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4. Results

The orbital elements, encounter data and other relevant information are listed in Table 2 (click here), which is available in electronic form at the CDS via anonymous ftp to "" ( or via "". A printed version can be requested from the authors. Also, a subset of data (the orbital information) will be available at the IAU Meteor Data Center in Lund, Sweden.

The content of Table 2 (click here) is listed in the table caption above. Data are ordered according to solar longitude at the time of the meteor. Angular units are in Equinox 2000. Uncertainty limits are based on the assessment of measurement accuracy. For two-station meteors, a value of tex2html_wrap_inline1172 0.2 degrees in RA and DEC was adopted for the uncertainty in the radiant position, unless Q was less than 10 degrees. The brightness of the meteors was not measured but obtained from the brightness estimates by the visual observers or merely guessed from the density of the images on the negatives. Photometric scans of a small number of meteors have been published in Radiant, the Journal of the Dutch Meteor Society (Betlem 1982; 1983; van Oudheusden & van Dijk 1991). The journal also gives many detailed descriptions of individual multi-station sets, including possible complications with the observational data. The best results are from long duration and not too bright meteors (-1 to -3 magnitude). Bright fireballs can result in blurred trails in which individual breaks are difficult to recognize. Weak meteors are usually also of short duration, with few measurable shutter breaks.

Indeed, the accuracy of the final orbital elements varies a lot. Apparently, his point is not recognized in previously published surveys of meteor orbits, which have never included error estimates.

4.1. Intrinsic dispersion in the Perseid meteor stream

Several major and minor meteor streams can be identified in our sample of meteor orbits. The Perseids and Geminids are especially well respresented. Stream membership was determined by comparing the orbital elements with mean values listed in Kresak & Porubcan (1970) and Cook (1973). We will now discuss two examples of how the observations can be used in the study of meteor stream evolution.

A significant number of orbits are of meteoroids of the Perseid meteor stream. From the spread in orbital elements and the estimated measurement uncertainties, we can calculate the intrinsic scatter in the orbital elements of this stream. Only those Perseids are considered that appeared between solar longitude 137.0 and 141.9 (J2000), which is the main peak of the Perseid shower (Jenniskens 1994). The median value for each orbital element, with an estimate of the accuracy of how well the median value could be determined, is listed in Table 3 (click here). The intrinsic dispersion was calculated as follows: Because the measurement uncertainty is only approximately known, we devided the sample in groups of about equal uncertainty in a given orbital element and plotted the square of the scatter in each group versus the mean of the calculated measurement error. The intercept for zero measurement uncertainty of a least squares fit to these data is the (square of the) intrinsic scatter. These values, with an uncertainty limit, are listed in Table 3 (click here).


N year q 1/a e i tex2html_wrap_inline1126 tex2html_wrap_inline1130
AU AU-1 o) o) o)
IAU 309 1940-1982 0.952tex2html_wrap_inline11720.002 0.027tex2html_wrap_inline11720.013 0.976tex2html_wrap_inline11720.013 113.40tex2html_wrap_inline11720.13 151.3tex2html_wrap_inline11720.4 291.2tex2html_wrap_inline11720.4
NMS 911964-19850.947tex2html_wrap_inline11720.0020.055tex2html_wrap_inline11720.0190.948tex2html_wrap_inline11720.018 113.40tex2html_wrap_inline11720.27 tex2html_wrap_inline1228 tex2html_wrap_inline1230
DMS 871981-19920.953tex2html_wrap_inline11720.0020.014tex2html_wrap_inline11720.0110.961tex2html_wrap_inline11720.007 113.22tex2html_wrap_inline11720.19151.3tex2html_wrap_inline11720.4291.9tex2html_wrap_inline11720.4
IAU 309 1960 0.041tex2html_wrap_inline11720.0020.24tex2html_wrap_inline11720.010.23tex2html_wrap_inline11720.012.4tex2html_wrap_inline11720.1 6.6tex2html_wrap_inline11720.46.6tex2html_wrap_inline11720.4
NMS 91 1978 0.019tex2html_wrap_inline11720.0020.19tex2html_wrap_inline11720.020.18tex2html_wrap_inline11720.022.6tex2html_wrap_inline11720.3 4.9tex2html_wrap_inline11720.54.7tex2html_wrap_inline11720.5
DMS 87 1990 0.015tex2html_wrap_inline11720.0020.11tex2html_wrap_inline11720.010.06tex2html_wrap_inline11720.011.8tex2html_wrap_inline11720.2 4.0tex2html_wrap_inline11720.44.1tex2html_wrap_inline11720.4
DMS 87 1990 0.009tex2html_wrap_inline11720.0010.04tex2html_wrap_inline11720.010.035tex2html_wrap_inline11720.0051.5tex2html_wrap_inline11720.2 2.3tex2html_wrap_inline11720.33.3tex2html_wrap_inline11720.8
Table 3: Perseid median orbit (J2000), the observed dispersion of orbital elements (1tex2html_wrap_inline1180), and the intrinsic dispersion after accounting for measurement error (1tex2html_wrap_inline1180), for meteors in the solar longitude interval tex2html_wrap_inline1184


