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19. New Evidence for Interplanetary Boulders?

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19. New Evidence for Interplanetary Boulders? 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 Downloaded from https://www.cambridge.org/core. IP address: 170.106.33.14, on 26 Sep 2021 at 19:13:21, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0252921100049083 200 EVOLUTIONARY AND PHYSICAL PROPERTIES OF METEOROIDS '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 Downloaded from https://www.cambridge.org/core. IP address: 170.106.33.14, on 26 Sep 2021 at 19:13:21, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0252921100049083 NEW EVIDENCE FOR INTERPLANETARY BOULDERS? 201 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 nongravi- tational 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.
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