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Re: (meteorobs) Distance to meteor ?
At 01:50 PM 11/1/98 -0500, Thomas wrote:
>
>
>I have some basic questions:
>
>
>I am wondering about the variables and distances a meteor is from the
>observer. If a meteor is directly overhead then it is about 100 plus
>kilometers from the observer if that is the height to the edge of the
>ionosphere at that certain moment? If a meteor shower radiant is 15
>degrees above the horizon then what are distance parameters to individual
>meteors?
>
>For examaple: If I observe the Leonids when the radiant is 15 degrees
>above the horizon then how close could a Leonid ever get to me in terms of
>miles/kilometers?
>
Hello Thomas,
A general idea of the distance to an individual meteor as a function of
meteor altitude can be gained using a law of cosines function, drawing a
triangle using the observer, the meteor, and the center of the Earth. This
will give the relationship:
(r + h)^2 = r^2 + d^2 - (2 * r * d * cos(90 + theta))
where:
r = Earth radius (km)
h = height of meteor above the surface (km)
d = disntace between observer and meteor (km)
theta = angular height of meteor above the horizon (degrees)
Using an Earth radius of r = 6370 km, and a meteor height range of h =
80-120 km we get:
theta, d
----------
90 deg, 80-120 km
80 deg, 81-122 km
70 deg, 85-128 km
60 deg, 92-138 km
50 deg, 104-156 km
45 deg, 112- 168 km
40 deg, 123-184 km
35 deg, 138-205 km
30 deg, 157-234 km
25 deg, 184-273 km
20 deg, 224-239 km
15 deg, 286-416 km
10 deg, 394-557 km
5 deg, 600-805 km
0 deg, 1013-1242 km
Note that the above approximate ranges are NOT a function of the shower
radiant altitude, but are instead a function of the actual meteor's
altitude. A shower radiant near the horizon (especially a fast shower) can
still produce one of those lovely "grazing" meteors almost directly
overhead -- albeit quite infrequently. This used to be one of my favorite
features of the Eta Aquarid shower during radiant rise; those rare trained
"streamers" which would cover 70-90 degrees of arc in an incredibly short
amout of time.
Note also that the above numbers bear a direct relationship to doing
forward-scatter meteor work, in that in order to cause a reflection, the
meteor trail must be located above the horizon for both transmitter and
receiver (using a direct, VHF skywave transmission). However, for most
forward-scatter links, about 500-1500 km (310-930 miles) great circle
distance between transmitter and receiver, the corresponding meteor trails
are at low angular altitudes: generally less than 30 degrees. The
magnitude attenuation due to the inverse square law and atmospheric
absorption makes these meteors difficult to see at low altitudes, except
for perhaps the brighter ones. Thus, coincidental visual and radio
observations of the same meteor are quite infrequent unless short link
distances (preferably a back-scatter setup) are used.
As a follow up to the above table, below is a table giving optimum antenna
beam altitudes and offset angles for forward-scatter links of various
distances, taken from AMS Bulletin No. 203, "The AMS Radiometeor Project."
RANGE (km) TEST ALTITUDE TEST AZIMUTH OFFSETS
50 44 75
100 41 62
150 38 51
200 34 43
250 30 37
300 27 32
350 24 29
400 22 26
450 20 23
500 18 21
550 17 20
600 15 18
650 14 17
700 13 16
750 12 15
800 11 15
850 10 14
900 9 14
950 9 13
1000 8 13
1050 8 12
1100 7 12
1150 6 12
1200 6 11
1250 6 11
1300 5 11
1350 5 11
1400 4 11
1450 4 10
1500 4 10
2000 1 10
The offset angles come from the fact that most meteor reflections will not
come from meteors directly between the transmitter and receiver, but
instead tend to most frequently come from two "hot spot" regions about
50-150 km to either side of the transmitter-receiver great circle path
midpoint. The offset angles are approximate angles which the antenna
should be pointed to either left or right away from the direct bearing of
the other station.
Keep in mind that the above numbers are meant to be used for optimizing a
particular link, and are NOT an indication of the only areas of the sky
from which reflections will occur. Non hot-spot meteor trails can, and do
cause reflections, just not as frequently.
One final note: I have often noted a strong desire among amateur
forward-scatter enthusiasts to place their receiving antennas at high axis
tilt angles, often 45 degrees or more. Based upon the above tables and
calculations, this is frequently unnecessary, considering that most 4-5
element yagis have a 30 degree or so beamwidth, and will work fine for link
distances of 600 km or more with a horizontal beam. The second very
important factor is that for a horizontally polarized (HP) antenna, ground
reflection and antenna height above the ground will play a more important
role in determining the beam altitude of the HP antenna than will the
actual angle of the antenna axis. At 2 wavelengths above ground, the two
will match (antenna axis and beam), but at lower heights, the beam will be
directed to higher and higher altitudes regardless of where you have the
antenna pointed. At 1 wavelength or less, even a horizontally mounted HP
antenna will have a nearly verticle beam. Thus, if you want to raise the
beam of a HP antenna, it is easier to lowr the hight than it is to mount
the antenna at some odd angle, and also a lot more effective. A vertically
polarized (VP) antenna does not enjoy this ground reflection effect, and
the beam generally matches the physical antenna axis.
Take care, all,
Jim Richardson
James Richardson
Tallahassee, Florida
Operations Manager / Radiometeor Project Coordinator
American Meteor Society (AMS)
http://www.serve.com/meteors/
References: