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WGN, the Journal of the IMO 27:2 (1999) 85
Ongoing Meteor Work
Leonid Dust Trails and Meteor Storms
Robert H. McNaught and David J. Asher
Leonid storms are caused by the Earth intersecting dense trails of dust ejected from Comet 55P/Tempel­Tuttle.
Here, we extend existing studies by examining the higher ejection­velocity regions of young dust trails and the
circumstances around the 2031 return of 55P/Tempel­Tuttle. A model of dust trail density is successfully fitted
to the observed ZHR of storms. Based on this, predictions are made for encounters in the next few years and
around 2031, giving both the times and rates of maxima. The most likely prospects for encounters are from
1999--2002, especially 2001 and 2002. Details of a storm in 1869 are presented and confirm that the time of
maximum is predictable to 10 minutes accuracy or better. The consequences of these findings are applied to the
satellite threat and to the methods of global analysis of Leonid rates.
1. Introduction
Meteor storms occur when the Earth passes through dense trails of meteoroids and dust such as
those observed by the Infra­Red Astronomical Satellite [1]. The motion of Comet 55P/Tempel­
Tuttle only has relevance, with regard to Leonid storms, in defining the initial orbits of the
meteoroids at ejection. To understand Leonid activity requires a study of the perturbed motion
of these meteoroids. It has been known for some time [2--4] that perturbations can be significantly
different on Leonid meteoroids that are separated in mean anomaly. Extensive calculations about
swarm/trail encounters covering the 19th and 20th centuries were first done by Kondrat'eva et
al. [5] and later (without prior knowledge) by Asher [6].
The natural tendency is for the spatial density of meteoroids to decrease, trails becoming dis­
persed after many orbital revolutions. However, there does exist a dynamical mechanism, namely
a mean motion resonance, that can cause meteoroids in the Leonid and other streams to remain
very concentrated on longer time scales [7]. Thus, a second source of Leonid storms is mete­
oroids many revolutions old in the 5/14 resonance with Jupiter. Meteoroids from every return
of the comet ultimately add to this, if ejection is within a suitable initial range of semi­major
axes. This has been investigated for the 1998 Leonid fireball shower [8], the observed time of
maximum for that outburst [9] being demonstrated to be consistent with the prediction from the
resonant meteoroids and quite discrepant from the comet node (a difference of 0.8 day). Further
study is required on these resonant meteoroids, but this source appears to have been involved
in the fireball display of 1965 and maybe also in the storms of 1799 and 1832. These resonant
meteoroids cover only around 10 ffi of mean anomaly and so could generally be encountered at
high strength only once per comet orbit.
It is not coincidental that the resonant mechanism leads to outbursts that are rich in fireballs.
Larger particles, which produce brighter meteors, are expected to have lower ejection speeds
from the comet nucleus. This means that they go on to orbits more similar to that of the
comet (which is itself in the resonance) and so are more likely to be resonant. However, smaller
particles are more numerous, and the highest ZHR storms result from younger trails, which are
our subject here.
2. Extended table of dust node
Readers should refer to [6] for a description of why our method is appropriate for calculating
dust trail positions. Briefly, the model has meteoroids ejected from 55P/Tempel­Tuttle at each
perihelion and integrated until nodal crossing in any specific year. Thus, at the time of ejection,
taken to be exactly at perihelion, the perihelion distance and the angular orbital elements are
set equal to those of the comet, and the process iterates to find the precise value of the semi­
major axis at ejection, a 0 , that gives passage through the descending node at the time when
the Earth reaches the orbital plane. We used the 15th order Radau integrator [10] in the

86 WGN, the Journal of the IMO 27:2 (1999)
Mercury integration package [11], kindly provided to us by John Chambers, with accuracy
parameter 10 \Gamma11 and perturbations from eight planets (Mercury to Neptune). Particles affected
by radiation pressure must have smaller a 0 than listed in Table 1 in order to cross the ecliptic
at the correct time. For example, fi = 0:001 (ratio of the forces of radiation pressure and solar
gravity) means that the correct effective a 0 is 0.2 smaller than that listed (cf. [6,12]). Possible
variations in the trail geometry due to ejection away from perihelion or radiation pressure are
discussed later (Sections 3 and 5).
Table 1 is an extended version of (some columns of) that given in [6], which included data for
trails generated 1, 2, and 3 revolutions earlier, in the two years prior to, and four years after, the
perihelion passage of 55P/Tempel­Tuttle. In the present paper, trails 4, 5, and 6 revolutions old
are considered in the same years, and a larger range of ejection velocities (allowing nodal crossing
to occur in years further from the comet's perihelion) are considered for the 1--3­revolution
trails. As more revolutions are considered, the range of \Deltaa 0 over these six years contracts,
and encounters with trails of this age outside these years could still produce notable activity,
albeit the ZHR will tend to decrease the older the trail. To save extensive further computation,
reference was made to [5] for other possible years and trails older than 6 revolutions worthy
of consideration; we selected for inclusion the 7­revolution trails in 1832 and 2001 and the 8­
revolution trail in 2000 (the values in Table 1 being derived by ourselves).
Table 1 -- Data for dust trails generated a reasonably small number of revolutions previously. Below, \Deltaa 0 is the initial
difference in semi­major axis from the comet that allows the nodal crossing to occur at exactly the relevant
time in November of the year in question; rD and rE are the heliocentric distances of the dust trail's descending
node and of the Earth at the same longitude; and fM , the ``mean anomaly factor,'' is inversely proportional
to the stretching in mean anomaly that has occurred since ejection, normalized to a fixed, small interval in a0
centered on the value of \Deltaa 0 in question (refer to Section 5). The spatial density of a trail encountered by
the Earth depends on \Deltaa 0 (ejected meteoroids being concentrated towards orbits nearer the comet), rE \Gamma rD
(which gives a measure of the distance between the Earth and the center of the trail), and fM (since the particle
density decreases as the trail lengthens), as investigated quantitatively in Section 5.
Finally,\Omega is equal to the
longitude of the Sun at the time of nodal crossing (calculated for orbit of Earth at relevant date, but expressed
in J2000). A dash indicates that the relevant part of the trail had been disrupted to a greater or lesser extent
(cf. [6]), a blank space simply that we did not attempt to calculate the data.
Year Trails 1 revolution old Trails 2 revolutions old Trails 3 revolutions old
\Deltaa 0 rE \Gamma rD fM
\Omega \Deltaa 0 rE \Gamma rD fM
\Omega \Deltaa 0 rE \Gamma rD fM
\Omega 1798 \Gamma0:28 +0:0043 1:08 233 ffi : 04 \Gamma0:15 +0:0058 0:53 233 ffi : 02 \Gamma0:09 +0:0017 0:41 232 ffi : 15
1799 \Gamma0:07 +0:0032 1:00 233 ffi : 04 \Gamma0:04 +0:0035 0:52 233 ffi : 03 \Gamma0:02 +0:0018 0:27 232 ffi : 84
1800 +0:14 +0:0028 1:00 233 ffi : 03 +0:07 +0:0020 0:52 233 ffi : 06 +0:02 +0:0060 0:17 233 ffi : 32
1801 +0:35 +0:0029 0:95 233 ffi : 02 +0:19 +0:0006 0:53 233 ffi : 17 +0:06 +0:0105 0:15 233 ffi : 58
1802 +0:56 +0:0029 0:95 233 ffi : 04 +0:31 \Gamma0:0011 0:55 233 ffi : 49 +0:09 +0:0134 0:18 233 ffi : 95
1803 +0:76 +0:0022 0:95 233 ffi : 18 +0:42 \Gamma0:0008 0:43 234 ffi : 45 +0:12 +0:0208 0:11 234 ffi : 84
1831 \Gamma0:25 +0:0034 1:00 233 ffi : 16 \Gamma0:13 +0:0051 0:55 233 ffi : 17 \Gamma0:10 +0:0068 0:40 233 ffi : 16
1832 \Gamma0:04 +0:0014 1:00 233 ffi : 18 \Gamma0:02 +0:0017 0:55 233 ffi : 18 \Gamma0:02 +0:0019 0:39 233 ffi : 17
1833 +0:17 \Gamma0:0003 0:95 233 ffi : 18 +0:09 \Gamma0:0015 0:53 233 ffi : 18 +0:07 \Gamma0:0028 0:45 233 ffi : 21
1834 +0:38 \Gamma0:0017 0:95 233 ffi : 18 +0:20 \Gamma0:0044 0:52 233 ffi : 17 +0:15 \Gamma0:0070 0:61 233 ffi : 27
1835 +0:59 \Gamma0:0026 0:95 233 ffi : 18 +0:31 \Gamma0:0065 0:50 233 ffi : 16 +0:24 \Gamma0:0107 0:39 233 ffi : 42
1836 +0:79 \Gamma0:0033 0:95 233 ffi : 18 +0:42 \Gamma0:0083 0:50 233 ffi : 18 +0:33 \Gamma0:0142 0:43 233 ffi : 80
1864 \Gamma0:25 +0:0124 1:06 233 ffi : 96 \Gamma0:13 +0:0138 0:55 233 ffi : 94 \Gamma0:10 +0:0156 0:41 233 ffi : 95
1865 \Gamma0:04 +0:0072 1:00 233 ffi : 32 \Gamma0:02 +0:0074 0:59 233 ffi : 31 -- -- -- --
1866 +0:17 +0:0036 1:00 233 ffi : 30 +0:09 +0:0026 0:55 233 ffi : 31 +0:07 +0:0012 0:40 233 ffi : 31
1867 +0:37 \Gamma0:0002 1:00 233 ffi : 42 +0:20 \Gamma0:0026 0:55 233 ffi : 43 +0:15 \Gamma0:0057 0:45 233 ffi : 42
1868 +0:58 +0:0012 0:95 234 ffi : 06 +0:31 \Gamma0:0044 0:54 234 ffi : 03 +0:24 \Gamma0:0096 0:40 234 ffi : 01
1869 +0:78 +0:0103 0:95 233 ffi : 43 +0:43 +0:0055 0:53 233 ffi : 49 +0:32 \Gamma0:0005 0:44 233 ffi : 54
1897 \Gamma0:35 \Gamma0:0020 1:00 234 ffi : 24 \Gamma0:18 +0:0008 0:45 234 ffi : 93 \Gamma0:12 +0:0013 0:25 235 ffi : 26
1898 \Gamma0:14 +0:0155 1:06 234 ffi : 84 \Gamma0:07 +0:0167 0:55 234 ffi : 96 \Gamma0:05 +0:0176 0:41 235 ffi : 04
1899 +0:07 +0:0138 1:02 235 ffi : 02 +0:04 +0:0132 0:54 234 ffi : 98 +0:03 +0:0126 0:41 234 ffi : 98
1900 +0:28 +0:0199 1:00 234 ffi : 07 +0:15 +0:0182 0:55 234 ffi : 02 +0:11 +0:0168 0:41 234 ffi : 05
1901 +0:48 +0:0146 1:00 233 ffi : 85 +0:25 +0:0125 0:53 233 ffi : 82 +0:19 +0:0097 0:46 233 ffi : 85
1902 +0:68 +0:0114 0:95 233 ffi : 85 +0:36 +0:0086 0:59 233 ffi : 85 +0:28 +0:0035 0:45 234 ffi : 03

