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Origin of the Taurid meteor stream
\
Pergamon
Planet[ Space Sci[\ Vol[ 35\ No[ 7\ pp[ 770Ð775\ 0887 Þ 0887 Elsevier Science Ltd All rights reserved 9921Ð9522:87:,*see front matter PII ] S9921Ð9522"87#99906Ð7
Origin of the Taurid meteor stream Jozef Klac³ka0 and Eduard M[ Pittich1 0
Department of Astronomy and Astrophysics\ Faculty of Mathematics and Physics\ Comenius University Mlynska Dolina\ 731 04 Bratislava\ Slovak Republic 1 Astronomical Institute\ Slovak Academy of Sciences\ Dubravska cesta 8\ 731 17 Bratislava\ Slovak Republic Received 12 August 0885 ^ revised 4 January 0887 ^ accepted 5 January 0887
Abstract[ The origin of the Taurid meteor stream is investigated on the basis of the assumption that the complete set of observable quantities may be explained as a simultaneous action of nongravitational forces acting on meteoroids ejected from the parent body represented only by comet P:Encke[ Discussion is concentrated on the problem of whether or not the assumption of the importance of nongravitational forces is acceptable[ Numerical values for nongravitational acceleration are presented[ A time evolution from 09\999 to 04\999 years is considered and graphically presented[ The test is made for dust particles ejected at perihelia of the orbit of the comet Encke[ The particles are released at velocities of 19Ð599 m s−0[ Gravitational perturbations of all planets and nongravitational e}ects are considered[ Þ 0887 Elsevier Science Ltd[ All rights reserved
Introduction The Taurid meteoroid complex "TMC# represents one of the known systems which are generally considered to be created by simultaneous action of comets and asteroids "Steel et al[\ 0882\ Klac³ka\ 0884\ Pittich and Klac³ka\ 0883\ 0884#[ The TMC seems to be produced by comet Encke\ and some dormant comet!asteroids[ Gravitational perturbations by the planets cannot gen! erate the observed dispersion of the TMC in space "e[g[ Pittich and Klac³ka\ 0882# if the only source of these meteoroids is comet Encke[ This is the reason why other sources of these meteoroids are considered[ They are pre! sently classi_ed as asteroids[ In spite of this general conception we have tried in several papers "Klac³ka\ 0883a\ Klac³ka and Pittich\ 0883\ 0884\ Pittich and Klac³ka\ 0885a\ 0885b# to test the possi! Correspondence to ] Eduard M[ Pittich
bility if nongravitational forces can produce the observed dispersion of the TMC[ The answer seems to be {{yes||[ The problem is in a quite di}erent _eld of investigation[ At the present state of knowledge it is not possible to calculate exactly the importance of nongravitational e}ects[ However\ we have shown that the observed dis! persion of the TMC can be produced by the joint e}ects of gravitational and nongravitational forces\ using\ in principle only one free parameter[ The question is whether or not the required value is consistent with the real one[
General considerations Several factors are important in dealing with the origin of the TMC[ Unfortunately\ each of these enter factors in the modelling of the real situation as a free parameter[ These free parameters are ] 0[ the age of the TMC\ 1[ the ejection velocities of meteoroids from parent bodies\ 2[ the importance of nongravitational forces "some of them may be unknown#\ 3[ the number of parent bodies[ Stochastic processes may also be important[ They can stir up the apparent importance of these considered factors[ None of the above mentioned factors may be considered as well known[ It seems that the ejection velocities are determined with the highest accuracy[ Unfortunately\ we know now that the values obtained from the IRAS data and presented by Sykes and Walker "0881# are incorrect "Gajdos³(k and Klac³ka\ 0885#[ Moreover\ the values of the ejection velocities derived from the IRAS data are in general\ not unambiguous[ Many other problems may arise from the fact that observational data of meteors are evaluated by incorrect methods "Klac³ka\ 0885\ and in preparation#[ In the pre! sent paper we point out the importance of the above mentioned factors[
