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Re: (meteorobs) Distance to meteor-followup question


Tom Ashcraft wrote:

>Jim R, Mark M, George Z, and all,
>
>Many thanks for the detailed replies. Now for a followup question on
>fireball travel distances. 
>
>How far could an Eta Aquarid fireball (or Leonid) travel across the sky in
>terms of miles/kilometers? Could one Eta Aquarid (or Leonid) travel a full
>400 miles before burning out? Further? 
>
>Specifically, could a Leonid enter the atmosphere when the shower radiant
>is at 15 degrees from the observer and streak to a point 90 degrees
>overhead? 


Hello Tom,

i guess I am a bit puzzled by your question, because it seems to imply that
you expect the meteor path to actually BEGIN at the radiant point.  If I am
reading this incorrectly, forgive me.

Recall that the radiant point is merely an effect of perspective, due to
the fact that meteor shower members are all travelling in nearly parallel
paths within our moving, geocentric reference frame.  This is identical to
the vanishing point used in art for showing perspective, with the well-worn
example of a set of railroad tracks converging at the horizon to a single
point.  However, individual meteors may appear and disappear  at any point
along those "tracks."  Shower meteors can theoretically appear within a
very large portion of the sky surrounding the radiant point, and all will
have paths which, if traced backwards, will converge upon the radiant
point.  In practice, however, the highest numbers of meteors will be seen
in the areas which are about 20-45 degrees away from the radiant.  Due to
fore-shortening, meteors which are closer to the radiant tend to be harder
to spot, and since the meteor "visual density" drops off rapidly with
increasing distance from the radiant, meteors which are farther away are
less numerous.  Most observers settle upon the compromise distance from the
radiant for their watches.

To answer your question about a bright Leonid with the radiant at low
angular altitude, i thought I might give examples of a bright Leonid
appearing directly overhead with the radiant at various altitudes.  The
meteor heights used are estimated (guestimated) from photographic data
published in McKinley, but are my no means accurately drived.  This is just
to give us a rough idea of what to expect.

I also used a flat Earth for these calculations, which serves as a nice
first approximation as long as the meteor angular altitudes involved remain
greater than about 20 degrees.  The radiant altitudes are not limited in
this fashion (at least for this set of simple calculations), because these
only determine the angle the meteor makes with the observation plane.  if
we keep the meteor overhead, we can simplify the problem a bit.  The
distances used can be gained from the formula which  was given earlier as:

d = h / cos(z)    or    d = h / sin(a)

where:
d = distance to meteor
z = zenith angle of meteor
a = meteor altitude angle

For a bright Leonid type meteor, centered directly overhead, we get very
rough sample values of:

1.  radiant at 75 deg altitude

* meteor heights used: 
begin:  115 km
end:  85 km
* travel:
verticle:  30 km
horizontal:  8.03 km
total path:  31.1 km
duration:  0.44 sec
* from the observer:
begin alt:  88 deg
begin distance:  115 km
end alt:  87 deg
end distance:  85 km
* summary
total angular travel:  5 deg
beginning distance from rradiant;  13 deg
angular speed;  11 deg/sec

2.  radiant at 45 deg altitude

* meteor heights used: 
begin:  115 km
end:  90 km
* travel:
verticle:  25 km
horizontal:  25 km
total path:  35.3 km
duration:  0.50  sec
* from the observer:
begin alt:  84 deg
begin distance:  116 km
end alt:  82 deg
end distance:  91 km
* summary
total angular travel:  14 deg
beginning distance from rradiant;  39 deg
angular speed;  28 deg/sec

3.  radiant at 15 deg altitude

* meteor heights used: 
begin:  115 km
end:  95 km
* travel:
verticle:  20 km
horizontal:  74.6 km
total path:  77.3 km
duration: 1.09 sec
* from the observer:
begin alt:  72 deg
begin distance:  121 km
end alt:  69 deg
end distance:  102 km
* summary
total angular travel:  39 deg
beginning distance from rradiant;  57 deg
angular speed;  36 deg/sec

4.  radiant at 2 deg altitude

* meteor heights used: 
begin:  115 km
end:  105 km
* travel:
verticle:  10 km
horizontal:  286.4 km
total path:  286.5 km
duration: 4.05 sec
* from the observer:
begin alt:  39 deg
begin distance:  184 km
end alt:  36 deg
end distance:  178 km
* summary
total angular travel:  105 deg
beginning distance from rradiant;  37 deg
angular speed;  26 deg/sec

The above numbers are quite hypothetical, and meant for illustrative
purposes only.  But they should give you a rough idea as  to the distances
you are asking about.  Most visible Leonids will probably have paths
ranging from roughly 20 to 100 km long, with a handful of low angle ones
reaching up to 200  km in length.  Beyond this would be quite rare,
although possible.  

Take care,

     Jim


James Richardson
Tallahassee, Florida

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

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