WGN, the Journal of the IMO 27:2 (1999) 87
Table 1 -- Data for dust trails (continued).
Year Trails 1 revolution old Trails 2 revolutions old Trails 3 revolutions old
\Deltaa 0 rE \Gamma rD fM
\Omega \Deltaa 0 rE \Gamma rD fM
\Omega \Deltaa 0 rE \Gamma rD
fM\Omega 1930 \Gamma0:36 +0:0075 1:00 235 ffi : 09 \Gamma0:17 +0:0071 0:40 235 ffi : 24 \Gamma0:12 +0:0018 0:32 235 ffi : 39
1931 \Gamma0:14 +0:0065 1:08 235 ffi : 09 \Gamma0:08 +0:0105 0:53 234 ffi : 90 \Gamma0:06 +0:0125 0:37 235 ffi : 09
1932 +0:07 +0:0060 0:95 235 ffi : 09 +0:03 +0:0059 0:46 235 ffi : 36 +0:02 +0:0059 0:31 235 ffi : 43
1933 +0:28 +0:0054 1:00 235 ffi : 15 +0:11 +0:0118 0:27 236 ffi : 01 +0:07 +0:0135 0:16 235 ffi : 99
1934 +0:49 +0:0040 0:95 235 ffi : 50 +0:16 +0:0173 0:28 236 ffi : 24 +0:10 +0:0182 0:21 235 ffi : 95
1935 +0:69 +0:0182 1:00 235 ffi : 96 +0:23 +0:0342 0:39 236 ffi : 20 +0:16 +0:0327 0:41 235 ffi : 66
1961 \Gamma0:75 +0:0109 1:14 235 ffi : 03 \Gamma0:39 +0:0160 0:57 235 ffi : 10 \Gamma0:25 +0:0078 0:42 234 ffi : 93
1962 \Gamma0:53 +0:0083 1:08 235 ffi : 06 \Gamma0:28 +0:0116 0:55 235 ffi : 10 \Gamma0:18 +0:0114 0:28 235 ffi : 27
1963 \Gamma0:31 +0:0059 1:00 235 ffi : 09 \Gamma0:17 +0:0077 0:55 235 ffi : 11 \Gamma0:13 +0:0136 0:34 235 ffi : 10
1964 \Gamma0:10 +0:0038 1:00 235 ffi : 12 \Gamma0:05 +0:0043 0:53 235 ffi : 12 \Gamma0:04 +0:0063 0:44 234 ffi : 95
1965 +0:11 +0:0023 1:00 235 ffi : 13 +0:06 +0:0017 0:59 235 ffi : 13 +0:04 +0:0015 0:37 235 ffi : 45
1966 +0:32 +0:0016 0:95 235 ffi : 13 +0:17 \Gamma0:0001 0:52 235 ffi : 16 +0:09 +0:0033 0:19 235 ffi : 94
1967 +0:53 +0:0012 0:95 235 ffi : 13 -- -- -- -- +0:12 +0:0063 0:16 236 ffi : 21
1968 +0:73 +0:0010 0:95 235 ffi : 15 +0:39 \Gamma0:0036 0:55 235 ffi : 44 -- -- -- --
1969 +0:93 0:0000 0:95 235 ffi : 27 +0:51 \Gamma0:0058 0:54 236 ffi : 09 +0:20 +0:0136 0:13 237 ffi : 37
1992 \Gamma0:45 +0:0176 0:43 235 ffi : 41
1993 \Gamma0:36 +0:0109 -- 235 ffi : 54
1994 \Gamma0:38 +0:0102 0:57 236 ffi : 40 \Gamma0:28 +0:0155 0:12 236 ffi : 43
1995 \Gamma0:26 +0:0168 0:57 235 ffi : 48 \Gamma0:19 +0:0211 0:42 235 ffi : 47
1996 \Gamma0:28 +0:0099 1:08 235 ffi : 29 \Gamma0:15 +0:0126 0:55 235 ffi : 27 \Gamma0:11 +0:0149 0:41 235 ffi : 27
1997 \Gamma0:06 +0:0085 1:00 235 ffi : 26 \Gamma0:04 +0:0091 0:55 235 ffi : 26 \Gamma0:03 +0:0095 0:40 235 ffi : 26
1998 +0:14 +0:0068 1:00 235 ffi : 26 +0:08 +0:0055 0:55 235 ffi : 27 -- -- -- --
1999 +0:35 +0:0047 0:95 235 ffi : 28 +0:19 +0:0019 0:53 235 ffi : 27 +0:14 \Gamma0:0007 0:38 235 ffi : 29
2000 +0:55 +0:0031 0:95 235 ffi : 29 +0:30 \Gamma0:0012 0:55 235 ffi : 27 +0:22 \Gamma0:0051 0:38 235 ffi : 32
2001 +0:76 +0:0022 0:95 235 ffi : 29 +0:41 \Gamma0:0034 0:52 235 ffi : 25 +0:30 \Gamma0:0086 0:39 235 ffi : 39
2002 +0:96 +0:0018 0:95 235 ffi : 27 -- -- -- -- +0:39 \Gamma0:0119 0:45 235 ffi : 56
2003 +1:16 +0:0019 0:90 235 ffi : 27 +0:63 \Gamma0:0061 0:49 235 ffi : 23 +0:48 \Gamma0:0151 0:78 236 ffi : 03
2004 +0:74 \Gamma0:0074 0:78 235 ffi : 30 +0:56 \Gamma0:0167 0:32 237 ffi : 14
2005 +0:85 \Gamma0:0099 0:50 235 ffi : 63 +0:61 \Gamma0:0111 0:13 238 ffi : 90
2006 +0:96 \Gamma0:0001 0:53 236 ffi : 62 +0:63 +0:0106 0:08 240 ffi : 21
2007 +0:65 +0:0214 0:08 238 ffi : 99
2008 +0:67 +0:0254 0:12 238 ffi : 24
2009 +0:70 +0:0264 0:18 237 ffi : 46
2025 \Gamma0:38 +0:0026 0:10 237 ffi : 13
2026 \Gamma0:34 +0:0122 0:20 237 ffi : 19
2027 \Gamma0:39 +0:0126 0:57 235 ffi : 82 \Gamma0:29 +0:0170 0:31 236 ffi : 57
2028 \Gamma0:28 +0:0104 0:37 235 ffi : 66 \Gamma0:22 +0:0156 0:42 235 ffi : 90
2029 \Gamma0:32 +0:0071 1:00 235 ffi : 88 \Gamma0:17 +0:0083 0:55 235 ffi : 93 \Gamma0:13 +0:0112 0:42 235 ffi : 97
2030 \Gamma0:11 +0:0219 1:00 236 ffi : 21 \Gamma0:06 +0:0224 0:95 236 ffi : 21 \Gamma0:04 +0:0232 0:44 236 ffi : 21
2031 +0:10 +0:0183 1:00 235 ffi : 42 +0:05 +0:0179 0:53 235 ffi : 42 +0:04 +0:0171 0:41 235 ffi : 42
2032 +0:30 +0:0154 0:95 235 ffi : 36 +0:16 +0:0140 0:55 235 ffi : 35 +0:12 +0:0114 0:46 235 ffi : 36
2033 +0:51 +0:0133 0:95 235 ffi : 38 +0:27 +0:0107 0:53 235 ffi : 37 +0:21 +0:0063 0:42 235 ffi : 36
2034 +0:71 +0:0112 0:90 235 ffi : 40 +0:38 +0:0072 0:53 235 ffi : 40 +0:29 +0:0010 0:44 235 ffi : 37
2035 +0:91 +0:0094 0:95 235 ffi : 43 +0:49 +0:0040 0:53 235 ffi : 41 +0:38 \Gamma0:0039 0:39 235 ffi : 35
2036 +0:60 +0:0013 0:52 235 ffi : 41 +0:46 \Gamma0:0079 0:38 235 ffi : 31
2037 +0:71 \Gamma0:0007 0:52 235 ffi : 38 +0:54 \Gamma0:0111 0:40 235 ffi : 26
2038 +0:82 \Gamma0:0021 0:50 235 ffi : 34 +0:62 \Gamma0:0135 0:38 235 ffi : 24
2039 +0:93 \Gamma0:0033 0:50 235 ffi : 33 +0:70 \Gamma0:0158 0:36 235 ffi : 30
2040 +0:78 \Gamma0:0192 0:38 235 ffi : 56
2041 +0:87 \Gamma0:0229 0:41 236 ffi : 73
2042 -- -- -- --
Year Trails 4 revolutions old Trails 5 revolutions old Trails 6 revolutions old
\Deltaa 0 rE \Gamma rD fM
\Omega \Deltaa 0 rE \Gamma rD fM
\Omega \Deltaa 0 rE \Gamma rD
fM\Omega 1798 \Gamma0:09 +0:0044 0:38 232:15 \Gamma0:08 +0:0069 0:29 232:36 \Gamma0:03 \Gamma0:0039 0:11 232:49
1799 \Gamma0:02 +0:0015 0:24 232:80 \Gamma0:01 +0:0015 0:25 232:77 \Gamma0:01 \Gamma0:0001 0:10 232:80
1800 +0:01 +0:0066 0:13 233 ffi : 32 +0:01 +0:0068 0:10 233 ffi : 32 0:00 +0:0083 0:04 233 ffi : 25

88 WGN, the Journal of the IMO 27:2 (1999)
Table 1 -- Data for dust trails (continued).
Year Trails 4 revolutions old Trails 5 revolutions old Trails 6 revolutions old
\Deltaa 0 rE \Gamma rD fM
\Omega \Deltaa 0 rE \Gamma rD fM
\Omega \Deltaa 0 rE \Gamma rD fM
\Omega 1801 +0:03 +0:0114 0:10 233 ffi : 47 +0:03 +0:0114 0:09 233 ffi : 42 +0:01 +0:0144 0:04 233 ffi : 24
1802 +0:06 +0:0139 0:15 233 ffi : 72 +0:05 +0:0134 0:14 233 ffi : 60 +0:02 +0:0174 0:10 233 ffi : 21
1803 +0:08 +0:0218 0:09 234 ffi : 45 +0:08 +0:0213 0:33 234 ffi : 25 +0:04 +0:0252 0:08 233 ffi : 56
1831 \Gamma0:07 +0:0035 0:34 232 ffi : 50 \Gamma0:07 +0:0056 0:42 232 ffi : 34 \Gamma0:07 +0:0091 0:08 232 ffi : 47
1832 \Gamma0:01 +0:0012 0:20 233 ffi : 10 \Gamma0:01 +0:0011 0:17 233 ffi : 09 \Gamma0:01 +0:0010 0:16 233 ffi : 07
1833 +0:02 +0:0010 -- 233 ffi : 47 -- -- -- -- -- -- -- --
1834 +0:05 +0:0013 0:12 233 ffi : 69 +0:03 +0:0022 0:08 233 ffi : 61 +0:02 +0:0023 0:07 233 ffi : 56
1835 +0:08 +0:0013 0:13 233 ffi : 90 +0:05 +0:0021 0:10 233 ffi : 72 +0:04 +0:0018 0:10 233 ffi : 63
1836 +0:11 +0:0022 0:12 234 ffi : 50 +0:07 +0:0032 0:09 234 ffi : 27 +0:06 +0:0029 0:09 234 ffi : 17
1864 \Gamma0:09 +0:0178 0:37 233 ffi : 93 -- -- -- -- \Gamma0:08 +0:0188 0:61 233 ffi : 07
1865 -- -- -- -- -- -- -- -- -- -- -- --
1866 +0:06 \Gamma0:0004 0:37 233 ffi : 33 +0:02 +0:0029 -- 233 ffi : 60 -- -- -- --
1867 +0:14 \Gamma0:0093 0:44 233 ffi : 51 +0:05 \Gamma0:0019 0:12 233 ffi : 93 +0:03 \Gamma0:0010 0:08 233 ffi : 86
1868 +0:21 \Gamma0:0147 0:35 234 ffi : 22 +0:07 \Gamma0:0037 0:12 234 ffi : 73 +0:05 \Gamma0:0030 0:10 234 ffi : 56
1869 +0:29 \Gamma0:0078 0:36 234 ffi : 05 +0:10 +0:0058 0:13 234 ffi : 80 +0:07 +0:0069 0:10 234 ffi : 62
1897 \Gamma0:10 +0:0023 0:12 235 ffi : 45 \Gamma0:09 +0:0039 0:17 235 ffi : 54 \Gamma0:07 +0:0008 0:17 234 ffi : 85
1898 \Gamma0:05 +0:0187 0:35 235 ffi : 12 \Gamma0:05 +0:0201 0:36 235 ffi : 17 \Gamma0:03 +0:0187 -- 234 ffi : 91
1899 +0:02 +0:0119 0:36 234 ffi : 97 +0:02 +0:0110 0:34 234 ffi : 98 +0:01 +0:0124 0:15 235 ffi : 13
1900 +0:10 +0:0145 0:59 234 ffi : 05 +0:10 +0:0112 0:35 234 ffi : 11 +0:04 +0:0165 0:05 234 ffi : 49
1901 +0:17 +0:0048 0:40 233 ffi : 87 +0:18 \Gamma0:0017 0:49 234 ffi : 11 +0:06 +0:0077 0:14 234 ffi : 67
1902 +0:25 +0:0044 0:24 234 ffi : 46 +0:24 +0:0062 0:44 234 ffi : 69 +0:09 +0:0187 0:11 235 ffi : 14
1930 \Gamma0:10 +0:0011 0:23 235 ffi : 55 \Gamma0:08 +0:0018 0:18 235 ffi : 70 \Gamma0:08 +0:0031 0:16 235 ffi : 82
1931 \Gamma0:05 +0:0134 0:31 235 ffi : 26 \Gamma0:05 +0:0143 0:13 235 ffi : 40 \Gamma0:05 +0:0154 0:24 235 ffi : 54
1932 +0:02 +0:0058 0:25 235 ffi : 48 +0:02 +0:0054 0:23 235 ffi : 52 +0:02 +0:0049 0:23 235 ffi : 57
1933 +0:05 +0:0137 0:13 235 ffi : 98 +0:05 +0:0132 0:12 235 ffi : 96 +0:05 +0:0121 0:15 235 ffi : 95
1934 +0:08 +0:0175 0:25 235 ffi : 81 +0:08 +0:0158 0:23 235 ffi : 69 +0:09 +0:0128 0:28 235 ffi : 59
1935 +0:14 +0:0299 0:35 235 ffi : 43 -- -- -- -- -- -- -- --
1961 \Gamma0:20 +0:0126 0:26 235 ffi : 42 \Gamma0:14 +0:0124 0:12 235 ffi : 90 \Gamma0:12 +0:0122 0:08 236 ffi : 07
1962 \Gamma0:14 +0:0054 0:32 235 ffi : 31 \Gamma0:12 +0:0064 0:20 235 ffi : 59 -- -- -- --
1963 \Gamma0:09 +0:0111 0:19 235 ffi : 48 \Gamma0:08 +0:0087 0:16 235 ffi : 66 -- -- -- --
1964 \Gamma0:04 +0:0088 0:04 234 ffi : 99 -- -- -- -- \Gamma0:04 +0:0128 0:27 235 ffi : 30
1965 +0:03 +0:0018 0:21 235 ffi : 57 +0:02 +0:0019 0:19 235 ffi : 66 +0:02 +0:0016 0:04 235 ffi : 71
1966 +0:06 +0:0051 0:11 236 ffi : 00 +0:05 +0:0056 0:09 236 ffi : 02 +0:04 +0:0053 0:08 236 ffi : 03
1967 +0:08 +0:0082 0:11 236 ffi : 10 +0:06 +0:0084 0:10 236 ffi : 04 +0:06 +0:0075 0:14 235 ffi : 98
1968 +0:11 +0:0096 0:16 236 ffi : 30 -- -- -- -- -- -- -- --
1969 +0:13 +0:0157 0:11 237 ffi : 00 +0:12 +0:0157 0:12 236 ffi : 81 +0:13 +0:0135 0:17 236 ffi : 60
1996 \Gamma0:10 +0:0215 0:33 235 ffi : 15 \Gamma0:08 +0:0217 0:18 235 ffi : 55 \Gamma0:07 +0:0195 0:14 235 ffi : 78
1997 \Gamma0:03 +0:0107 0:40 235 ffi : 14 \Gamma0:03 +0:0130 0:59 235 ffi : 11 -- -- -- --
1998 +0:04 +0:0040 0:29 235 ffi : 63 +0:03 +0:0044 0:18 235 ffi : 79 +0:03 +0:0044 0:04 235 ffi : 85
1999 +0:08 +0:0016 0:17 236 ffi : 04 +0:06 +0:0034 0:10 236 ffi : 13 +0:05 +0:0039 -- 236 ffi : 16
2000 +0:11 +0:0008 0:13 236 ffi : 28 +0:07 +0:0028 0:09 236 ffi : 23 +0:06 +0:0030 0:08 236 ffi : 19
2001 +0:14 +0:0002 0:13 236 ffi : 46 +0:09 +0:0017 0:11 236 ffi : 29 +0:08 +0:0014 0:13 236 ffi : 20
2002 +0:17 0:0000 0:15 236 ffi : 89 +0:12 +0:0015 0:12 236 ffi : 72 +0:11 +0:0014 0:13 236 ffi : 67
2003 +0:20 +0:0031 0:10 237 ffi : 62 +0:14 +0:0059 0:08 237 ffi : 29 +0:12 +0:0062 0:08 237 ffi : 12
2029 \Gamma0:11 +0:0144 0:49 236 ffi : 02 \Gamma0:12 +0:0228 0:34 236 ffi : 05 \Gamma0:09 +0:0204 0:19 236 ffi : 53
2030 \Gamma0:04 +0:0242 0:38 236 ffi : 21 -- -- -- -- \Gamma0:05 +0:0321 0:50 236 ffi : 18
2031 +0:03 +0:0161 0:36 235 ffi : 42 -- -- -- -- +0:03 +0:0150 -- 235 ffi : 84
2032 +0:11 +0:0086 0:36 235 ffi : 36 +0:07 +0:0092 0:14 236 ffi : 02 +0:05 +0:0107 0:10 236 ffi : 15
2033 +0:18 +0:0016 0:35 235 ffi : 39 +0:11 +0:0054 -- 236 ffi : 29 +0:07 +0:0072 0:09 236 ffi : 29
2034 +0:25 \Gamma0:0054 0:36 235 ffi : 43 +0:13 +0:0012 0:13 236 ffi : 46 +0:09 +0:0028 0:10 236 ffi : 33
Year Trails 7 revolutions old Trails 8 revolutions old
\Deltaa 0 rE \Gamma rD fM
\Omega \Deltaa 0 rE \Gamma rD fM
\Omega 1832 0:00 +0:0004 0:06 233 ffi : 09
2000 +0:06 +0:0008 0:27 236 ffi : 10
2001 +0:08 \Gamma0:0004 -- 236 ffi : 11