771
J[ Klac³ka and E[ M[ Pittich ] Origin of the Taurid meteor stream
Computational model We traced the 09\999 and 04\999 years orbital evolution of model particles ejected from the Encke comet perihelion\ using numerical integration with the RA04 integrator "Everhart\ 0874#[ The input data for the integration\ ellip! tical rectangular coordinates and velocities\ were cal! culated from the Encke comet orbital elements for the epoch 13 July 0876 "Marsden\ 0878#[ The adopted ejection velocity 39 m s−0 corresponds to the value determined by Sykes and Walker "0881# for comet Encke[ The value 599 m s−0 seems to be realistic for some comets and asteroids "Harris et al[\ 0884#[ The model particles were released from the Encke comet peri! helion 04\999 and 09\999 years ago in three directions* tangential to the cometary motion\ normal to the comet|s orbital plane\ and perpendicular to the preceding ones* and for two orientations in each direction[ The motion of comet Encke was calculated as well[ We have made 09\999 and 04\999 years backward numerical integration of the comet Encke orbit\ beginning from the epoch 13 July 0876[ Then\ the forward numerical integration for the model dust particles*meteoroids* was performed taking into account the gravitational per! turbations of all planets "G# as well as nongravitational e}ects "Klac³ka\ 0883b#*solar electromagnetic and cor!
puscular radiations "R# and transversal component of additional nongravitational forces "T#*acting on the model meteoroids[ Particles with the ratio of the radiation force to the gravity force b 4[6×09−4:"7s# 3×09−3 were taken into account ^ 7 is the mass density measured in g cm−2 and s is the radius of the particle in cm[
Results of orbital integration For a better understanding of the discussed origin of the TMC\ we have expanded our previous model com! putations "see references of our previous papers# with additional model examples ] orbital integration for 04\999 years with the ejection velocity of 39 m s−0\ orbital inte! gration for 09\999 years with the ejection velocity of 599 m s−0\ and various values of transversal components rep! resenting a set of nongravitational forces[ The results of our numerical integrations are depicted in Figs 0Ð2[ The symbols of the orbital elements are standard ] v\ argument of perihelion ^ V\ ascending node ^ i\ inclination ^ p\ longi! tude of perihelion ^ e\ eccentricity\ a\ semi!major axis ^ q\ perihelion distance and Q\ aphelion distance[ Figure 0 shows the evolution of these elements for the
Fig[ 0[ Time evolution of orbital elements of comet Encke "= \ 9 m s−0# "ejection velocity#\ and of the model meteoroids ejected from the Encke comet perihelion 09\999 years ago[ The meteoroids were disturbed by gravitational perturbations of planets and by solar electromagnetic and corpuscular radiations forces[ For the meteoroids b 3×09−3[ The meteoroids parameters are ] r\ ¦599 m s−0 in the direction of the cometary motion ^ ¦\ −599 m s−0 in the direction of the cometary motion\ ×\ ¦599 m s−0 in the direction normal to the comet|s orbit ^ e\ −599 m s−0 in the direction normal to the comet|s orbit\ \ ¦599 m s−0 in the direction perpendicular to the preceding directions and × Þ\ −599 m s−0 in the direction perpendicular to the preceding directions
