No model of distribution of meteor substance is known to explain the observed diurnal and annual variations of meteor rates, if that distribution is assumed to be constant during the year. Differences between the results of observations and the prediction of diurnal variation rates leads to the conclusion that the density of the orbits of meteor bodies changes with the motion of the Earth along its orbit. The distributions of the flux density over the celestial sphere are obtained by the method described previously by Svetashkova, 1984. The results indicate that the known seasonal and latitudinal variations of atmospheric conditions does not appear to significantly affect the value of the mean flux density of meteor bodies and the matter influx onto the Earth

Svetashkova, N. T.

English

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DENSITY VARIATIONS OF METEOR FLUX ALONG THE EARTH'S ORBIT 
N.T. Svetashkova 
Tomsk State University 
Tomsk, USSR 
No model of distribution of meteor substance is known to explain the 
observed diurnal and annual variations of meteor rates, if that 
distribution is assumed to be constant during the year. A prediction of 
diurnal variation of rates carried out using statistical modeling (KOSTYLEV 
and SVETASHKOVA, 1977) for the meteor radar station in Mogadishu on the 
assumption that the distribution of the flux density of meteor bodies does 
not change during the year gives nearly the same average rates for all the 
different months. The analysis of the results of actual observations 
obtained from Mogadishu shows that the actual average rate of meteors 
reaches its maximum in July and minimum in March with the ratio of 5.7. 
Such a difference between the results of observations and the prediction 
leads to the conclusion that the density of the orbits of meteor bodies 
changes with the motion of the Earth along its orbit. 
In the present paper, the distributions of the flux density over the 
celestial sphere are obtained by the method described previpusly 
(SVETASHKOVA, 1984). The system of equations of the form Ax = u are 
constructed on the basis of the observational results and adequately 
formulated prediction equations, where A is the matrix whose elements are 
hourly rates for separate areas of the celestial sphere obtain_ed as a 
result of prediction; u is the vector of the observed rates; x is the 
unknowns vector whose elements represent the meteor bodies flux density 
normalized for the assigned density in the prediction model. The solution 
of systems with inaccurately assigned u components and the unknown 
coefficient matrix is performed by the Tikhonov regularization method. 
Radar observations in Mogadishu covering the interval from December 1968, 
to May 1970, are used. The observations are taken for four azimuths ( O o ,  
90°, 180", 270") with the time step of At = 30's .  The celestial sphere is 
subdivided into 76 areas. In the prediction algorithm of the meteor rates, 
a physical model of interaction of the meteor body with the Earth's 
atmosphere suggested by Tokhtasyev is employed. The distribution of the 
flux density parameter S over the celestial sfhere is determined by the 
Pupyshev formula: S ( E )  = 1.0 t 0.126: t 0 . 0 1 ~  where E is the elongation 
angle from the apex in radians and the geocentric and heliocentric 
distributions of velocities are taken from the paper by ANDREEV et al., 
(1982). simplicity that half of the meteor bodjes have 
the mean density of 2 g/cm' while the other half - that of 0.2 g/cm . 
It is supposed fo 
Variations of the average for-fhe celestial sphere flux density of 
meteor bodies with masses over 10 g are in the geocentric system of 
coordinates and the flux density changes ab ut four times-$ ye-y,-lthe 
minimum values being observed-+n March: Q( 10 -3)  -3 t167 -'f 10 km h sr; 
the maximum - in July: Q(l0 g) = 1.83 x 10 km h sr . The character 
of hourly rate variation is determined completely by the variations of the 
geocentric flux density during the year. This conclusion can only be valid 
provided the physical model of a meteor phenomenon and models of mass and 
velocity distribution over the celestial sphere remain invariable when the 
results of homogeneous observations for different months are interpreted. 
The verage annual value of the influx in the interval of masses from 
lO-'g to 10 g is 10 tons a day. The average annual flux density reduced 
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2 
https://ntrs.nasa.gov/search.jsp?R=19880005163 2020-03-20T09:11:22+00:00Z
312 
to the mass M = 5 ~ 1 0 - ~ g  ( 1 2 g O - ~  -y -9m-2s-1) agrees well witht9 ytimates 
of ELFORD (1967) ( 2  x 10 m s ) and Pupyshev ( 6 - 9  x 10 m s ). The 
estimates of other-guthors- tained on the basis of radar observations are 
of the order of 10 or 10 PB 
The minimum of the flux density in the heliocentric system of 
coordinates shifts to February, the maximum being observed in 
September-October. The maximum-minimum ratio is 3.6. 
1. Distribution of the flux density over the ecliptic longitude. 
a) The geocentric system of coordinates. The region of highest flux 
density is in the interval of longitudes from X-X = 165" to A-Xo = 
15",  where the flux density value varies witfin the limits of 
approximately one order of magnitude reaching the maximum value at 
A-A. = 225 to 255". A characteristic feature is the lowering of the 
flux density in the immediate proximity to the apex (with the 
exception of August-September). The region of the lowered flux 
density lies within the interval of longitudes A-X = 45 to 135". The 
ratios20f th? flux density in the regions of theo apex and anti-apex 