WGN, the Journal of the IMO 27:2 (1999) 89
3. Use of comet and dust node to predict peak time
Much of the uncertainty in predicting Leonid storms in the past has been due to the reliance on
the comet's nodal longitude and distance, to predict activity. Based on the dust trail data in
[6] and the observed times of maxima in [13], it has been shown [14] that the comet's orbit only
gives a first approximation to predicting storms, but that the dust trails represent the time of
maximum of a storm to within the uncertainty of the observed maximum (\Sigma8 minutes in the
best observed cases).
It must be stated that the priority in these calculations belongs to Reznikov for the general
technique and to Kondrat'eva, Murav'eva, and Reznikov [5] for application to the Leonids.
However, the independent work by Asher [6] provided a resolution in nodal longitude of 0 ffi : 01
(about 15 minutes) as opposed to the ¸ 0 ffi : 1 (2.4 hours) of [5]. It is this additional resolution in
the nodal longitude that has allowed a critical check on past showers [14] and gives us reason to
be confident in predicting the time of maximum of future Leonid storms. The results in [6] and
in this paper confirm the times and distances of encounters given in [5] with only some minor
differences. Between 100 and 200 years in the past, there appears to be a slight but systematic
and unexplained difference in encounter distance (r E \Gamma r D ) of between +0:0001 and +0:0002 AU
([5] relative to [6]). One date in [5] appears to be wrong: from [6], we find November 13.8 UT for
1802, whereas Kondrat'eva et al. [5] have November 13.2 UT, possibly duplicated in error from
their line immediately above. The encounter distance for the 1866 trail in 2000 is misprinted in
[5] and should be +0:00078 AU (Emel'yanenko, private communication), confirmed in Table 1.
The validity of a 5th decimal in r D is questionable as a result of various unconsidered factors
like ejection away from perihelion and solar radiation pressure. Preliminary simulations incor­
porating these suggest that the structure of the dust trail is not uniform. On these grounds,
we believe the true center of the dust trail is slightly beyond r D , but that the peak density is
towards the inside of the trail (see Figure 1, later). For these reasons, the 5th decimal in r D is
only partly justifiable. Comparison of our values of r E \Gamma r D and those in [5] also suggest the
differences in this 5th decimal are partly random.
In Table 2, the observed and calculated nodes are given to 3 decimal places for the four showers
with well­observed maxima. The simulations just mentioned suggest that the longitude is less
sensitive to the unconsidered factors than r D is, and, even if the accuracy is not quite 1 in the
3rd decimal, the very small residuals against the observed time of maximum given in [13] seem
instructive. Even the worst of these well­defined maxima has an O\GammaC of only 7 minutes! The
maximum in 1833 is poorly defined and the large residual (45 minutes) may be unimportant.
McNaught [14] showed that, for years with maximum ZHR smaller than around 500, the time of
maximum may be poorly defined using predictions based on distant dust trails. This is largely
a result of the background dominating the activity curve. However, hidden within the activity,
a peak due to the dust trails (the ``storm peak'') can sometimes be discerned. This was the case
in 1965 and 1998 with a peak of faint meteors present close to the correct longitude, but of lower
rates than the fireball shower. Several years from the comet's return, when the background rates
of Leonids are sufficiently low, a close approach to a dust trail can produce a distinct, short­lived
and well­predictable shower. This occurred in 1969 [13], when the observed peak reached a ZHR
of 300, and differed in time by only 7 minutes from the calculated dust trail node.
4. Storms since 1833
Over the next four years, the Earth will closely encounter individual dust trails at various
distances. To predict the circumstances, it is necessary to examine the past close approaches to
such dust trails. Table 2 lists the circumstances of storms using the dust trail data from Table 1
and the observed ZHR from [13]. The ZHRs quoted in [13] are not fully corrected owing to
the heterogeneous data and lack of information in many of the primary sources used, but the
uniform analysis by Brown makes the data set as uniform as might ever be expected. The data
for 1867 have been adjusted to correct for moonlight interference using the value suggested in
[13].

90 WGN, the Journal of the IMO 27:2 (1999)
Table 2 -- Data for storms (excluding 1799 and 1832) and the well­defined 1969 outburst.
Year Trail Obs. node Calc. node O \Gamma C \Deltaa 0 r E \Gamma r D f M ZHR
(J2000) (J2000) (AU) (AU)
1966 2 rev 235 ffi : 160 235 ffi : 158 +0 ffi : 002 +0:17 \Gamma0:00014 0:52 90 000
1833 1 rev 233 ffi : 15 233 ffi : 184 \Gamma0 ffi : 03 +0:17 \Gamma0:00029 0:95 60 000
1866 4 rev 233 ffi : 337 233 ffi : 333 +0 ffi : 004 +0:06 \Gamma0:00036 0:37 8 000
1867 1 rev 233 ffi : 423 233 ffi : 420 +0 ffi : 003 +0:37 \Gamma0:00021 1:00 4 500
1969 1 rev 235 ffi : 277 235 ffi : 272 +0 ffi : 005 +0:93 \Gamma0:00005 0:95 300
Since 1833, specific attention has been paid to recording Leonid activity; so, looking for other
years that had close approaches to dust trails would be a useful check on the validity of using
the dust trails as the main predictor of high activity. The circumstances of encounter with trails
up to 6 revolutions old and passing within 0:0010 AU of the Earth are given in Table 3.
Table 3 -- All additional approaches to dust trails since 1833 that are within 0:0010 AU and up to 6
revolutions old.
Year Trail Obs. node Calc. node O \Gamma C \Deltaa 0 r E \Gamma r D fM ZHR
(J2000) (J2000) (AU) (AU)
1869 3 rev 233 ffi : 533 \Lambda 233 ffi : 536 \Gamma0 ffi : 003 \Lambda +0:32 \Gamma0:00053 0:44 1 000
1897 6 rev 234 ffi : 852 \Gamma0:07 +0:00079 0:17
1897 2 rev 234 ffi : 929 \Gamma0:18 +0:00075 0:43
1968 1 rev 235 ffi : 65 235 ffi : 147 +0 ffi : 50 +0:73 +0:00095 0:95 ¸ 110
\Lambda Time assumed to be local and converted from longitude. See text.
Activity in 1869 could have been expected around November 14.02 UT from western Asia,
eastern Europe, and the Middle East. This shower is mentioned by Kronk [15], and the author
was contacted regarding the details. We are most indebted to Gary Kronk for his immediate
reply giving the full text from his primary reference [16]. Mr. Meldrum and six other observers
at Port Louis Observatory and other parts of the island of Mauritius in the Indian Ocean made
a specific watch for Leonids on the nights of November 12­13, 13­14, and 14­15. It was on the
morning of the November 13­14 night, just at the start of twilight that the peak was observed.
Meldrum wrote the following:
``I have not had time to analyze the observations carefully, but the time of maximum
intensity was about 4 h 09 m a.m. The only source of doubt in this subject arises from
the circumstance that after 4 h 15 m daylight was setting in.''
Observations continued until 4 h 40 m a.m. On the assumption that the time system used was
local, as was the function of such observatories for the setting of ship's chronometers, we have
corrected these times to UT using a longitude of – = 57 ffi 30 0 for Port Louis as given in the
Times Atlas of the World . This is 3 h 50 m ahead of UT, and the observed time of maximum
converts to November 14, 0 h 19 m UT. The calculated longitude for the responsible dust trail was
– fi = 233 ffi : 536 (J2000), which converts to November 14, 0 h 24 m UT. As Meldrum notes that
twilight could have affected the time of maximum, the influence through loss of meteors in the
morning twilight would act to make the true maximum later than observed, if it had any influence
at all. This could bring the observed and predicted times into even closer agreement. Nautical
twilight is calculated to have started at 4 h 20 m a.m., in accord with Meldrum's statement.
Meldrum quotes a number of watch durations and meteor counts from which an effective ZHR
at maximum of close to 1000 seems to be a reasonable conclusion after making appropriate
corrections for factors they mention. It is probable that the rates at maximum were double
those half an hour earlier. A fuller account of this shower will be presented as a separate paper.