J[ Klac³ka and E[ M[ Pittich ] Origin of the Taurid meteor stream
Fig[ 1[ Time evolution of orbital elements of comet Encke "= \ 9 m s−0# "ejection velocity#\ and of the model meteoroids ejected from the Encke comet perihelion 03\699 years ago[ The meteoroids were disturbed by gravitational perturbations of planets\ by solar electromagnetic and corpuscular radi! ations and by the other nongravitational forces[ For the meteoroids b 3×09−3 and T ¦4×09−3[ The meteoroids parameters are ] r\ ¦39 m s−0 in the direction of the cometary motion ^ ¦\ −39 m s−0 in the direction of the cometary motion\ ×\ ¦39 m s−0 in the direction normal to the comet|s orbit ^ e\ −39 m s−0 in the direction normal to the comet|s orbit ^ \ ¦39 m s−0 in the direction −0 perpendicular to the preceding directions and × Þ \ −39 m s in the direction perpendicular to the preceding directions
772
773
J[ Klac³ka and E[ M[ Pittich ] Origin of the Taurid meteor stream
Fig[ 2[ Time evolution of orbital elements of comet Encke "= \ 9 m s−0# "ejection velocity#\ and of the model meteoroids ejected from the Encke comet perihelion 04\999 years ago[ The meteoroids were disturbed by gravitational perturbations of planets and by solar electromagnetic and corpuscular radiations forces[ For the meteoroids b 3×09−3[ The meteoroids parameters are ] r\ ¦39 m s−0 in the direction of the cometary motion ^ ¦\ −39 m s−0 in the direction of the cometary motion ^ ×\ ¦39 m s−0 in the direction normal to the comet|s orbit ^ e\ −39 m s−0 in the direction normal to the comet|s orbit\ \ ¦39 m s−0 in the direction perpendicular to the preceding directions and × Þ \ −39 m s−0 in the direction perpendicular to the preceding directions
J[ Klac³ka and E[ M[ Pittich ] Origin of the Taurid meteor stream
774
Fig[ 3[ Time evolution of orbital elements of comet Encke " = \ 9 m s−0# "ejection velocity#\ and of the model meteoroids ejected from the Encke comet perihelion 04\999 years ago[ The meteoroids were disturbed only by gravitational perturbations of planets[ For the meteoroids b 3×09−3[ The meteor! oids parameters are ] r\ ¦39 m s−0 in the direction of the cometary motion ^ ¦\ −39 m s−0 in the direction of the cometary motion ^ ×\ ¦39 m s−0 in the direction normal to the comet|s orbit ^ e\ −39 m s−0 in the direction normal to the comet|s orbit ^ \ ¦39 m s−0 in the direction perpendicular −0 to the preceding directions and × Þ \ −39 m s in the direction perpendicular to the preceding directions
Table 0[ Longitudes of perihelia of model particles for one parent body*comet Encke Ejection velocity m s−0 19 39 39 39 049 599 39 39 39 39 39 39 39
Longitude of perihelion
Force
Evolution period years
>
>
Reference Klacka + Pittich
G¦R G G G¦R G¦R G¦R G¦R G¦R¦T ð¦4×09−2Ł G¦R¦T ð−4×09−3Ł G¦R¦T ð¦4×09−3Ł G¦R¦T ð¦4×09−3Ł G¦R¦T ð¦4×09−3Ł G¦R¦T ð−4×09−3Ł
09\999 09\999 04\999 09\999 09\999 09\999 04\999 09\999 09\999 09\999 03\699 04\999 04\999
019 047 048 014 010 000 47 39 093 059 041 000 34
059 059 067 059 059 059 059 059 059 079 089 059 059
0884 0884 This study 0884 0885b This study This study 0885a 0885a 0885a This study This study This study
model particles ejected from the comet perihelion 09\999 years ago with the velocity 599 m s−0 in all selected direc! tions[ Figures 1 and 2 show the evolution of the orbital elements of the same model particles ejected from the Encke comet perihelion 03\699 and 04\999 years ago with the velocity 39 m s−0[
Moreover\ Fig[ 3 depicts the time evolution of orbital elements for the same particles\ ejected 04\999 years ago with ejection velocity 39 m−0\ whose orbits were in~u! enced only by gravitational forces[ The Taurid meteor stream is characterized by the longi! tude of perihelion p $"099>\ 199>#\ determined from obser!
