velocity is known, the + mass of the nucleus determines the magnitude of The fit is now good except for Nc = 1. Finally, if we take the impulse exerted by a boulder impact, which 1 2 2 equals the momentum gained by the material 0(r) dr= (2f)~ r-" exp[-r" /f] dr (31) expelled from the nucleus. The momentum, in 1 turn, determines the mass of the boulder. iV+(r)=iVcexp[-r /Vf] (32) 2 An upper limit for a cometary radius can be rc=(Moge2) (33) derived from dynamical considerations of a we get a very good fit to all the seven data. cometary splitting. For P/Biela (classed as an Unfortunately, the testing data are too scanty 'erratic' comet) the requirement that the separa to resolve the ambiguity in <£(r) unequivocally, tion velocity be higher than the velocity of escape and the best fit does not necessarily mean the best from the surface of the nucleus of radius R and solution. Indeed, a fit at least as good as that by mean density p gives a condition equation (32) is obtained from fip1'2<1.3km(gcm-3)1/2 (35) 1 4 (34) ivc+(r)=2.7r- - For p~0.2 g cm-3 we find R<3 km. If we require which gives no prediction for Nc whatsoever. that the separation velocity exceeds the escape Table 4 lists the characteristic rate Tc and the velocity from the sphere of action of the nucleus extrapolated Nc for the four applied <£(r). The we must use another formula (Sekanina, 1968) dependence of the two parameters on the char and get for P/Biela acter of 0(r) is significant. The mean rate of Rpli3<12km(gcmr3yi3 (36) disturbances computed in Paper 1 from equations of the impact hypothesis, certain physical assump or R<20 km for a low-density snowball. These tions and dynamical evidence comes out 0.25 per estimates are too crude to be used for the cal 100 AU (solid line in fig. 3 of paper 1), which is culation of an 'erratic' comet's mass. in order-of-magnitude agreement with the data The photometry of faint cometary images at of table 4. large solar distances appears to be more fruitful

TABLE 4.—'Erratic' Comets: Total Number and Characteristic Disturbance Rate as a Function of the Disturbance Frequency Distribution

Characteristic disturbance Total of expected Distribution 4>{r) assumed rate re 'erratic' comets Nc Data fit (per 100 AU)

Three dimensional Maxwellian 0.77 8 poor + Two dimensional Maxwellian 0.70 10 good for Nc >2 + Damped exponential in r 0.50 15 good for Nc >1 Damped exponential in \/r 0.06 50 good

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for analyzing the dimensions of cometary nuclei. cometary radii, and thus bring down the un However, the practical solution of the problem is certainty in the mass of individual comets by at very delicate not only because of the obvious least one order of magnitude. observational difficulties (very faint images; coma Unfortunately, nuclear magnitudes of the contamination must be reduced as much as quality required by the suggested phase-dis possible), but also because of an ambiguity in crimination method are not available. To illustrate interpretation. the difficulties encountered in an attempt to Disregarding the sources of periodic or quasi- detect phase variations in published sets of periodic variations in brightness (such as the magnitudes we have compiled table 5 from the shape of the nucleus), we shall deal with the homogeneous series of photographic magnitudes geometrical albedo and phase law, the two of comets at large solar distances, obtained by quantities that are determined by the optical Roemer and her collaborators (Roemer, 1965, properties of the nuclear surface and enter the 1967, 1968; Roemer and Lloyd, 1966; Roemer reduction photometric formula, from which the et al., 1966). The table lists a sample of more nuclear diameter is computed. extensively observed comets of the two types There is no chance to obtain direct information considered in Paper 1 ('erratic' and core-mantle). about the nuclear reflectivity from ground-based The type identification based on the dynamical observations. However, it might be possible to evidence is given in column 2, the degree of con determine the phase law from very accurate sistency with the phase-law evidence is com photometric observations. mented on in the last column. Two phase laws The two candidates for the surface texture to be have been tested in terms of the dispersion in the -1 considered in reference to the impact hypothesis absolute magnitude, H0: /° = 0.00 mag deg , an proposed in Paper 1, namely snow of H20 and approximation good for a smooth snow surface asteroid-like compact but porous material, differ and therefore presumably suitable for the 'erratic' considerably from each other in both the reflec comets; and /3 = 0.03 mag deg-1, which is assumed tivity and the phase variations (Sekanina, 1971). to work reasonably well for the core comets. The A smooth surface of unpacked H2O snow has a absolute magnitudes have been computed from geometrical albedo 0.5, a phase coefficient 0~O.OO2 apparent magnitudes, applying the inverse square mag deg-1 for small phase angles and generally reduction law. Only magnitudes from solar dis resembles a Lambert surface (Veverka, 1970). On tances larger than 1.2 AU have been made use of, the other hand, a typical geometrical albedo for so that phase angles have been conveniently kept asteroids is about 0.15, and the phase coefficient is within 50°. Table 5 reveals that except for characteristically /3^0.03 mag deg-1. For Icarus, P/Arend-Rigaux and perhaps P/Encke, the dis this law is still correct at phase angles as large as persion in Ho is rather high and the results there 100° (Gehrelsetal., 1970). fore inconclusive. A particularly bothering trouble Incorporation of the significant phase effect into is a systematic difference between the absolute the photometric formula brings the absolute magnitudes at successive apparitions of the same brightness up by 0.5m at phase angle 18°, by lm at comet. This effect is most noticeable in the case 42°, and by more than lm everywhere between 42° of P/Giacobini-Zinner. and 127°, as compared to the Lambert law. For the sake of comparison we have also cal Because a strong phase effect also implies a lower culated the quantities of columns 3 to 5 of table 5 albedo, hence a larger cross section, an average for two minor planets of the Apollo type. For asteroid-like nucleus would be larger in diameter Adonis, using photographic magnitudes by six than a snow covered nucleus by a factor 2.5, 3 observers, we obtain respectively +0.7m, ±0.47m and 3.5, while both nuclei have equal apparent and ±0.39m (the minimum being ±0.36m for magnitudes under equal geometrical conditions at /3 = 0.06 mag dog"1). For 1960 UA, Object Giclas, phase angles 25°, 48° and 75°, respectively. we have used photographic magnitudes by Roemer Obviously, the discrimination of cometary (1965) and photoelectric B magnitudes (reduced nuclei by the phase effect can significantly improve to the photographic system) by Rakos (1960), the accuracy of the photometric determinations of and found, respectively, +0.5m, ±0.37m and

TABLE 5.—Phase effect [f} = Phase Coefficient {mag/deg}]

Interpretation Average effect of phase Dispersion in Ho Agreement: of dynamical in absolute magnitude: phase effect Comet evidence* Ho(i8 = 0.00)- vs dynamics Fo(i8 = 0.03) 0 = 0.00 0 = 0.03 (mag) (mag) (mag)

P/Encke core +0.5 ±0.47 ±0.29 yes P/Giacobini-Zinner erratic "0.8 °0.70 "0.75 yes? P/Schaumasse erratic 0.8 0.41 0.54 yes P/Tempel 2 core 0.7 0.45 0.60 no P/Arend-Rigaux core 0.6 0.39 0.15 yes P/Forbes erratic? 0.7 0.76 0.65 no? P/Schwassmann-Wachmann 2 core? 0.5 0.49 0.59 no? P/Whipple +0.5 0.36 0.40 ~^~^~

a See: Sekanina (1971), Marsden and Sekanina (1971). b Equals to +0.8m before perihelion in 1959; and +0.7m after perihelion in 1959 and in 1965. c Equals to ±0.40m and ±0.57m, respectively, before perihelion in 1959; and to ±0.34m and ±0.40°", respectively, after perihelion in 1959 and in 1965.

±0.26m. This may suggest that a difference of different interpretation of the observed phe m 0.1 in the H0 dispersion between the two phase nomena, but we do not see any at present that laws might already be a meaningful discrimination could compete with the impact hypothesis. We level, if the dispersion itself is within, say, ±0.5m. also feel that collisional processes involving fairly To obtain more convincing results precise pho large objects of the solar system should be sub tometry must be applied. jected to extensive investigations rather than rejected as ad hoc assumptions without seriously considering the chances, effects and characteristics FINAL REMARKS of the collisional mechanism itself. We conclude that the hypothesis of fairly frequent collisions of interplanetary boulders with ACKNOWLEDGMENTS cometary nuclei, suggested in Paper 1 and The writer's thanks are due to B. G. Marsden for pro examined from specific viewpoints in the present viding ephemerides of the comets and asteroids studied paper, looks reasonably consistent with the above, and to J. F. Veverka for discussing photometry limited information available on the character problems. and rate of disturbances observed in the motions NOTE of the 'erratic' short-period comets. Precise photometry of cometary nuclei, if conducted in Since the time of the IAU Colloquium # 13 our under the future, is believed to improve significantly our standing of the problems discussed in this paper has knowledge of the amount of mass and energy further advanced. We know of two more "erratic" comets, P/Finley and P/Comas Sola (Marsden, B. G., Sekanina, involved in the sort of collisions under con Z., and Yeomans, D. K., 1973 Comets and Nongravi- sideration. We do not exclude a possibility of a tational Forces. V. Astron. J. 78, 211-225).

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