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Re: (meteorobs) Unrealistic ejection model?

>> We
>> demonstrated in our original paper that the cross-section of a dust
>> trail at nodal passage using the instantaneous orbits of dust ejected
>> isotropically at perihelion, is basically invariant for some future
>> nodal passage *for those specific particles that have the precise orbital
>> period to be encountered at this later date.*  (This last sentence is the
>> stumbling block and I hope you can understand the way I've put it).
>> Thus, the "center" we calculate will produce a dynamically invariant
>> reference point on the dust trail on which all subsequent calculations
>> are based.
> 

Rob, I can certainly understand why your point is not understood: it's a
really tricky point! Indeed, I myself certainly don't understand it. The
sentence has six clauses and eight prepositional phrases! I am not
criticizing your writing -- I don't think that the idea can be expressed any
more clearly. All those clauses and prepositional phrases constitute a
measure of the complexity of the idea. The only way to make the point more
simply would be to expand each clause, and possibly each prepositional
phrase, into a full sentence. It would be easier to read, but much longer,
and I don't know that it would then be clearer. So please be patient with
the misunderstandings that arise from such a complex point.

I will try to help by articulating my first point of confusion. Cutting out
the terminology that doesn't play a role in my confusion, I get:

"The cross-section ... is invariant ... for those specific particles that
have the precise orbital period..."

So you are eliminating from consideration all particles that do NOT have the
precise orbital period. But when you say "precise", what do you mean? Taking
your sentence literally, you are saying that the cross-section is invariant
for zero particles, because the number of particles with orbital period in
the range T plus or minus 0.00000... is zero. Clearly, you're talking about
T plus or minus some very small amount. The inference I draw is that the
cross-section expands as you take in more and more particles with greater
variance from T. Of course, those particles with some variance from T won't
be there at the moment of truth, because they'll be advanced or retarded
along the orbit. This is where I become confused: what kind of time bracket
are we talking about here? What about particles with orbital periods 15
minutes shorter or longer than the central value? Will the cross-section at
such values be dramatically different?

At this point, you may well throw up your hands and say, "The math is too
hairy to explain in email -- read the paper." If so, I can certainly
understand. And thanks for taking the time to explain it to us amateurs.

Chris Crawford


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