775
vations "e[g[\ Stohl and Porubc³an\ 0881#[ Table 0 shows that transversal nongravitational accelerations may gen! erate not only an increase of p with time\ but also a decrease for some particles[ Also a comparison of the results presented in Table 0 only for gravitational forces shows that close encounters with planets may generate large dispersions of the orbital elements[ The real situation is highly sensitive to the exact form of the equation of motion for gravitational and nongravitational forces and to the initial conditions[ This fact may eliminate asteroids as alternative secondary parent bodies for the TMC[ Conclusions We have constructed models of the time evolution of meteoroids ejected from comet Encke\ considering gravi! tational perturbations of planets and nongravitational e}ects[ At our present state of knowledge\ it can be con! cluded that we are able to explain the observed TMC as a consequence of comet Encke|s meteoroids alone if we include nongravitational and gravitational e}ects[ However\ the problem can be precisely solved only if exact action of all nongravitational e}ects on meteoroids and the corresponding initial conditions are fully known[ Acknowled`ements[ This work was supported by the Slovak Academy of Sciences Grant VEGA 0949:0885 and the par! ticipation of the author "Pittich# on the ACM85 Cospar Col! loquium 09 was supported by the Acces grant of the {{Ministere de l|Education\ de l|Enseignement Superieur et de la Recherche||[
References Asher\ D[ J[\ Clube\ S[ V[ M[ and Steel\ D[ I[ "0882# The Taurid complex asteroids[ In Meteroids and Their Parent Bodies\
J[ Klac³ka and E[ M[ Pittich ] Origin of the Taurid meteor stream ed[ J[ Stohl and I[ P[ Williams\ pp[ 82Ð099[ Astronomical Institute\ Bratislava[ Everhart\ E[ "0874# An e.cient integrator that used Gauss! Radau spacing[ In Dynamics of Comets ] Their Ori`in and Evolution ed[ A[ Carusi and G[ B[ Valsecchi\ pp[ 074Ð191[ Reidel\ Dordrecht[ Gajdos³(k\ M[ and Klac³ka\ J[ "0885# Cometary dust trails and ejection velocities from comets[ Poster presented at the ACM85[ Versailles\ 0885[ Harris\ N[ W[\ Yau\ K[ K[ C[ and Hughes\ D[ W[ "0884# The true extent of the nodal distribution of the Perseid meteoroid stream[ Mon[ Not[ R[ Astron[ Soc[ 162\ 888Ð0904[ Klac³ka\ J[ "0883a# Nongravitational forces and meteoroid stre! ams[ Earth\ Moon and Planets 54\ 080Ð085[ Klac³ka\ J[ "0883b# Interplanetary dust particles and solar radi! ation[ Earth\ Moon and Planets 53\ 014Ð021[ Klac³ka\ J[ "0884# The taurid complex of asteroids[ Astron[ and Astrophys[ 184\ 319Ð311[ Klac³ka\ J[ "0885# Meteor stream membership criteria[ Poster presented at the ACM85[ Versailles[ Klac³ka\ J[ and Pittich\ E[ M[ "0883# Long!term integration of dust particles released from comet Encke[ Planetary and Space Science 31\ No[ 1\ 098Ð001[ Klac³ka\ J[ and Pittich\ E[ M[ "0884# Orbital dispersion of comet Encke|s meteoroids[ Earth\ Moon\ and Planets 57\ 258Ð268[ Marsden\ B[ G[ "0878# Catalo`ue of cometary orbits[ SAO Press\ Cambridge\ MA[ Pittich\ E[ M[ and Klac³ka\ J[ "0885a# On the importance of the Poynting!Robertson e}ect on meteoroids[ Earth\ Moon\ and Planets 61\ 222Ð227[ Pittich\ E[ M[ and Klac³ka\ J[ "0885b# Taurid meteoroid and asteroid complex[ In Dynamics\ Ephemerides and Astrometry in the Solar System[ ed[ S[ Ferraz!Mello et al[\ Netherlands\ pp[ 104Ð119[ Sykes\ M[ V[ and Walker\ R[ G[ "0881# Cometary dust trails[ I[ Survey[ Icarus 84\ 079Ð109[
Stohl\ J[ and Porubc³an\ V[ "0881# Dynamical aspects of the Taurid meteor complex[ In Chaos\ Resonances and Collective Dynamical Phenomena in the Solar System ed[ S[ Ferraz! Mello\ pp[ 204Ð213[ Dordrecht\ Holland[
Pergamon