WGN, the Journal of the IMO 27:2 (1999) 91
The two trails in 1897 represent meteoroids on orbits with smaller semi­major axis than 55P/Tem­
pel­Tuttle, something that is known to be less common following ejection. Hasegawa [17] men­
tions strong activity as seen from Beijing Observatory on November 14--15, 1897, but the maxima
predicted from the dust trails are November 15.50 and November 15.57. These would have been
visible from western North America, but it would appear that nothing substantial was observed.
The trail in 1968 is of meteoroids with high ejection velocity, although of lower velocity than in
the 1969 outburst. This trail and the two trails of 1897 are not approached closely. With values
of \Deltaa 0 somewhat outside the range of known storms no substantial activity would be expected.
The 1­revolution trail in 1968 is evidently not what was observed at longitude – fi = 235 ffi : 65.
5. A model of the relative spatial density
As noted in the Introduction, Leonid storms can result from two causes: close approaches to a
single recent dust trail or an encounter with the dense resonant zone. As the storms of 1799
and 1832 were rich in fireballs and probably contain a component of such resonant meteoroids,
they are excluded from this analysis. It is also clear from [5] that both these storms comprised
encounters with multiple dust trails.
Here, making the assumption that all recent dust trails are created equal, an attempt is made
to fit the dust trail parameters, \Deltaa 0 , r E \Gamma r D , and f M , of the storms listed in Tables 2 and 3, to
the observed ZHR. If this can be done, then storm ZHRs can be predicted.
All the observed storms had small negative values of r E \Gamma r D . This need have no special signif­
icance as there simply happen to be no values of r E \Gamma r D between \Gamma0:0001 and +0:0008 since
1833. The values for 1799 and 1832 were \Gamma0:0005 and +0:0005, respectively, for the several dust
trails given in [5] that are older than the ones we considered here. An attempt to fit the observed
ZHRs for storms was made initially on the assumption that the density profile in r E \Gamma r D is a
Gaussian distribution centered on zero. The simulations mentioned earlier (Section 3) produce
an elliptical cross section on intersection with the ecliptic, but with a concentration towards the
inside of the ellipse (Figure 1). Thus, calculations were also made with the center of the dust
trail at distances r D + 0:0001 AU and r D + 0:0002 AU, values that seem appropriate for the
possible outward shift of the trail center.
Figure 1 -- Cross section in (x; y) ecliptic coordinates of trail generated in 1899, at epoch of ejection and
at nodal crossing in 1999. Initial elements of particles were generated by assuming ejection
uniform in true anomaly, isotropic, and at 25=r m/s (cf. Figure 2), but only particles with
appropriate a 0 were integrated and plotted. In the 1899 plot, the cross is the comet's node
(which is in a different part of the ecliptic and so not on the 1999 plot). The line on the
1999 plot is the Earth's orbit; slightly higher ejection speeds would bring orbits to Earth
intersection.

92 WGN, the Journal of the IMO 27:2 (1999)
To fit the observed ZHR to the dust trails, it is necessary to have a relationship defining the
relative spatial density of the trails. In a given trail encounter, particles have a tightly constrained
value of \Deltaa 0 (Section 2). Therefore, trails' relative densities depend on the relative amount of
material ejected on to orbits with different values of \Deltaa 0 (Figure 2), with an effective value of
\Deltaa 0 of about +0:2, believed to be a good representation for the bulk of the meteoroids in the
stream that are of a size that produce visual meteors. Lower and higher values of \Deltaa 0 will be
represented by lower spatial densities and also by a variation in mass. Higher mass meteoroids
will tend to be at values of \Deltaa 0 closer to zero.
The initial density is diluted by the stretching of the trail as it evolves. The contribution of this
stretching factor to the density can be derived from integrations. Unlike the r E \Gamma r D and \Deltaa 0
factors, it is not dependent on the ejection model, and no parameters need fitting. To calculate
the stretch of a particular trail, a few particles were ejected at perihelion with orbits identical
except for increments in e of 0:000 001, all of which crossed the ecliptic very close to the correct
time in November in the relevant year (Earth encounter occurring if jr E \Gamma r D j is small). The
average difference in mean anomaly M between these particles at the time of encounter gives
an indication of the linear stretching, and we introduce a ``mean anomaly factor'' f M (Table 1)
which decreases as the stretch increases.
Examination of Figure 1 indicates that, to a high degree of accuracy, the dispersion in the other
elements does not increase from that at formation during the early evolution of dust trails. It
would appear, therefore, that the spatial density decreases linearly with the stretch in M . Thus
the variable that is fitted is ZHR=fM , where f M normalizes the data to the median stretch value
of a 1­revolution trail. No account of dispersion of particles with size due to radiation pressure
is considered although it undoubtedly occurs and has the effect of a small outward shift of the
center. This would indicate that the mass index will be higher for encounters at positive r E \Gamma r D .
Figure 2 -- Initial distribution in semi­major axis of particles ejected uniformly in true anomaly within
heliocentric distance r ! 3:4 AU, ejection velocities being isotropic at 25=r m/s. This is prob­
ably a reasonable ejection model (see [18]) but there are still free parameters. For example,
lower ejection velocities would narrow the distribution. The distribution is centered on the
comet's a 0 . Particles affected by radiation pressure having the same a 0 as the comet will fall
behind the comet, i.e., their effective value of a 0 will be greater. This shifts the distribution
to the right, but the shift depends on the radiation pressure parameter, which varies among
meteoroids. However, to keep our model manageable, it appears acceptable to use a Gaussian
distribution, with mean and dispersion to be fitted.

WGN, the Journal of the IMO 27:2 (1999) 93
The fit to the data was by a two dimensional Gaussian profile to \Deltaa 0 and r E \Gamma r D . With the
observed ZHR being only proportionately correct, a least­squares fit to the fractional residuals
was made. This put the maximum in \Deltaa 0 at +0:16 to +0:17 for radial profiles with the center
assumed to be in the range r D to r D +0:0002 AU. These fits are good for most of the storm data
(mean fractional error 10--15%). These data and the observed ZHRs (normalized to 1 revolution)
are plotted in Figure 3. It is clear that there is both a paucity of data and a paucity of potential
data from past encounters to help refine the fit. The center of the Gaussian can be fitted to a
center as small as r D \Gamma 0:0002 AU, but with errors of around 25%. Larger values of r E \Gamma r D
are fitted with decreasing errors, but then an anomaly arises that a major storm should have
occurred over western Europe in 1801, when at present no activity is known. This is discussed
later (Section 7).
The parameters of the fit are given in Table 4. The peak ZHR is the rate that would be
encountered by passage through the center of a 1­revolution old dust trail. This potential peak
value has to be reduced by the f M for a specific dust trail.
Table 4 also displays the drop off in rates over the radius of the Earth (0.000043 AU) on the flanks
of the profile of a 1­revolution trail. This has significance in the global analysis of meteor rates.
The effect is modified by f M for older trails, and would have to be calculated individually for
every storm. With the indication that parts at least of dust trails retain their shape over many
revolutions (at least in the case of the Leonid trail cross section simulation mentioned here), this
effect will have to be considered for a short outburst from any shower. The center and shape of
the profile would have to be known for the specific correction factor to be calculated.
Figure 3 -- Variation of ZHR with the three parameters, r E \Gamma r D , \Deltaa 0 , and fM , given in Table 1. As the effect of
fM on the ZHR is calculable from integrations, ZHR=fM is fitted to r E \Gamma r D and \Deltaa 0 . The five solid
squares are the points (Tables 2 and 3) used to derive the fit (observed ZHR=fM in parentheses), and
the elliptical contours represent the fit itself. Three fits have been done, successively assumed to be
centered on r D , r D + 0:0001 AU, and r D + 0:0002 AU, shown as lines of decreasing thickness. In each
case the inner, middle, and outer contours correspond respectively to values of ZHR=fM of 10 5 , 10 4 ,
and 10 3 . Larger squares are drawn for larger values of f M , the size of square being illustrated for
values of fM of 1.0, 0.5, and 0.25. Multiplying the fitted ZHR/fM by fM gives the estimated ZHR.

94 WGN, the Journal of the IMO 27:2 (1999)
Table 4 -- Characteristics and consequences of the fit. Fit 0 is centered radially on r D , Fit 1 on r D +
0:0001 AU, and Fit 2 on r D + 0:0002 AU.
Fit Mean Peak ZHR \Deltaa 0 FWHM FWHM Percentage drop over 1 Earth radius
no. fractional \Deltaa 0 r at distance from trail center, AU
error, %
0:0002 0:0004 0:0006 0:0008
0 14 160 000 +0:17 0:19 0:00056 13% 25% 35% 45%
1 11 210 000 +0:16 0:19 0:00062 10% 21% 30% 37%
2 10 290 000 +0:16 0:19 0:00064 8% 17% 25% 32%
Extrapolation of the double Gaussian storm profile predicts a ZHR of zero for the 1­revolution
trail encountered in 1969, when, as mentioned, the observed peak ZHR was 300. This is hardly
surprising, with the sparse and unreliable data used in the fit, and the likelihood that a Gaussian
is not a good representation of the spread in \Deltaa 0 this far from the dense storm region. The wings
of the Gaussian profiles represented in [13] in every case show activity enhanced above the profile.
Whilst the storm peak seems well represented, it appears necessary to use another profile for
the overall structure of the dust trail. One such attempt has been made by Jenniskens [19].
6. Predicting time and ZHR of maximum
Encounters at the current epoch
Figure 4 shows that some of the dust trails encountered in the next few years, 1999, 2001 (7­
revolution), and 2002, can be interpolated or reasonably extrapolated from the existing data (cf.
Figure 3).
Figure 4 -- Values of r E \Gamma r D , \Deltaa 0 , and f M (Table 1) for future trails plotted against the fitted contours of
Figure 3. The estimated value of ZHR=fM is shown by a point's position relative to the contours (see
caption to Figure 3), and this should be multiplied by f M (shown by size of square as in Figure 3) to
yield the ZHR.