These results are compared to the median values of Perseid orbits listed in the 1990 version of the IAU Meteor Data Center catalog for precisely reduced orbits (Lindblad 1991a, 1995; Lindblad & Steel 1994). We consider separately the recent dataset of the Nippon Meteor Society (NMS) and the other data (IAU). All were restricted to the interval 137.0-141.9 and the most obviously deviating cases were removed (7 in the IAU list). Subsequently, the mean values and observed dispersion were calculated.

We find good agreement between the mean orbits in our sample and the IAU data. On the other hand, the NMS data show significant deviations with both our data and the IAU data. The errors in the NMS data are partially caused by the fact that some orbits were computed using R = 1 for the Earth-Sun distance (Lindblad 1991). Both the NMS and IAU data have dispersions in orbital elements that are systematically larger than our new sample of orbits, and all datasets contain a significant amount of dispersion due to measurement error.

4.2. The evolution of the Geminid orbit

A dedicated observing campaign in France in 1990 resulted in about 100 precise orbits of the Geminid stream (Jenniskens et al. 1991; Betlem et al. 1994a,b). Together with some 30 orbits obtained in a similar campaign in the Netherlands in 1991, the sample doubles the number of precise Geminid orbits in the IAU archive.

Again, the orbits obtained by the Nippon Meteor Society (NMS) in the period 1970-1980 show significant differences compared to the older IAU data obtained mostly in the 1950's (Table 4 (click here)).


N year q 1/a e i tex2html_wrap_inline1126 tex2html_wrap_inline1130
AU AU-1 tex2html_wrap_inline1314 tex2html_wrap_inline1314 tex2html_wrap_inline1314
IAU 93 1936-82 (1953) 0.1410tex2html_wrap_inline11720.0007 0.726tex2html_wrap_inline11720.004 0.8980tex2html_wrap_inline11720.0009 23.60tex2html_wrap_inline11720.19 324.28tex2html_wrap_inline11720.17 226.20tex2html_wrap_inline11720.19
NMS 99 1969-85 (1977) 0.1460tex2html_wrap_inline11720.0029 0.806tex2html_wrap_inline11720.011 0.882tex2html_wrap_inline11720.0037 23.6tex2html_wrap_inline11720.4 324.83tex2html_wrap_inline11720.28 226.9tex2html_wrap_inline11720.29
DMS 132 1990-91 (1990) 0.1410tex2html_wrap_inline11720.0009 0.729tex2html_wrap_inline11720.004 0.8980tex2html_wrap_inline11720.0008 24.02tex2html_wrap_inline11720.21 324.42tex2html_wrap_inline11720.14 226.55tex2html_wrap_inline11720.15
3200 Phaeton 19830.13950.7860.890322.04321.67227.18
Table 4: Geminid median orbit (J2000), for meteors in solar longitude interval tex2html_wrap_inline1296


This might suggest a fast stream evolution. However, we do not confirm such fast stream evolution from our data and conclude that the difference is probably due to errors in (some of) the NMS orbits.