Planet[ Space Sci[\ Vol[ 35\ No[ 7\ pp[ 770Ð775\ 0887 Þ 0887 Elsevier Science Ltd All rights reserved 9921Ð9522:87:,*see front matter PII ] S9921Ð9522"87#99906Ð7
Origin of the Taurid meteor stream Jozef Klac³ka0 and Eduard M[ Pittich1 0
Department of Astronomy and Astrophysics\ Faculty of Mathematics and Physics\ Comenius University Mlynska Dolina\ 731 04 Bratislava\ Slovak Republic 1 Astronomical Institute\ Slovak Academy of Sciences\ Dubravska cesta 8\ 731 17 Bratislava\ Slovak Republic Received 12 August 0885 ^ revised 4 January 0887 ^ accepted 5 January 0887
Abstract[ The origin of the Taurid meteor stream is investigated on the basis of the assumption that the complete set of observable quantities may be explained as a simultaneous action of nongravitational forces acting on meteoroids ejected from the parent body represented only by comet P:Encke[ Discussion is concentrated on the problem of whether or not the assumption of the importance of nongravitational forces is acceptable[ Numerical values for nongravitational acceleration are presented[ A time evolution from 09\999 to 04\999 years is considered and graphically presented[ The test is made for dust particles ejected at perihelia of the orbit of the comet Encke[ The particles are released at velocities of 19Ð599 m s−0[ Gravitational perturbations of all planets and nongravitational e}ects are considered[ Þ 0887 Elsevier Science Ltd[ All rights reserved
Introduction The Taurid meteoroid complex "TMC# represents one of the known systems which are generally considered to be created by simultaneous action of comets and asteroids "Steel et al[\ 0882\ Klac³ka\ 0884\ Pittich and Klac³ka\ 0883\ 0884#[ The TMC seems to be produced by comet Encke\ and some dormant comet!asteroids[ Gravitational perturbations by the planets cannot gen! erate the observed dispersion of the TMC in space "e[g[ Pittich and Klac³ka\ 0882# if the only source of these meteoroids is comet Encke[ This is the reason why other sources of these meteoroids are considered[ They are pre! sently classi_ed as asteroids[ In spite of this general conception we have tried in several papers "Klac³ka\ 0883a\ Klac³ka and Pittich\ 0883\ 0884\ Pittich and Klac³ka\ 0885a\ 0885b# to test the possi! Correspondence to ] Eduard M[ Pittich
bility if nongravitational forces can produce the observed dispersion of the TMC[ The answer seems to be {{yes||[ The problem is in a quite di}erent _eld of investigation[ At the present state of knowledge it is not possible to calculate exactly the importance of nongravitational e}ects[ However\ we have shown that the observed dis! persion of the TMC can be produced by the joint e}ects of gravitational and nongravitational forces\ using\ in principle only one free parameter[ The question is whether or not the required value is consistent with the real one[
General considerations Several factors are important in dealing with the origin of the TMC[ Unfortunately\ each of these enter factors in the modelling of the real situation as a free parameter[ These free parameters are ] 0[ the age of the TMC\ 1[ the ejection velocities of meteoroids from parent bodies\ 2[ the importance of nongravitational forces "some of them may be unknown#\ 3[ the number of parent bodies[ Stochastic processes may also be important[ They can stir up the apparent importance of these considered factors[ None of the above mentioned factors may be considered as well known[ It seems that the ejection velocities are determined with the highest accuracy[ Unfortunately\ we know now that the values obtained from the IRAS data and presented by Sykes and Walker "0881# are incorrect "Gajdos³(k and Klac³ka\ 0885#[ Moreover\ the values of the ejection velocities derived from the IRAS data are in general\ not unambiguous[ Many other problems may arise from the fact that observational data of meteors are evaluated by incorrect methods "Klac³ka\ 0885\ and in preparation#[ In the pre! sent paper we point out the importance of the above mentioned factors[
