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Re: (meteorobs) Leonid radiant rise



> > It seemed the case last year that Earth grazers were at a great
> > height.  Their angular velocity was quite low compared to Leonids
> > with the radiant higher in the sky.  I assume someone can quantify this
> > from observational data.
>
> Visual observers tend to give a wrong impression here. If this
> result is from video, I'd be surprised. A shower meteor appearing
> overhead from a radiant at 0deg elevation has maximum angular
> speed. (Because angular speed depends on sin(hR) and sin(distance
> from radiant).)
>
> The mistake is that a very loooong meteor must be a very sloooow meteor.
> If one sees an Earth-grazer of 120 deg length lasting an impressive
> 4 seconds -- imagine a 4-sec meteor, which is really lengthy --, it
> has an angular speed of 120/4 = 30 deg/sec though and is thus one
> of the fastest meteors in the sky.
>
> Leonids could appear slower if higher in the atmosphere. This can
> certainly be quantified from video data. I suppose speeds may vary
> by ~30% due to varying heights. But this change does not cover the
> low speeds sometimes reported by visual observers.

Given that Leonids with a grazing incidence will have had a prolonged
heating in the upper atmosphere for some tens of seconds before reaching
perigee, one would expect a higher start elevation.  Also, the object
will continue out of the atmosphere after perigee and the distance from
the observer will *tend* to increase in most instances.  Thus two effects
apply to the apparent velocity of Earth-grazing meteors

1) They likely have greater start, mean and end heights
2) The start and end elongations from the radiant tend to be closer and
   further respectively to average Leonids, so their *mean* angular
   velocity is less than Leonids occuring in the middle of the track.

There can thus be both physical and psychological reasons for this effect
and neither involves observational error.  Whilst one is aware of the the
angular acceleration and deceleration of an Earth-grazer that crosses the
sky, the overall *impression* is of a rather slower meteor than the maximum
angular velocity.  This isn't an error, it is how the perceptual system
works.  Also, if I remember my studies of perception from over two decades
ago, the importance given to perceptual data is weighted by closeness in
time.  In other words, the angular velocity at the end of a long duration
meteor has a greater weight on the overall perceived angular motion
than the mean motion, as it is more recent in memory.  The end of all
the Earth-grazers I saw were at rather long radiant elongations so would
have had slow angular velocity due to both large distance and compressed
geometry.  Quantifying angular velocity is something best done by machines!

Single station video or photography with a rotating shutter can quantify
this easily.  The start velocity and elongation from the radiant are known
and there is a direct relationship between these and the angular velocity
as Rainer says.  In fact, with an assumption of no deceleration, the
position in space (height, lat, long) can be determined uniquely from single
camera data given the above assumptions.  Actually, the deceleration
assumption isn't even a problem if the radiant is known in advance and the
deceleration can be derived for single station data.  Deceleration makes
the object appear closer and the distance must be increased to keep the
motion vector coincident with the 3 dimensional coordinates of the start of
the trail.  The velocity decline is inversely proportional to this required
increase in distance.  The inverse problem is that if the radiant isn't
known and deceleration is assumed zero, e.g. the first 1/3 of a trail, then
the radiant can be derived uniquely as I've mentioned many times!!!

Cheers, Rob

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