are 10 to 10 . The results show that the geocentric distributions of 
the flux density over ecliptic longitude can be considered symmetrical 
to the plane of the ecliptic for all months except March and the 
period of July to November. 
b) The heliocentric system of coordinates. Taking into account 
(according to the Levin technique) the motion of the Earth around the 
Sun, we obtain the distribution of the flux density in a heliocentric 
system of coordinates (Fig. 1). The regions of the maximum 
heliocentric flux density are actually located near the geocentric 
anti-apex. Though right at that point (A-X = 105 to 135" in Fig. 1) 
there is for many months, a flux density reauction comparable in value 
with the minimum that now appears in the geocentric apex direction. 
The average annual distribution of the heliocentric flux density near 
the plane of the ecliptic can be imagined in the form of two petals 
about 60" wide, the maxima falling on X - X o  = 45" and 165". The 
ratio of the mean values of the heliocentric flux density in the 
geocytric anti-apex region to the geocentric apex regions is about 3 
x 10 . The asymmetry of distributions over the plane of ecliptic is 
especially noticeable in January and in the period of July to October. 
In August to October, the heliocentric flux density in the geocentric 
apex region of the Northern hemisphere is only about one order of 
magnitude higher than in other months and therefore the excess number 
of orbits with direct motion is 10 to 40, which is below what is 
considered normal. In the Southern hemisphere, a rise in 
heliocentric flux density of about one order of magnitude is observed 
in January and July. Thus, the distribution of the flux density over 
ecliptic longitude is not constant during the year. For sporadic 
meteors, a heliocentric component in the geocentric anti-apex 
direction near the ecliptic plane is thus always present. In January 
and July, the Earth similarly crosses a complex of meteors with 
retrograde motion whose radiants are located in the geocentric apex 
hemisphere at ecliptic latitudes 0" to 20". In the Southern 
hemisphere meteor bodies going from the geocentric apex also have a 
high flux density in June, August and February. In August-October an 
analogous component of meteor bodies is present in the latitudes of 0" 
to 20". 
313 
6 
10-4 
10-4 
10-4 
10-4 
10-4 
10-3 
10-4 
&&-- 
I 
5 
3 
11 
Fig. 1 Distribution of the heliocentric-flux density of meteoric bodies 
with the masses greater than 10 g over the ecliptic longitude. 
The figures denote the number of a month. The continuous line 
shows distributions for latitudes 0" to 20" and the dashed lines 
represent 0" to -20". A v symbol represents distributions with 
seasonal latitudinal variations of the density of the atmosphere 
being taken into account. 
314 
2. Distribution of the flux density over the ecliptic latitude. 
Heliocentric distributions of the latitudinal flux density are 
presented in Fig. 2 .  In different months, 70-80 percent of meteor body 
orbits are located in the ecliptic latitudes I p l  < 35" and less than 10 
percent in the latitudes 1/31 > 50". The maximum flux density is observed 
near the ecliptic plane in the interval of latitudes < 20". 
Distributions over latitude can be considered symmetrical to the plane of 
ecliptic only for two months - namely December and January. Assymmetry 
becomes particularly apparent in February, April and May when the flux 
density of particles in the Northern hemisphere is 1.7, 1.9 and 1.7 times 
respectively higher than in the Southern one. On the contrary, in October, 
the Southern hemisphere is 1.5 times more active than the Northern one. 
Geocentric distributions of the flux density over latitude are also shown 
in Fig. 2. It can be seen that the Earth's motion along its orbit distorts 
the heliocentric distributions considerably. 
The known seasonal and latitudinal variations of atmospheric 
conditions does not appear to significantly affect the value of the mean 
flux density of meteor bodies and the matter influx onto the Earth. 
The analysis of the data obtained over the equator makes it possible 
to draw a conclusion that variations of meteor activity of the celestial 
sphere during the year are a reflection of variations of the meteor body 
flux density along the Earth's orbit. 
References 
1. 
2. 
3. 
4 .  
5. 
Kostylev, K.V., Svetashkova, N.T., 1977, The method of statistical 
modeling of radar observations of a meteor shower, Astronomichesky 
Vestnik, No. 1, pp. 53-59. 
Svetashkova, N.T., 1984, Determination of sporadic meteor flux 
density, Astronomy and Geodesia, Tomsk, No. 10, pp. 167-174. 
Andreev, V.V., Belkovich, O.I., Zabolotnikov, V.C., 1982, Structure of 
meteor complex in the vicinity of the Earth's orbit, Meteor Matter In 
Interplanetary Space, Moscow, pp. 8-27. 
Elford, W.G., 1967, Incidence of meteors on the Earth derived from 
radio observations, Smithson. Contrib. Astrophys., vol. 11, pp. 121. 
Ramasov, A.A., Sikharulidze Yu, G., 1979, The Model of Seasonal 
latitudinal variations of the density of the Earth's atmosphere, 
pre-print of the USSR Academy of Sciences Institute of Applied 
Mathematics, Moscow, No. 72, p. 30. 
315 
10 
- 
_‘I- 
- -I 
Fig. 2 Distributions of- he flux density of meteoric bodies with masses 3 greater than 10 g over the ecliptic latitude. The continuous 
line represents the geocentric distributions; the dotted line 
shows the heliocentric distributions. 


Density variations of meteor flux along the Earth's orbit

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