WGN, the Journal of the IMO 27:2 (1999) 95
It is also clear that several trails will be encountered in the previously unobserved zone, 2000
and 2001 (4­revolution). The trails in 2000 probably lie beyond the uncertain peak and on the
steep descending profile, making any rate prediction for these years rather uncertain. As previ­
ously mentioned, the effect of radiation pressure may increase the number of smaller meteoroids
encountered in these years.
The data from each year will allow the fit to be recalculated, or a better model developed. It
is possible that before the potential storms of 2001 and 2002 the predictions could be very well
defined.
Based on the dust trail parameters in Table 5, predictions for the next few years are given in
Table 6. As the trails encountered in 1999 and 2000 (8­revolution) were responsible for the
1966 and 1866 storms, respectively, we should be confident that the cores of these streams are
dense. Trails that have never previously been encountered are assumed to be similar to other
trails and for our simple analysis all are necessarily assumed equal. Encounters with the same
trails at different values of \Deltaa 0 will allow the structure and evolution of specific dust trails to
be investigated.
Table 5 -- Circumstances of dust trail encounters for the current epoch. The last
column indicates previous encounters with the same dust trail.
Year Trail \Deltaa 0 r E \Gamma r D fM Previous encounters
1999 3 rev +0:14 \Gamma0:00066 0:38 1966 storm
2000 8 rev +0:06 +0:00077 ¸ 0:27 1866 storm
2000 4 rev +0:11 +0:00077 0:13 none
2001 7 rev +0:08 \Gamma0:00043 ¸ 0:14 1869 storm, 1893 \Lambda
2001 4 rev +0:14 +0:00022 0:13 none
2002 4 rev +0:17 \Gamma0:00005 0:15 none
2006 2 rev +0:96 \Gamma0:00009 0:53 1969
\Lambda Mentioned in [5] (\Deltaa 0 = \Gamma0:10, r E \Gamma r D = \Gamma0:00019).
Outside range of years considered as potentially storm­producing.
Table 6 -- Predictions for the current return of 55P/Tempel­Tuttle.
Time (UT) Estimated ZHR Trail Moon age Visible from
1999, Nov 18.089 (02 h 08 m ) 1500 3 rev 10 Europe, Middle East, Africa
2000, Nov 18.156 (03 h 44 m ) 100--5000? 8 rev 22 Europe, Africa
2000, Nov 18.327 (07 h 51 m ) 100--5000 4 rev 22 E. USA, E. Canada, Atlantic
2001, Nov 18.417 (10 h 01 m ) 2500? 7 rev 3 Americas
2001, Nov 18.763 (18 h 19 m ) 10000--35000 4 rev 3 E. Asia, W. Pacific, Australia
2002, Nov 19.442 (10 h 36 m ) 25000 4 rev 15 Americas
2006, Nov 19.198 (04 h 45 m ) 150 2 rev 28 W. Europe, W. Africa
The 8­revolution trail in 2000 has nearby sections both in front and behind that have been
disrupted owing to close approaches to Earth between 1733 and the present, albeit the section
with the critical mean anomaly for intersection with the Earth should just survive. For the
7­revolution trail in 2001, f M is quite rapidly varying at the critical M . The derived ZHRs for
these two trails are therefore denoted with a question mark in Table 6. No other close encounters
to dust trails 6 or less revolutions old occur prior to 1999 in the current return of 55P, consistent
with observations. Kondrat'eva et al. [5] do mention an 8­revolution trail on 1991 Nov 20.2 UT
at \Deltaa 0 = \Gamma0:16 and r E \Gamma r D = \Gamma0:00041. We would expect activity from this to have been low,
but probably detectable.
The time of maximum is derived from the nodal longitude of the dust trails. The uncertainty of
these predictions is probably better than 10 minutes (see Tables 2 and 3 and reference [14]).

96 WGN, the Journal of the IMO 27:2 (1999)
ZHR predictions may be ``reliable'' (within a factor of 2?) for 1999 and 2002. It is in the region
of Figure 3 at positive r E \Gamma r D that the data are extrapolated with the largest uncertainty. This
includes the 4­ and 8­revolution trails in 2000 and the same 4­revolution trail in 2001.
Observations in 1999 may not affect the predictions for following years, due to the constraining
effect of the steeply rising profile fitted through the storm data. However, the observations of
the trails in 2000 should dramatically lower the uncertainty for future years. One especially
interesting feature is that the same (4­revolution) trail will be encountered in 2000, 2001, and
2002. Following observation in 2000, predictions for this trail in 2001 and 2002 should be
especially well­defined. The assumption that all trails are created equal is certainly the case
here, although the mass distribution will probably change over the three years and will be an
important observational result.
In 2006, the Earth encounters an adjoining section of the same dust trail that produced the 1969
outburst. The circumstances in these two years are almost identical, but the stretch in M is
double in 2006, giving a prediction of half the ZHR of 1969. This prediction is unrelated to the
profile fitted to the storm data.
The Last­Quarter Moon will reduce the observed rates in 2000 and the near­Full Moon will be
a bigger problem in 2002. The highest observable rates at this epoch may be in 2001, despite
the uncertain rates, as no moonlight will be present.
Encounters around the 2031 return
It has long been assumed that no significant activity could occur around the next perihelion
passage of 55P/Tempel­Tuttle. However, this conclusion was based on the use of the comet's
orbit alone. The data in Table 7 are for three outlying trails approached in 2033 and 2034.
These are plotted in Figure 4. Unfortunately, they are probably too distant for any reasonable
chance of high activity, but, again, the region is one of very uncertain extrapolation. Predictions
based on this data appear in Table 8. The substantial data that can be gathered between 1999
and 2006, with seven close approaches to dust trails during that period, should allow a realistic
assessment of activity to be made before this next return. In particular, the possibility of a storm
in 2034 will likely be decided by the strength of activity in 2000. The prediction of zero ZHR is
from an unreasonable extrapolation of the model, and it refers only to that particular dust trail
and not the shower that year as a whole. Some activity from such a dust trail will probably
occur, but strong activity is highly improbable. Background activity will still be present, but
this will also be rather uncertain in the changed circumstances.
Table 7 -- Circumstances of dust trail encounters for next return of 55P/Tem­
pel­Tuttle. The last column indicates previous encounters with the
same dust trail.
Year Trail \Deltaa 0 r E \Gamma r D fM Previous encounters
2033 4 rev +0:18 +0:00161 0:35 1966 storm, 1999
2034 3 rev +0:29 +0:00098 0:44 1969, 2006
2034 5 rev +0:13 +0:00119 0:13 2000, 2001, 2002
Table 8 -- Predictions for the next return of 55P/Tempel­Tuttle.
Time (UT) Estimated ZHR Trail Moon age Visible from
2033, Nov 17.904 (21 h 42 m ) 0 4 rev 26 E. Asia, W. Pacific,
W. Australia
2034, Nov 18.139 (03 h 20 m ) 0--1000 3 rev 7 Europe, Africa
2034, Nov 19.222 (05 h 19 m ) 0--100 5 rev 8 W. Europe, W. Africa

WGN, the Journal of the IMO 27:2 (1999) 97
7. Historical studies
The form of this analysis could profitably be carried back to examine the dust trail characteristics
of Leonid storms throughout history. This would provide more data on the parameters relevant
to storm production and give information on dust trail evolution. In fact, such data could
locate the position of the center of the dust trail. They could also be used to check the dates
ascribed to storms from historical references. Some apparent discrepancies between dates of
storms as reported in different parts of the world could conceivably be the result of multiple
storms separated by a day or more.
The circumstances of approaches to Leonid dust trails within 0.005 AU in the last 200 years and
up to the year 2039 are given in Table 9. This lists the encounters in chronological order giving
the nodal crossing time, revolution number, and the ZHR derived from the fits to the storm data
using three assumed center positions. As previously mentioned, a value of zero does not indicate
the Leonid ZHR was zero in that year, but only that the contribution of that specific dust trail
to the overall ZHR was zero. It has also been noted that this extrapolation to well outside the
storm region is unwarranted.
Table 9 -- Predictions of time of nodal crossing and ZHR for individual dust trails up to 6 revo­
lutions old (and selected older ones) passing within 0.0050 AU of the Earth. The three
ZHR predictions are for the highest density in the dust trail assumed to be centered
at r D (ZHR 0 ), r D + 0:0001 AU (ZHR 1 ), and r D + 0:0002 AU (ZHR 2 ). The factor
fM represents the extent of dispersion of the trail relative to the median density of a
1­revolution trail and has been used in the calculation of the ZHRs. The symbol `` \Lambda ''
refers to trail encounters used in the ZHR fit (Section 5).
Date (UT) Trail fM ZHR 0 ZHR 1 ZHR 2 Moon age
1798, Nov 11.431 (10 h 20 m ) 3 0:41 0 0 0 3
1798, Nov 11.431 (10 h 20 m ) 4 0:38 0 0 0 3
1798, Nov 11.772 (18 h 32 m ) 6 0:11 0 0 0 4
1798, Nov 12.317 (07 h 36 m ) 1 1:08 0 0 0 4
1799, Nov 12.306 (07 h 21 m ) 5 0:25 0 0 1 15
1799, Nov 12.339 (08 h 08 m ) 6 0:10 1 500 2 000 2 000 15
1799, Nov 12.336 (08 h 04 m ) 4 0:24 0 0 0 15
1799, Nov 12.377 (09 h 02 m ) 3 0:27 0 0 0 15
1799, Nov 12.567 (13 h 37 m ) 2 0:52 0 0 0 15
1799, Nov 12.575 (13 h 48 m ) 1 1:00 0 0 0 15
1800, Nov 12.823 (19 h 45 m ) 1 1:00 0 0 0 25
1800, Nov 12.856 (20 h 33 m ) 2 0:52 0 0 0 25
1801, Nov 13.065 (01 h 34 m ) 1 0:95 0 0 0 7
1801, Nov 13.211 (05 h 04 m ) 2 0:53 2 500 15 000 50 000 7
1802, Nov 13.344 (08 h 15 m ) 1 0:95 0 0 0 18
1802, Nov 13.795 (19 h 04 m ) 2 0:55 0 1 1 18
1803, Nov 13.737 (17 h 41 m ) 1 0:95 0 0 0 29
1803, Nov 14.995 (23 h 53 m ) 2 0:43 2 2 3 0
1831, Nov 13.244 (05 h 52 m ) 4 0:34 0 0 0 9
1831, Nov 13.897 (21 h 31 m ) 1 1:00 0 0 0 9
1832, Nov 13.076 (01 h 50 m ) 6 0:16 0 10 100 20
1832, Nov 13.088 (02 h 07 m ) 5 0:17 0 6 80 20
1832, Nov 13.091 (02 h 11 m ) 7 0:06 200 800 2 000 20
1832, Nov 13.103 (02 h 28 m ) 4 0:20 0 1 20 20
1832, Nov 13.176 (04 h 14 m ) 2 0:55 0 0 0 20
1832, Nov 13.175 (04 h 13 m ) 1 1:00 0 0 3 20
1832, Nov 13.174 (04 h 11 m ) 3 0:39 0 0 0 20
1833, Nov 13.429 (10 h 17 m ) 2 0:53 0 0 0 2
\Lambda 1833, Nov 13.435 (10 h 26 m ) 1 0:95 70 000 70 000 70 000 2
1833, Nov 13.455 (10 h 56 m ) 3 0:45 0 0 0 2