771
J[ Klac³ka and E[ M[ Pittich ] Origin of the Taurid meteor stream
Computational model We traced the 09\999 and 04\999 years orbital evolution of model particles ejected from the Encke comet perihelion\ using numerical integration with the RA04 integrator "Everhart\ 0874#[ The input data for the integration\ ellip! tical rectangular coordinates and velocities\ were cal! culated from the Encke comet orbital elements for the epoch 13 July 0876 "Marsden\ 0878#[ The adopted ejection velocity 39 m s−0 corresponds to the value determined by Sykes and Walker "0881# for comet Encke[ The value 599 m s−0 seems to be realistic for some comets and asteroids "Harris et al[\ 0884#[ The model particles were released from the Encke comet peri! helion 04\999 and 09\999 years ago in three directions* tangential to the cometary motion\ normal to the comet|s orbital plane\ and perpendicular to the preceding ones* and for two orientations in each direction[ The motion of comet Encke was calculated as well[ We have made 09\999 and 04\999 years backward numerical integration of the comet Encke orbit\ beginning from the epoch 13 July 0876[ Then\ the forward numerical integration for the model dust particles*meteoroids* was performed taking into account the gravitational per! turbations of all planets "G# as well as nongravitational e}ects "Klac³ka\ 0883b#*solar electromagnetic and cor!
puscular radiations "R# and transversal component of additional nongravitational forces "T#*acting on the model meteoroids[ Particles with the ratio of the radiation force to the gravity force b 4[6×09−4:"7s# 3×09−3 were taken into account ^ 7 is the mass density measured in g cm−2 and s is the radius of the particle in cm[
Results of orbital integration For a better understanding of the discussed origin of the TMC\ we have expanded our previous model com! putations "see references of our previous papers# with additional model examples ] orbital integration for 04\999 years with the ejection velocity of 39 m s−0\ orbital inte! gration for 09\999 years with the ejection velocity of 599 m s−0\ and various values of transversal components rep! resenting a set of nongravitational forces[ The results of our numerical integrations are depicted in Figs 0Ð2[ The symbols of the orbital elements are standard ] v\ argument of perihelion ^ V\ ascending node ^ i\ inclination ^ p\ longi! tude of perihelion ^ e\ eccentricity\ a\ semi!major axis ^ q\ perihelion distance and Q\ aphelion distance[ Figure 0 shows the evolution of these elements for the
Fig[ 0[ Time evolution of orbital elements of comet Encke "= \ 9 m s−0# "ejection velocity#\ and of the model meteoroids ejected from the Encke comet perihelion 09\999 years ago[ The meteoroids were disturbed by gravitational perturbations of planets and by solar electromagnetic and corpuscular radiations forces[ For the meteoroids b 3×09−3[ The meteoroids parameters are ] r\ ¦599 m s−0 in the direction of the cometary motion ^ ¦\ −599 m s−0 in the direction of the cometary motion\ ×\ ¦599 m s−0 in the direction normal to the comet|s orbit ^ e\ −599 m s−0 in the direction normal to the comet|s orbit\ \ ¦599 m s−0 in the direction perpendicular to the preceding directions and × Þ\ −599 m s−0 in the direction perpendicular to the preceding directions
J[ Klac³ka and E[ M[ Pittich ] Origin of the Taurid meteor stream
