On the Method for Isolating Radio Echoes Caused by Meteor Shower Meteors
Abstract Generated abstract
This paper addresses the difficulty of separating radio echoes from meteor shower meteors from sporadic and anomalous reflections, especially in observations at wavelengths near 10 m where the sporadic background may be strong. It derives a geometric criterion relating the elevation and azimuth of a normally reflecting point on a meteor trail to the zenith distance of the shower radiant, and discusses why this condition is necessary but not sufficient for shower membership. The proposed identification procedure combines this relation with restrictions on azimuth, elevation, and the presence of diffraction patterns when velocity measurements are available, providing a practical method for selecting normal reflections attributable to a given meteor stream.
Full Text
On the Method for Identifying Radio Reflections Caused by Meteors of a Stream
E. I. Fialko
(Presented by the scientific seminar of the Radio Engineering Faculty)
In solving many problems it is necessary to identify radio reflections from meteors belonging to a stream from the entire set of recorded echo signals. Such problems include precise studies of the distributions of meteoric bodies by mass, distributions of meteor heights, etc.
In observations at \(\lambda \simeq 4\ \mathrm{m}\), such identification does not present any special difficulty, since the sporadic background is usually small in number, and the appearance of a stream is accompanied by a sharp increase in the number of detected meteors. At the times of “peaks” the number of recorded sporadic meteors is relatively small and therefore, even if it is not possible to separate sporadic meteors from stream meteors, this will not lead to a noticeable error.
In the case of observations at \(\lambda \simeq 10\ \mathrm{m}\), however, the picture changes substantially: in many cases the sporadic background proves to be very intense, and the appearance of a stream is accompanied by a relatively small increase in the number of observed meteors. In addition, a noticeable number of abnormal reflections appears.
If the processing is carried out for the entire set of detected meteors, then even during the hours of “peaks” in number, substantial errors may be introduced in determining some parameters of the stream. If, however, the calculations are made under the assumption that all echo signals are the result of normal reflection of radio waves from ionized trails, the errors may increase still further.
Therefore, in observations at \(\lambda \simeq 10\ \mathrm{m}\), in a number of cases it is necessary to identify the normal reflections from meteors of the stream.
For this purpose one may use the simple relation between the angular coordinates of the normally reflecting portion of the meteor trail and the zenith distance of the radiant of the meteor stream.
As follows from Fig. 1,
\[ h = R \cdot \sin \beta, \tag{1} \]
where \(h\) is the height of the portion of the meteor trail (above the earth’s surface) that normally reflects radio waves (point \(M\) in Fig. 1); \(R\) is the slant range from the radar to the trail (along the normal); \(\beta\) is the elevation angle.
The height \(h\) can also be determined in another way,
\[ h = R \cdot \cos \Theta \cdot \sin \chi, \tag{2} \]
where \(\chi\) is the zenith distance of the radiant of the stream; \(\Theta\) is the angle in the echo plane \([1]\), measured from the direction \(OA\) to \(OM\); \(OA\) is the line of intersection of the echo plane with the plane passing through the location of the radar \((O)\), the radiant, and the zenith.
Fig. 1. Relation between \(\alpha\) and \(\beta\) of the reflecting center of a meteor and the zenith distance of the radiant \(\chi\). \(P\)—direction toward the radiant of the stream; \(z\)—zenith; \(\Pi\)—echo plane (i.e., the plane perpendicular to the direction toward the radiant); \(\Gamma\)—horizontal plane; \(M\)—point of intersection of the meteor trail with the echo plane; \(O\)—location of the radar; \(OA\)—line of intersection of the echo plane with the plane passing through the zenith, the radiant, and the location of the radar \((O)\); \(\Theta\)—angle in the echo plane, measured from the line \(OA\) to the direction \(OM\).
In addition, as is evident from Fig. 1,
\[ OB = R \cdot \cos \Theta \cdot \cos \chi \tag{3} \]
and
\[ OB = R \cdot \cos \beta \cdot \cos \alpha, \tag{4} \]
where \(\alpha\) is the azimuth.
From (1) and (2) we obtain
\[ \sin \beta = \sin \chi \cdot \cos \Theta . \tag{5} \]
From (3) and (4),
\[ \cos \beta \cdot \cos \alpha = \cos \Theta \cdot \cos \chi . \tag{6} \]
Dividing (5) by (6), we obtain the relation between the elevation angle and azimuth of the normally reflecting center of the meteor trail and the zenith distance of the radiant of the stream:
\[ \frac{\operatorname{tg}\beta}{\cos \alpha} = \operatorname{tg}\chi . \tag{7} \]
Knowing the coordinates of the radiant of the stream, we find \(\chi(t)\). Having measured the angular coordinates of the reflecting center \((\alpha\) and \(\beta)\), we check whether the condition for normal reflection of radio waves (7) is satisfied for the given stream.
Reflections that do not satisfy condition (7) are assigned to the sporadic background, to other streams, and also to abnormal reflections from meteors of the given stream.
However, equation (7) is a necessary but not sufficient condition for a meteor to belong to the given stream. Indeed, condition (7) will also be satisfied by meteors of other streams
and sporadic meteors whose radiant zenith distances at the given instant of time are equal to \(\chi\).
As is easily verified, equation (7) can be satisfied by all meteors whose directions to the radiants are generators of a cone with vertex at the observing point, with its axis directed toward the zenith and with vertex angle equal to \(2\chi\) (Fig. 2).
Fig. 2. Geometric locus of possible directions to radiants (for a given \(\chi\)) for which condition (7) is satisfied; \(z\)—zenith; \(Л\)—point at which the radar is located; \(Г\)—horizontal plane; \(\chi\)—zenith distance of the radiant.
Therefore, when using weakly directional antennas, one should make use of additional criteria, namely:
\[ \text{a) } \beta \ll \chi; \tag{8} \]
\[ \text{b) } \alpha = \alpha_p + \pi \pm \Delta\alpha, \tag{9} \]
where \(\alpha_p\) is the azimuth of the radiant of the given stream; \(\Delta\alpha\) is an angle (depending on \(\chi\) and on the range of the radar), equal to several tens of degrees.
Identification of stream meteors is greatly facilitated if meteor velocities are measured. This also makes it possible to reject anomalous reflections satisfying conditions (7), (8), and (9), since such reflections do not give diffraction patterns.
Thus, identification of stream meteors may be carried out in the following way.
First we perform a preliminary selection:
1) we exclude from consideration meteors whose azimuths lie outside the sector \(\alpha = \alpha_p + \pi \pm \Delta\alpha\);
2) from the remaining ones, we remove measurements with \(\beta > \chi\);
3) we exclude reflections that do not satisfy the condition
\[ \frac{\tg \xi}{\cos \alpha} = \tg \chi; \tag{7} \]
4) we exclude anomalous reflections satisfying conditions (7)—(9), on the basis of the absence of diffraction patterns.
The meteors selected in this way are assigned to the given stream.
LITERATURE
- T. R. Kaiser. Radio-echo studies of meteor ionization, J. Adv. Phys., v. 2, No. 8, p. 495, 1953.