98 WGN, the Journal of the IMO 27:2 (1999)
Table 9 -- Predictions of time of nodal crossing and ZHR (continued).
Date (UT) Trail fM ZHR 0 ZHR 1 ZHR 2 Moon age
1834, Nov 13.681 (16 h 20 m ) 2 0:52 0 0 0 12
1834, Nov 13.692 (16 h 37 m ) 1 0:95 0 0 0 12
1834, Nov 14.070 (01 h 40 m ) 6 0:07 0 0 0 13
1834, Nov 14.112 (02 h 42 m ) 5 0:08 0 0 0 13
1834, Nov 14.192 (04 h 36 m ) 4 0:12 0 1 15 13
1835, Nov 13.948 (22 h 44 m ) 1 0:95 0 0 0 23
1835, Nov 14.396 (09 h 30 m ) 6 0:10 0 0 0 23
1835, Nov 14.487 (11 h 42 m ) 5 0:10 0 0 0 23
1835, Nov 14.667 (16 h 00 m ) 4 0:13 0 0 15 24
1836, Nov 13.202 (04 h 51 m ) 1 0:95 0 0 0 4
1836, Nov 14.181 (04 h 20 m ) 6 0:09 0 0 0 5
1836, Nov 14.281 (06 h 45 m ) 5 0:09 0 0 0 5
1836, Nov 14.507 (12 h 10 m ) 4 0:12 0 0 0 5
1866, Nov 14.017 (00 h 24 m ) 1 1:00 0 0 0 7
1866, Nov 14.022 (00 h 31 m ) 3 0:40 0 9 200 7
1866, Nov 14.024 (00 h 34 m ) 2 0:55 0 0 0 7
\Lambda 1866, Nov 14.046 (01 h 06 m ) 4 0:37 8 000 8 000 8 000 7
\Lambda 1867, Nov 14.392 (09 h 25 m ) 1 1:00 4 500 4 500 4 500 18
1867, Nov 14.401 (09 h 38 m ) 2 0:55 0 0 0 18
1867, Nov 14.829 (19 h 54 m ) 6 0:08 1 1 2 18
1867, Nov 14.896 (21 h 30 m ) 5 0:12 0 0 0 18
1868, Nov 14.252 (06 h 02 m ) 2 0:54 0 0 0 29
1868, Nov 14.281 (06 h 45 m ) 1 0:95 0 0 0 29
1868, Nov 14.777 (18 h 39 m ) 6 0:10 0 0 0 30
1868, Nov 14.940 (22 h 33 m ) 5 0:12 0 0 0 30
\Lambda 1869, Nov 14.016 (00 h 24 m ) 3 0:44 900 900 1 000 10
1897, Nov 14.890 (21 h 22 m ) 1 1:00 0 0 0 20
1897, Nov 15.498 (11 h 57 m ) 6 0:17 2 20 100 20
1897, Nov 15.574 (13 h 47 m ) 2 0:45 0 1 4 21
1897, Nov 15.907 (21 h 46 m ) 3 0:25 0 0 0 21
1897, Nov 16.086 (02 h 04 m ) 4 0:12 0 0 0 21
1897, Nov 16.184 (04 h 25 m ) 5 0:17 0 0 0 21
1901, Nov 15.557 (13 h 21 m ) 4 0:40 0 0 0 4
1901, Nov 15.790 (18 h 57 m ) 5 0:49 0 0 0 4
1902, Nov 15.971 (23 h 18 m ) 3 0:45 0 0 0 16
1902, Nov 16.391 (09 h 23 m ) 4 0:24 0 0 0 16
1930, Nov 17.497 (11 h 56 m ) 3 0:32 0 0 0 27
1930, Nov 17.657 (15 h 46 m ) 4 0:23 0 0 2 27
1930, Nov 17.804 (19 h 18 m ) 5 0:18 0 0 0 27
1930, Nov 17.917 (22 h 01 m ) 6 0:16 0 0 0 27
1932, Nov 17.189 (04 h 33 m ) 6 0:23 0 0 0 19
1934, Nov 17.628 (15 h 04 m ) 1 0:95 0 0 0 10
1964, Nov 16.946 (22 h 43 m ) 2 0:53 0 0 0 13
1964, Nov 16.944 (22 h 40 m ) 1 1:00 0 0 0 13
1965, Nov 17.219 (05 h 16 m ) 2 0:59 0 0 0 24
1965, Nov 17.215 (05 h 10 m ) 1 1:00 0 0 0 24
1965, Nov 17.527 (12 h 40 m ) 3 0:37 0 0 1 24
1965, Nov 17.653 (15 h 41 m ) 4 0:21 0 0 0 24
1965, Nov 17.739 (17 h 44 m ) 5 0:19 0 0 0 24
1965, Nov 17.786 (18 h 52 m ) 6 0:04 0 0 0 24
1966, Nov 17.467 (11 h 12 m ) 1 0:95 0 0 1 5
\Lambda 1966, Nov 17.495 (11 h 53 m ) 2 0:52 70 000 75 000 75 000 5
1966, Nov 18.270 (06 h 28 m ) 3 0:19 0 0 0 6

WGN, the Journal of the IMO 27:2 (1999) 99
Table 9 -- Predictions of time of nodal crossing and ZHR (continued).
Date (UT) Trail f M ZHR 0 ZHR 1 ZHR 2 Moon age
1967, Nov 17.721 (17 h 18 m ) 1 0:95 0 0 0 16
1968, Nov 17.000 (23 h 59 m ) 1 0:95 0 0 0 26
1968, Nov 17.293 (07 h 02 m ) 2 0:55 0 0 0 26
1969, Nov 17.374 (08 h 58 m ) 1 0:95 0 0 0 7
1998, Nov 18.168 (04 h 02 m ) 4 0:29 0 0 0 29
1998, Nov 18.329 (07 h 54 m ) 5 0:18 0 0 0 29
1998, Nov 18.392 (09 h 24 m ) 6 0:04 0 0 0 29
1999, Nov 18.072 (01 h 44 m ) 2 0:53 0 0 0 10
1999, Nov 18.078 (01 h 53 m ) 1 0:95 0 0 0 10
1999, Nov 18.089 (02 h 08 m ) 3 0:38 1 200 1 400 1 500 10
1999, Nov 18.830 (19 h 55 m ) 4 0:17 0 0 0 11
1999, Nov 18.916 (21 h 59 m ) 5 0:10 0 0 0 11
2000, Nov 17.329 (07 h 53 m ) 2 0:55 0 0 1 21
2000, Nov 17.348 (08 h 22 m ) 1 0:95 0 0 0 21
2000, Nov 18.156 (03 h 44 m ) 8 0:27 90 1 000 5 000 22
2000, Nov 18.244 (05 h 51 m ) 6 0:08 0 0 0 22
2000, Nov 18.280 (06 h 44 m ) 5 0:09 0 0 0 22
2000, Nov 18.327 (07 h 51 m ) 4 0:13 80 1000 5 000 22
2001, Nov 17.559 (13 h 24 m ) 2 0:52 0 0 0 2
2001, Nov 17.595 (14 h 17 m ) 1 0:95 0 0 0 2
1 2001, Nov 18.417 (10 h 01 m ) 7 0:14 2 500 2 500 2 500 3
2001, Nov 18.505 (12 h 08 m ) 6 0:13 0 0 10 3
2001, Nov 18.595 (14 h 18 m ) 5 0:11 0 0 0 3
2001, Nov 18.763 (18 h 19 m ) 4 0:13 13 000 25 000 35 000 3
2002, Nov 17.842 (20 h 13 m ) 1 0:95 0 0 0 13
2002, Nov 19.225 (05 h 24 m ) 6 0:13 0 0 4 14
2002, Nov 19.274 (06 h 35 m ) 5 0:12 0 0 3 14
2002, Nov 19.442 (10 h 36 m ) 4 0:15 25 000 25 000 30 000 15
2003, Nov 18.100 (02 h 23 m ) 1 0:90 0 0 0 24
2003, Nov 20.425 (10 h 11 m ) 4 0:10 0 0 0 26
2 2006, Nov 19.198 (04 h 45 m ) 2 0:53 150 150 150 28
2025, Nov 19.582 (13 h 58 m ) 3 0:10 0 0 0 29
2033, Nov 17.904 (21 h 42 m ) 4 0:35 0 0 1 26
2034, Nov 18.139 (03 h 20 m ) 3 0:44 4 130 1 200 7
2034, Nov 19.094 (02 h 15 m ) 6 0:10 0 0 0 8
2034, Nov 19.222 (05 h 19 m ) 5 0:13 0 6 120 8
2035, Nov 18.379 (09 h 06 m ) 3 0:39 0 0 0 18
2035, Nov 18.447 (10 h 43 m ) 2 0:53 0 0 0 18
2036, Nov 17.691 (16 h 35 m ) 2 0:52 0 0 0 29
2037, Nov 17.918 (22 h 01 m ) 2 0:52 0 0 0 10
2038, Nov 18.143 (03 h 26 m ) 2 0:50 0 0 0 21
2039, Nov 18.382 (09 h 10 m ) 2 0:50 0 0 0 2
1 The 7­revolution trail in 2001 has a slightly uncertain value of f M causing the predictions
for that year to be additionally uncertain.
2 In 2006, the formal prediction based on the Gaussian fit to \Deltaa 0 predicts a ZHR of 0 as in
1969. However, the circumstances are almost identical as in 1969 and the encounter is with
the same trail. The ZHR given is from the observed 1969 ZHR corrected by f M .
Most years of substantial activity in Table 9 correspond to known showers. One year does stand
out, though. Some activity should have occurred in 1801 from a 2­revolution trail with low
stretch in M . This is of particular interest as the circumstances are similar to both trails in
2000. The r E \Gamma r D of +0:0006 is an intermediate value missing from the encounters since 1833
when more attention has been paid to Leonid activity. A strong shower or minor storm could
have occurred as seen from western Europe or western Africa on November 13.21 UT in 1801.