Fig[ 1[ Time evolution of orbital elements of comet Encke "= \ 9 m s−0# "ejection velocity#\ and of the model meteoroids ejected from the Encke comet perihelion 03\699 years ago[ The meteoroids were disturbed by gravitational perturbations of planets\ by solar electromagnetic and corpuscular radi! ations and by the other nongravitational forces[ For the meteoroids b 3×09−3 and T ¦4×09−3[ The meteoroids parameters are ] r\ ¦39 m s−0 in the direction of the cometary motion ^ ¦\ −39 m s−0 in the direction of the cometary motion\ ×\ ¦39 m s−0 in the direction normal to the comet|s orbit ^ e\ −39 m s−0 in the direction normal to the comet|s orbit ^ \ ¦39 m s−0 in the direction −0 perpendicular to the preceding directions and × Þ \ −39 m s in the direction perpendicular to the preceding directions
772
773
J[ Klac³ka and E[ M[ Pittich ] Origin of the Taurid meteor stream
Fig[ 2[ Time evolution of orbital elements of comet Encke "= \ 9 m s−0# "ejection velocity#\ and of the model meteoroids ejected from the Encke comet perihelion 04\999 years ago[ The meteoroids were disturbed by gravitational perturbations of planets and by solar electromagnetic and corpuscular radiations forces[ For the meteoroids b 3×09−3[ The meteoroids parameters are ] r\ ¦39 m s−0 in the direction of the cometary motion ^ ¦\ −39 m s−0 in the direction of the cometary motion ^ ×\ ¦39 m s−0 in the direction normal to the comet|s orbit ^ e\ −39 m s−0 in the direction normal to the comet|s orbit\ \ ¦39 m s−0 in the direction perpendicular to the preceding directions and × Þ \ −39 m s−0 in the direction perpendicular to the preceding directions
J[ Klac³ka and E[ M[ Pittich ] Origin of the Taurid meteor stream
774
Fig[ 3[ Time evolution of orbital elements of comet Encke " = \ 9 m s−0# "ejection velocity#\ and of the model meteoroids ejected from the Encke comet perihelion 04\999 years ago[ The meteoroids were disturbed only by gravitational perturbations of planets[ For the meteoroids b 3×09−3[ The meteor! oids parameters are ] r\ ¦39 m s−0 in the direction of the cometary motion ^ ¦\ −39 m s−0 in the direction of the cometary motion ^ ×\ ¦39 m s−0 in the direction normal to the comet|s orbit ^ e\ −39 m s−0 in the direction normal to the comet|s orbit ^ \ ¦39 m s−0 in the direction perpendicular −0 to the preceding directions and × Þ \ −39 m s in the direction perpendicular to the preceding directions
Table 0[ Longitudes of perihelia of model particles for one parent body*comet Encke Ejection velocity m s−0 19 39 39 39 049 599 39 39 39 39 39 39 39
Longitude of perihelion
Force
Evolution period years
>
>
Reference Klacka + Pittich
G¦R G G G¦R G¦R G¦R G¦R G¦R¦T ð¦4×09−2Ł G¦R¦T ð−4×09−3Ł G¦R¦T ð¦4×09−3Ł G¦R¦T ð¦4×09−3Ł G¦R¦T ð¦4×09−3Ł G¦R¦T ð−4×09−3Ł
09\999 09\999 04\999 09\999 09\999 09\999 04\999 09\999 09\999 09\999 03\699 04\999 04\999
019 047 048 014 010 000 47 39 093 059 041 000 34
059 059 067 059 059 059 059 059 059 079 089 059 059
0884 0884 This study 0884 0885b This study This study 0885a 0885a 0885a This study This study This study
model particles ejected from the comet perihelion 09\999 years ago with the velocity 599 m s−0 in all selected direc! tions[ Figures 1 and 2 show the evolution of the orbital elements of the same model particles ejected from the Encke comet perihelion 03\699 and 04\999 years ago with the velocity 39 m s−0[
Moreover\ Fig[ 3 depicts the time evolution of orbital elements for the same particles\ ejected 04\999 years ago with ejection velocity 39 m−0\ whose orbits were in~u! enced only by gravitational forces[ The Taurid meteor stream is characterized by the longi! tude of perihelion p $"099>\ 199>#\ determined from obser!
