Draconids 1901-2100

Draconids take their place among the most outstanding meteor showers. They are active far not annually. Actually it shows activity only once in 5-6 years on average, around perihelia of their parent comet - 21P Giacobimi-Zinner. This comet was discovered in 1900, just after its orbit was moved by Jupiter close to the Earth orbit. In the second half of 1910s some astronomers pointed out that there is possibility of meteor action from this comet in the beginning of October and such activity was actually observed. The meteor shower had its radiant in the head of Draco, which was suitable for 21P orbit. During 20 century and up to the present days the orbit of 21P passed through some perturbations, but was remaining near the Earth orbit. In this period Draconids produced two strong storms in 1933 and 1946 and a number of non-stormy outbursts. The latest activity enhancements occured in 1998 and 1999, when the comet passed its previous perihelion, as well as in 2005. In 1998 ZHR reached 700 meteors and in 1999 - 15-20 meteors. 2005 gave an enhancement up to 30-35 meteors on ZHR scale [4].
The vast majority of Draconid outbursts is traced with the modelling very good (but there are some exceptions, first of all, the 1985 case). Particles ejected by the comet form lengthy trails. One of the reasons is radiation pressure force, which acts parallel with gravitational forces. Gravitational force is dependent on a particle mass, i.e. it is proportional to the third power of particle radius. The outcrying radiation pressuse is defined by the second power of particle radius. So far the influence of radiation pressure is the more the less is size of a particle. Its action is equivalent to the diminishing of gravitational constant G. So it increases the orbital period of particles, and the tinier a particle is, the more it is continuously retarded from larger particles after their ejection be the comet. This process therefore leads to the formation of lengthy comet trails.
Meteor modelling is done through computation of orbital evolution of particles ejected by the comet with different velocities in directions tangential to the comet trajectory at the moment of perihelion. In the reality, of course, particles are ejected not only at the point of perihelion, but also within several months around it. However, comets are close to perihelion during quite a little time comparing to their overall orbital period and main perturbations happen around their aphelions, so when comets are closer to the Sun newly ejected particles are moving very close to them in a compact dust cloud. This is the reason we can take that cloud as completely ejected in the point of perihelion, it doesn't virtualy influence the results of computations.
Speaking of directions in which particles are ejected we can say that, again, in the reality they are ejected far not only in tangential directions, but in all possible ones. However, ejection velocities (from 0 to 100 m/s, and the overwhelming majority of real ejections - from 0 to 20 m/s) are negligibly small comparing to the own comet velocity (from 30 to 40 km/s) near the Earth's orbit), ejected particles have only slightly changed orbits and don't "fly away in all directions". Radial part of ejection velocity defines only thickness of a trail, which usually reaches several hundreds thousands kilometers. The shape of the trail is defined by tangential part of ejection velocity.
And the last. Non-gravitational forces are often not taken into consideration in meteor calculations, as is in our case. However, some of them, say, radiation pressure, can be considered indirectly. As far as this kind of force works as diminishing of gravitational constant G, this is equivalent to increase of ejection velocity which could be easily accounted in the model. So this non-gravitational force, as many others doesn't change the configuration of trails, but leads to shifting of particles with different masses along them.
Draconid trails modelling allowed to prepare very good predictions of shower activity in the previous years, real maximums differed from predicted ones mostly no more than on several minutes - not very much considering that computations are made for dozens and hundreds years of particles movement. More serious problem is prediction of outburst intensity - how strong the maximum could be. For such predictions special empirical models were elaborated (the single way in this case) but as before for their improvment new observations are very necessary.
This paper presents descriptions of suggested past and future Draconid activity during the period of 1901-2100 years. Computations were made for each year in this period, and, as the paper is presented in 2007, they are truly predictive for 2007-2100 years, while for the rest of them "postpredictions" were compiled. Also, as the models, used in computations are based after all on observations of real activity in the past, we will not compare each postpredition with real Draconid activity in respective years.
We also should mention that besides "traditional analisys", which is interpretation of direct encounters with dust trails, we'll use approachs called "non-perihelion particles" and "vertical trails". The latter is described in a separate chapter of the paper. These approached are purely hypotetical now, though they are quite logical internally. Still, results obtained from the use of those two approaches should be considered less reliable as with the use of traditional analysis.

Computation characteristics
We'd like to present the results of Draconid meteor stream simulation aimed to the prediction of shower activity in the years 1901-2100. Simulation was made for the trails of latest 27 revolutions, i.e, from the 1817 trail. The Author used the program by S. Shanov and S. Dubrovsky "Comet's Dust 2.0" to calculate orbital elements of ejected meteor particles. To estimate expected ZHRs for different encounters the model described in [4] was used with some Author's alterations made in order to adopt the model for ejection velocity (v) instead of da0 (difference in a-semimajor axis) and to turn the model from the Leonid stream (for which it was originally created) to the Perseids. The computation considered only gravitational forces, however, the results are on the whole in good accordance with these of other researchers. The prediction includes all encounters found within interval +/-0.007 a.u. The following parts of trails were computed: the first 15 rev. trails for ejection velocities [-50;100] m/s, 16-30 rev. trails - [-30;50] m/s, 31-50 rev. trails - [-20;30] m/s.
Draconid predictions are given as short conclusions from the years for which possible activity enhancements are found. Also, we present tables showing characteristics of trails interacting with the Earth. Its typical shape is showed in Table A1.
Table А1
encounters with trails
where 2000 - described year of Draconid activity; trail - year of trail ejection; rD-rE - the distance between the Earth's orbit and trail particles orbits (positive value means the descending node of trail is outside the Earth's orbit, negative - the node is inside it); Vej - velocity of particles ejection on the given trail part (positive values means the particles were ejected against the comet movement, negavive - particles were ejected along the comet movement); fM(fMD) - the characteristic of longitudinal density of the trail, it is derived from the time interval between passages of minimal distance to the Earth's orbit by particles with different ejection velocities; SL - solar longitude corresponding to the maximum; MT - assumed time of maximum.
We should note that such tables will be given for direct encounters with stream trails. Table presenting results of "vertical trails" approach will differ in one parameter - rD-rE, which will be substituted by effective distance between the Earth's and trail particles orbits - rD-rE_e. The meaning of this parameter in given in the section describing this approach, so we do not give much details here.
As it is impossible to display in tables all nuances and detales for each prediction, information given in comments has priority-driven character comparing to the data in tables. It doesn't mean that it will be in contradiction with tables (at least, not in the Author's point of view), but formal figures far not always can tell the reader how to understand prediction correcly.

Orbit of the comet 21P in 1901-2100
The Author used initial orbital elements of 21P, starting from perihelion of 1817 and up to 2092, presented by Kazuo Kinosita [2]. Orbital elements of 21P in the period 1901-2100, as well as values of minimal distances to the Earth orbit for these elements and relative solar longitudes are given in Table A2.
                                                                   Table А2
time of perih.	     q       e      AOP      Node     i       МD.      SL. 
      -             AU       -       °        °       °       AU        ° 
1907.5.8.4782 	  0.93267 0.73133 171.0696 198.0877 29.8291 -0.05992 199.1620
1913.10.23.5631   0.97787 0.72023 171.3795 197.0886 30.7277 -0.01581 197.3229
1920.5.10.9250 	  0.98179 0.71957 171.4379 197.0380 30.6982 -0.01199 197.2153
1926.12.5.8194 	  0.99596 0.71655 171.6606 196.9581 30.7217  0.00180 196.9327
1933.7.11.4684 	  1.00178 0.71552 171.6787 196.9582 30.6671  0.00756 196.8524
1940.2.15.6659 	  0.99786 0.71623 171.7004 196.9650 30.7245  0.00365 196.9145
1946.9.19.0074	  0.99795 0.71619 171.7200 197.0085 30.7102  0.00374 196.9552
1953.4.19.3773 	  0.99093 0.71740 171.7988 196.9545 30.8077 -0.00333 196.9999
1959.10.30.9223	  0.93625 0.72885 172.7954 196.7324 30.8807 -0.05870 197.5486
1966.3.31.8768 	  0.93384 0.72927 172.8725 196.6675 30.9202 -0.06118 197.5129
1972.8.8.5808 	  0.99423 0.71493 171.9024 195.8280 31.7089 -0.00049 195.8355
1979.2.15.4250 	  0.99630 0.71449 171.9706 195.7664 31.6993  0.00148 195.7481
1985.9.6.9461 	  1.02826 0.70745 172.4812 195.4096 31.8723  0.03267 195.0426
1992.4.14.0370    1.03400 0.70642 172.5194 195.3852 31.8216  0.03834 194.9583
1998.11.21.3211	  1.03370 0.70643 172.5456 195.3992 31.8586  0.03802 194.9782
2005.7.2.1164 	  1.03789 0.70565 172.5469 195.4315 31.8104  0.04220 194.9639
2012.2.10.6593	  1.03047 0.70703 172.6079 195.3992 31.9098  0.03475 195.0145
2018.9.9.0942     1.01292 0.71045 172.8661 195.3961 31.9963  0.01705 195.2084
2025.3.24.5696	  1.00904 0.71104 172.9408 195.3363 32.0488  0.01311 195.1926
2031.8.29.8422	  1.06861 0.69949 170.8471 194.4373 31.6448  0.07415 193.5100
2038.5.16.7180	  1.07033 0.69915 170.9179 194.3695 31.6419  0.07575 193.4297
2045.2.12.2144	  1.09877 0.69310 171.3435 194.0841 31.7564  0.10353 192.9112
2051.11.27.2539	  1.10515 0.69206 171.3753 194.0710 31.7043  0.10985 192.8379
2058.9.10.5332	  1.10118 0.69271 171.3967 194.0778 31.7597  0.10588 192.8887
2065.6.20.3662    1.09949 0.69295 171.4294 194.1227 31.7559  0.10418 192.9530
2072.3.28.7692    1.09338 0.69395 171.5567 194.0513 31.8501  0.09795 192.9602
2078.10.29.9343   1.00616 0.71880 171.2049 192.3660 28.2182  0.01109 192.1745
2085.8.9.3003     1.00683 0.71870 171.2877 192.2931 28.2262  0.01164 192.0948
2092.6.1.6464     1.04080 0.71142 171.9683 191.7372 28.5344  0.04450 191.0857
2099.4.13.5361    1.04605 0.71064 172.0148 191.7120 28.5021  0.04967 190.9945
Orbital elements are given for the Epoch J2000. The following of them are denoted with symbols: q - perihelion distance; e - eccentricity; AOP - argument of perihelion; Node - longitude of ascending node; i - inclination, MD - minimal distance to the Earth orbit, SL - solar longitude of MD-point. Positive value of minimal distance means that point of such minimum lies outside the Earth orbit, and negative value means that this point is inside the Earth orbit.