100 WGN, the Journal of the IMO 27:2 (1999)
An initial examination by Mark Bailey and John McFarland of the observing log of Armagh
Observatory indicates that observations were in progress that night, but no mention was made
of meteor activity. Examination of other records in western Europe and western Africa for that
date would be useful. Reports that can put constraints on the meteor activity at that time will
have a substantial bearing on what to expect over the next several years. It would seem unlikely
that a major storm was overlooked in a moonless sky, and this does tend to rule out Fit 2 and
possibly even Fit 1. This would unfortunately mean that activity in the next several years would
be at the lower end of the predictions.
8. Threat to satellites
Should the Earth pass through the center of a 1­revolution trail at \Deltaa 0 ú +0:17, the predicted
peak ZHR would likely be in the range 150 000--300 000. The higher rates would be predicted
if the maximum density were located beyond our calculated value of r D . Whilst the Earth is
8:6 \Theta 10 \Gamma5 AU in diameter, and presents a small target (nominally, ``collision'' if jr E \Gamma r D j !
4:3 \Theta 10 \Gamma5 AU), the region inhabited by satellites is very much larger. Geostationary (GEO)
satellites can pass through this dense zone of meteoroids when jr E \Gamma r D j ! 2:7 \Theta 10 \Gamma4 AU. This
will occur in 2001 and 2002, when the same 4­revolution trail is encountered.
The maximum density in the center of these trails is likely to have an equivalent ZHR of 20 000--
40 000. These estimates are much lower than what was actually encountered in 1966 (about
90 000), although the effective rates in parts of the GEO region in that year could have been
some 50% higher still. The risk to an individual satellite is probably much lower than in 1966,
when no satellites were damaged, but GEO and low­Earth orbit (LEO) space is now much more
crowded with active satellites.
In 2001, the densest part of the dust trail at the time of encounter is almost certainly near the
GEO satellite belt over the Far­Eastern Pacific. GEOs over the Indian Ocean and Indonesia
will be least affected. Should the densest part of the dust trail be beyond r D , GEO satellites at
intermediate longitudes will be most affected.
The most threatened GEO satellites in 2002 are on the leading (South­American) and trailing
(Indonesian) longitudes of the Earth. If the densest part of the trail is further out than r D , this
will affect GEO satellites closer to the central Pacific. This potential ``direct hit'' of a dust trail
with the Earth in 2002 will result in LEO satellites being directly threatened.
Given that we may be able to predict the time of Leonid maximum activity to a few minutes
accuracy, and that the direction and distance of the closest approach to the dust trail are
known (to a somewhat lesser accuracy), there are two strategies that satellite operators could
use to minimize the threat. These are only available to satellites other than GEOs. The first
is to position the satellite in its orbit furthest from the dust trail at the time of maximum.
This position would be at the satellite's maximum distance towards or away from the Sun, the
Leonid dust stream at its node being nearly perpendicular to the direction of the Sun. For a
circular orbit, this point would be the longitude given in Table 10 for a trail that passes inside
the Earth's orbit (2000, 4­revolution and 8­revolution, and 2001, 4­revolution), but would be
180 ffi opposite (and latitude negated) for trails that pass outside the Earth's orbit (1999 and
2001, 7­revolution). If the peak flux in 2001 and 2002 is encountered on one side of the GEO
belt (either towards or away from the Sun), the other side may only experience about 10% of
that flux.
GEO satellites (0 ffi inclination) will lie some 14 000 km below the ecliptic at the longitude opposite
the Sun. They will experience the peak some 25 minutes earlier than the times given; so the
longitude would be modified by +6 ffi . GEO satellites towards the Sun have maximum 25 minutes
later centered at a longitude – = +174 ffi from that given.

WGN, the Journal of the IMO 27:2 (1999) 101
Table 10 -- Orientation of Earth during forthcoming trail encounters.
Date (UT) Trail Point opposite Sun Center Leonid ``shadow''
– ' – '
1999, Nov 18.089 3 rev 324 ffi E 19 ffi N 245 ffi E 22 ffi S
2000, Nov 18.156 8 rev 300 ffi E 19 ffi N 220 ffi E 22 ffi S
2000, Nov 18.327 4 rev 238 ffi E 19 ffi N 158 ffi E 22 ffi S
2001, Nov 18.417 7 rev 205 ffi E 19 ffi N 126 ffi E 22 ffi S
2001, Nov 18.763 4 rev 80 ffi E 19 ffi N 1 ffi E 22 ffi S
2002, Nov 19.442 4 rev 196 ffi E 19 ffi N 116 ffi E 22 ffi S
The second strategy would apply to satellites whose orbits pass into Leonid ``eclipse.'' For
satellites with this potential geometry, it is simple for the satellite to pass through this zone
at the predicted time of maximum. Slight maneuvers in height are made to alter the mean
anomaly to the appropriate value. The satellite would then maximize its time in the shadow,
shielded from any storm. The maximum duration a satellite could be in the Earth's shadow is
around 36 minutes for LEO satellites out to around 5000 km. Above this, the duration increases,
reaching 70 minutes at GEO distances. However, GEO satellites, with inclinations of 0 ffi , orbit
totally outside the Leonid shadow. Estimates of several storms (given in [13]) give a FWHM
of around 0 ffi : 011 to 0 ffi : 022 in solar longitude (15 to 30 minutes). Given a probable uncertainty
in the predicted time of maximum of less than 10 minutes, a satellite with optimum geometry,
placing it in the middle of the Leonid ``shadow'' at the time of predicted maximum, would have
a vastly reduced overall threat.
One possible caveat is that, as a satellite enters and leaves the Leonid shadow, meteoroids will
be encountered that have passed through the Earth's tenuous outer atmosphere. It might be
expected that a dustball structure would fragment under such circumstances increasing the flux
of particles in this narrow zone. The maximum gravitational deflection such a Leonid would
experience on skirting the atmosphere is 1 ffi : 4.
Satellites a considerable distance perpendicularly out of the ecliptic will have the time of en­
counter altered by 1.8 minutes per 1000 km. This is earlier than the predicted maximum if below
the ecliptic and later if above. The cause is the 163 ffi inclination of the dust trail to the ecliptic.
GEO satellites at the same (opposite) longitude as the Sun during the Leonids are 14 000 km
above (below) the ecliptic and will thus experience the peak some 25 minutes after (before) the
Earth. GEO satellites leading (trailing) the Earth have the maximum about 40 minutes earlier
(later). This interval is partly due to the GEO satellites in these directions being over 9000 km
out of the ecliptic, but also being in front of (behind) the Earth in its orbit. GEO satellites
ahead and behind the Earth will experience identical rates, unless passage through the near­
Earth environment led to a breakup of particles. The trailing GEO satellites are well outside
the Leonid shadow.
9. Conclusion
Study of the perturbed motion of dust trails from 55P/Tempel­Tuttle indicates that the Earth
will begin a series of close approaches to trails starting with a possible minor storm in 1999.
Storms can be expected in the years 2001 and 2002, but estimation of their intensity is strongly
limited by the lack of observational data. The effect of the Full Moon in 2002 will reduce the
observed rates making 2001 potentially the year of highest observed rates at this epoch.
During the next return, activity is likely to be low, but a storm in 2034 is possible. Data from
the current epoch will allow a much better assessment of what may occur.

102 WGN, the Journal of the IMO 27:2 (1999)
The instant of maximum appears to be predictable with around 10 minutes uncertainty or
better.
Encounters with multiple trails in a single year can be separated by several hours or days. Rate
analysis would require separate profiles fitted to each trail. If the time of maximum is confirmed
to be very close to the prediction of when single dust trails are encountered, then, for years
with multiple encounters, use of the predicted time of maximum for each trail could help fit
overlapping profiles. The general background activity would require an additional profile to be
fitted as the activity from the dust trails exists within the population of older Leonid meteoroids
that have an indistinct or disrupted trail structure. The spatial density in radius vector can drop
off by up to 40% over the radius of the Earth whilst rates are still high. This has implications
for global analyses of observations. At the instant of maximum, the greatest separation in radial
distance is between the point on the Earth's surface at latitude ' = 19 ffi N with the radiant
rising, and all points with the radiant in the sky at around morning twilight. If the trail passes
inside the Earth's orbit, the gradient in the profile results in the morning twilight region of the
Earth having an enhanced incident flux over regions further into darkness at that same moment.
With the intensity contours plotted in Figure 3 being based on ZHRs derived from visual obser­
vations, they are directly comparable with the activity curve observed in a single shower. The
observed stream duration in any year, when measured at a suitable intensity level, allows the
ellipticity of the dust trail cross­section to be derived. This will be presented in a separate paper.
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