With the NMS data unavailable for analysis, this leaves a gap in coverage of the Geminid stream between the 1950's surveys and our recent work. Our data span a 35 year range that was not present in the older data and for the first time we can now measure the change in the orbital elements of the Geminid shower over time.

The IAU and DMS data were correlated with the node of the particle orbit in order to find the daily variation of the orbital elements. Examples of such correlation plots are shown in Williams & Wu (1993). The IAU dataset spans a wider range in node and, therefore, we have adopted the relationships found for this set to correct for the daily variation or all Geminid orbital elements (Table 5 (click here)).


element mean DMS mean IAU | tex2html_wrap_inline1364 tex2html_wrap_inline1364 || mean IAU+DMS | tex2html_wrap_inline1360 tex2html_wrap_inline1360 tex2html_wrap_inline1360
261.4 261.4 | [1] || t=2000 | [2] [3]
q (AU) 0.1400 0.1399 | +0.0010 +0.0023 || 0.1400 | +1.97e-7 2.1e-6
1/a (AU-1) 0.730 0.721 | -0.011 (0.00) || 0.737 | +0.00038 +0.00031 (+0.00016)
tex2html_wrap_inline1412) 24.19 24.27 | -0.13 -0.20 ||24.27 | +0.0097 +0.0017 +0.0030
tex2html_wrap_inline1430) 324.45 324.28 | -0.41 -0.33 || 324.63 | +0.0078 +0.0048 +0.0027
tex2html_wrap_inline1448) 261.40 261.40 | +1.00 +1.00 || 261.433 | +0.00068 -0.00508 -0.0025
Table 5: Change in orbital elements of the Geminid stream between 1955 and 1990. The mean value at node tex2html_wrap_inline1128 = 261.4 is given for DMS and IAU data, and the change of orbital elements with node. [1] is a theoretical estimate by Kresak & Porubcan (1970) assuming tex2html_wrap_inline1358 = 0. After correction for the nodal dependence, the orbital elements of IAU and DMS data were correlated in time, which resulted in the mean value for the year 2000 and the annual variation tex2html_wrap_inline1360 in Cols. 6 and 7. The latter value is compared to results derived for the shower members in the model of: [2] Williams & Wu (1993) and [3] Jones & Hawkes (1986)


All data were then corrected for this daily variation by normalisation to solar longitude 261.4 (at the peak of the shower) and plotted as a function of the year of the observation. The resulting mean value of the orbital elements for the year 2000 and the mean annual shift are given in Table 5 (click here).

We conclude that the perturbation of the particles is mainly at aphelion, because the perihelion distance does not significantly change. The change of the node is positive and two times the value for the annual Perseid shower. The inclination (i) and the longitude of perihelion tex2html_wrap_inline1466 are increasing in time, while the semi major axis is decreasing with -0.00068 AU per year (the table lists 1/a).

The measurements are in good agreement with the theoretical model of Jones & Hawkes (1986) and Williams & Wu (1993) for the case of ejection of particles at some distant point in time (1000 yrs ago). The only exception is the change of the ascending node with time. We do not find the strong negative precession of the mean orbit of the model Geminids with time. The nodal change is small and consistent with the observation that the peak of the shower has not significantly changed in the past century (Fox et al. 1982; Jenniskens 1994). Fox et al. (1983) pointed out that the intersection points of Geminids with the ecliptic plane are at an angle with the normal line to the Earth's orbit and, as a result, the gradual outward movement of the stream shifts the mean node forward for the subset of particles that intersect with the Earth's orbit. This compensates the negative movement due to precession from planetary perturbations on the prograde orbits. In the model of Jones & Hawkes (1986), the nodal change is tex2html_wrap_inline1472 for the shower as opposed to -0.152 degree per year for the stream as a whole. Our measurements confirm this behavior and, perhaps, suggest the effect to be even slightly stronger than calculated, with tex2html_wrap_inline1476 degree per year.

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