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Re: (meteorobs) Celestrial Math Help Needed

Hello Steave,

I am up to my eyebrows in schoolwork this semester, and thus have very
little time to read mail -- much less respond to it.  However, your post to
MeteorObs got my attention as i was wading through my over-stuffed mailbox
this weekend.

Your ideas are intriguing, but unfortunately, the physics and geometry
involved do not make for easy solutions or geometry when forward-scatter is
involved.  I very much hate to criticize the work or ideas of others,
especially when I don't have the time to fully explain or back up my
opinions.  Therefore, I would strongly recommend that you obtain a copy of
"Meteor Science and Engineering," D.W.R. McKinley, 1961, McGraw-Hill Book
Co, to obtain some better answers than what I can provide here.

This has been out of print for some time, but it is the best source on
radio-meteor work ever published, and comprehensively contains the majority
of the theory, models, and ongoing problems being worked on up to the time
of publication in 1961.  While some progress has been made since then in
doing radio studies, the field rapidly declined after the mid-1960's, and
no easily obtainable companion or update to this book has been written.
After gaining a thorough knowledge of Mckinley (which i do not have!!) the
potential meteor scientist must then plow through journal articles and
papers to bring himself/herself up to date.

Sometimes used paper-back copies of McKinley can be obtained through
Knollwood Books, email:  books@tdsnet.com, phone:  (608) 835-8938

To give you a little comentary on your proposal:

Steve wrote:

>Howdy,
>
>Here's a possible new thread. Recently, three of we radio amateurs were
>conducting a meteor scatter schedule one morning; the locations of we three
>are:
>
>            Lat           Long          City/State
>Maarten:  41.9015      -71.47260     Lincoln, RI
>Steve:    42.27480     -71.74790     Shrewsbury, MA
>Shelby:   37.6875      -85.84510     Elizabethtown, KY
>
>Maarten and Steve (myself) were transmitting simultaneously on 144.157 MHz
>using high-speed morse code (1000 words per minute) while Shel was
>listening. Shel heard two strong meteor reflections; first from Maarten,
>then from myself. The time between the start of Maarten's reflection and
>the start of my reflection was about 0.706 seconds. Further, however, there
>was a great difference in the time duration of the reflections heard from
>Maarten and myself; Maarten's reflection lasted about 0.072 seconds, while
>my reflection lasted about 0.35 seconds. The durations of these reflections
>are estimated based on similar signal strengths. Initially, because of the
>great difference in the length of the signal reflections, it seemed to me
>as if Maarten and I were heard by Shel on two separate meteor reflections.
>However, the distance between the homes of Maarten and myself is only about
>46 kilometers as compared to a direct path between Maarten/myself to Shel
>of roughly 1300 kilometers.
>
>If I assume that one meteor illuminated the sky halfway between Shel, and a
>line drawn between Maarten and myself, then it seems to me that such a
>single meteor would travel only half that distance, or about 23 kilometers,
>during the total time from the beginning of Maarten's and the end of my own
>reflections. And that total time was about 1.09 seconds from start to end.

Jim:

While the primary "hot-spot" regions for a forward scatter link are roughly
located about 50-150 km to either side of the great-circle chord midpoint
(between transmitter and reciever), you have to be careful in assuming that
any one reflection came from this region.  A narrow-beam antenna at either
receiver or transmitter (or both) can help to "narrow" down your most
likely reflection locations.

The basic geometry is that in order to cause a forward scatter reflection,
the meteor trail must lie within a plane (called the tangent plane) which
is tangent to an ellipsoid having the transmitter and receiver as its foci.
 The entire reflection path will also lie within a plane (called the plane
of propagation), which contains the transmitter, reflection point, and
receiver.  The plane of propagation will be normal to (at right angles to)
the meteor tangent plane.  

Important note:  the meteor itself can be at any orientation within the
tangent plane -- it need not be normal itself to the propagation path.
There is, however, greater signal loss when the meteor trail is parallel to
the propagation plane than when it is normal to the propagation plane.