775
vations "e[g[\ Stohl and Porubc³an\ 0881#[ Table 0 shows that transversal nongravitational accelerations may gen! erate not only an increase of p with time\ but also a decrease for some particles[ Also a comparison of the results presented in Table 0 only for gravitational forces shows that close encounters with planets may generate large dispersions of the orbital elements[ The real situation is highly sensitive to the exact form of the equation of motion for gravitational and nongravitational forces and to the initial conditions[ This fact may eliminate asteroids as alternative secondary parent bodies for the TMC[ Conclusions We have constructed models of the time evolution of meteoroids ejected from comet Encke\ considering gravi! tational perturbations of planets and nongravitational e}ects[ At our present state of knowledge\ it can be con! cluded that we are able to explain the observed TMC as a consequence of comet Encke|s meteoroids alone if we include nongravitational and gravitational e}ects[ However\ the problem can be precisely solved only if exact action of all nongravitational e}ects on meteoroids and the corresponding initial conditions are fully known[ Acknowled`ements[ This work was supported by the Slovak Academy of Sciences Grant VEGA 0949:0885 and the par! ticipation of the author "Pittich# on the ACM85 Cospar Col! loquium 09 was supported by the Acces grant of the {{Ministere de l|Education\ de l|Enseignement Superieur et de la Recherche||[
References Asher\ D[ J[\ Clube\ S[ V[ M[ and Steel\ D[ I[ "0882# The Taurid complex asteroids[ In Meteroids and Their Parent Bodies\
J[ Klac³ka and E[ M[ Pittich ] Origin of the Taurid meteor stream ed[ J[ Stohl and I[ P[ Williams\ pp[ 82Ð099[ Astronomical Institute\ Bratislava[ Everhart\ E[ "0874# An e.cient integrator that used Gauss! Radau spacing[ In Dynamics of Comets ] Their Ori`in and Evolution ed[ A[ Carusi and G[ B[ Valsecchi\ pp[ 074Ð191[ Reidel\ Dordrecht[ Gajdos³(k\ M[ and Klac³ka\ J[ "0885# Cometary dust trails and ejection velocities from comets[ Poster presented at the ACM85[ Versailles\ 0885[ Harris\ N[ W[\ Yau\ K[ K[ C[ and Hughes\ D[ W[ "0884# The true extent of the nodal distribution of the Perseid meteoroid stream[ Mon[ Not[ R[ Astron[ Soc[ 162\ 888Ð0904[ Klac³ka\ J[ "0883a# Nongravitational forces and meteoroid stre! ams[ Earth\ Moon and Planets 54\ 080Ð085[ Klac³ka\ J[ "0883b# Interplanetary dust particles and solar radi! ation[ Earth\ Moon and Planets 53\ 014Ð021[ Klac³ka\ J[ "0884# The taurid complex of asteroids[ Astron[ and Astrophys[ 184\ 319Ð311[ Klac³ka\ J[ "0885# Meteor stream membership criteria[ Poster presented at the ACM85[ Versailles[ Klac³ka\ J[ and Pittich\ E[ M[ "0883# Long!term integration of dust particles released from comet Encke[ Planetary and Space Science 31\ No[ 1\ 098Ð001[ Klac³ka\ J[ and Pittich\ E[ M[ "0884# Orbital dispersion of comet Encke|s meteoroids[ Earth\ Moon\ and Planets 57\ 258Ð268[ Marsden\ B[ G[ "0878# Catalo`ue of cometary orbits[ SAO Press\ Cambridge\ MA[ Pittich\ E[ M[ and Klac³ka\ J[ "0885a# On the importance of the Poynting!Robertson e}ect on meteoroids[ Earth\ Moon\ and Planets 61\ 222Ð227[ Pittich\ E[ M[ and Klac³ka\ J[ "0885b# Taurid meteoroid and asteroid complex[ In Dynamics\ Ephemerides and Astrometry in the Solar System[ ed[ S[ Ferraz!Mello et al[\ Netherlands\ pp[ 104Ð119[ Sykes\ M[ V[ and Walker\ R[ G[ "0881# Cometary dust trails[ I[ Survey[ Icarus 84\ 079Ð109[
Stohl\ J[ and Porubc³an\ V[ "0881# Dynamical aspects of the Taurid meteor complex[ In Chaos\ Resonances and Collective Dynamical Phenomena in the Solar System ed[ S[ Ferraz! Mello\ pp[ 204Ð213[ Dordrecht\ Holland[