A third useful constraint  is that most meteor reflections will occur
within the narrow altitude band of about 85 to 105 km altitude.  Thus, the
sphere formed by the 95 km altitude band, the meteor tangent plane, and the
ellipsoid having the transmitter and receiver as foci must all meet (or be
tangential) at the reflection point.

Steve:

>So this might indicate, were the meteor actually located halfway between
>Kentucky and New England, that the apparent speed of the meteor was roughly
>23 kilometers per second. This seems very slow, particularly considering
>the frequency at which the reflections were heard of 144 MHz, where it is
>generally thought that meteor entry speeds need to be several times faster,
>particularly for such strong signal reflections as Shel recorded.

Jim:

This is somewhat of an over-simplification.  While there are many factors
affecting the electron line density of the meteor trail (Q), the three
major ones are meteor magnitude, meteor speed, and trail altitude.  In the
underdense relm, Q increases exponentially with meteor magnitude, but then
drops bakc to a more linear (or even flat) relationship when the overdense
relm is reached.  Generally, the brighter the meteor, the better is the
trail reflection, but there are some little recognized limitations.

While it is true that higher speed meteors have higher ionization
efficiencies, this advantage is undercut by trail altitude.  With
increasing altitude, the electron diffusion rate also increases.  Thus,
while faster meteors have higher and higher ionization (and visible)
altitudes, the trails they create also diffuse faster and faster.  At very
high altitudes, the fastest faint meteors create no usable trail at all and
become head-echoes only.  Thus, with high-speed showers, it is only the
brighter meteors which can penetrate low enough in altitude to cause useful
trail echoes.  The fainter ones are out of reach (even for the professional
facilities).  This creates a sort of "height-ceiling" effect with regard to
radio echoes.

On the other end of the altitude band, when one gets below about 85 km,
electron attachment and recombination begin to seriously effect trail
durations.  Even the "brightest" of trails can be quickly destroyed by this
effect if the meteor penetrates low enough.  Thus, when slow showers are
examined, only the fainter meteors will give proper radio reflections, as
the brighter ones penetrate below this "height-floor."  Very slow,
low-altitude fireballs may not cause a radio reflection at all, despite the
fact that they are brilliant from the ground.  It 

is generally only within that middle 85-105 km band that the attachment and
diffusion effects are both low enough to give full-strength, full-duration
echoes.  It is therefore the mid-range meteors which display the best
reflection characteristics, with brighter fast meteors, and fainter slow
meteors also appearing.

Don't take my word for it -- research it!

Steve:

>>There are several other considerations, however, such as the field of view
>of all three of us, which was somewhat different because we all were using
>antennas with varying beamwidths. And then, too, is the question of whether
>the meteor's path was perfectly oblique to the direct path between Kentucky
>and New England.
>
>Anyway, I'd like to discuss this further with someone who has a better
>understanding of the physics involved. Any volunteers? We three are willing
>to conduct further experiments of this type (essentially bistatic CW radar
>analysis of meteor entries), and there is also the possibility of others
>becoming involved.
>

Jim:

Based upon your description of the event, and your operating frequency, I
can also add another plausable hypothesis to the event.  if the two
reflections were from the same trail, it was almost certainly an overdense
one for a 2-meter band reflection -- especially at the distance cited.
Overdense trrails undergo noticeable changes in signal characteristics as
the trail expands and is broken apart by upper atmospheric winds.  The
trail can even break apart to form separate "glints" -- each capable of
causing a separate reflection.  Due to this, overdense trail reflections
are not nearly as geonetry sensitive to original trail location and
orientation.  It is possible that a trail formed with favorable geometry
for one of you, and then expanded/drifted/broke apart to give favorable
geometry for the other person -- especially since it would only have taken
a minor geometry change to do so.  Thus, what you observed may not have
been due to a trail formation effect (indicative of meteor speed), but
instead an effect of changing overdense trail characteristics.  

I hope that the above has been helpful, and not overly critical.  I still
have an aweful lot to learn in the area, so please feel free to challenge
my statements with a more knowledgeable source.

Take care,

     Jim


James Richardson
Graceville, Florida
richardson@digitalexp.com

Operations Manager / Radiometeor Project Coordinator
American Meteor Society (AMS)
http://www.serve.com/meteors/
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