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Re: (meteorobs) Re: predictions for Perseids 2001?
On 6 Aug 2001, at 14:31, Robert Lunsford wrote:
> below your field of view. By aiming your camera low it is viewing a
> thicker column of atmosphere which in theory should produce more
> activity. The zenith is actually the worse area to view meteor activity
> both visually and photographically.
When I read this my initial thought was it appears this way - the
lower you look the more airmass you see therefore more meteors
will be visible. However, on further analysis it appears not to be so
in most cases. As you look lower, atmospheric attenuation and
inverse-square law dimming of the meteors will reduce the
numbers, (since on the average they are further away) but how
much?
I did a quick back of envelope derivation and got the following
results:
I assumed 3 factors governs the number of meteors seen as a
function of elevation (or airmasses (X) where X=1/sin(elev)).
1. the number potentially visible increases linearly with airmass (X)
2. atmospheric extinction reduces their average magnitude
0.5*(X+1)*A, where A is the average attenuation in magnitudes per
airmass (typically 0.28 mag)
3. inverse square dimming in magnitudes is 5*log((X+1)/2)
Then, using the familiar "r" population index, we can write the
meteor rate (n) as a function of airmass and magnitude dimming
(M) will be n = Z * X * r^(-M) where Z is the rate at the zenith.
Combining (2) and (3) to get M= 0.5*(X+1)*A + 5*log((X+1)/2) we
get n = Z * X * r^(-0.5*(X+1)*A - 5*log((X+1)/2 )
To find at what airmass (X) this rate is a maximum, we differentiate
it with respect to X, set it to zero and solve for X.
This yields a quadratic equation in X:
(0.5*A*ln(r)) * X^2 + (ln(r)*5/ln(10) + 0.5*A*ln(r) - 1) * X - 1 = 0
Since X must be at least 1 airmass, this tells us that r < exp(2/(A
+ 5/ln(10))) for a solution to yield a maximum rate value at some
elevation BELOW the zenith. So for a typical value of A=0.28 we
see that r < 2.26.
So, in conclusion only the bright showers with population index <
2.26 would benefit from looking below the zenith to achieve a better
rate. For a very bright shower like the Quadrantids with r=2.1, the
maximum rate will occur by looking at airmass (X) = 1.19 or 57°
elevation above the horizon. If you observe from a very transparent
sky with A=0.15, for the same bright shower with r=2.1, the best
occurs at X = 1.35 or 48° elevation.
While this is based on a simple model, it shows that only for the
brightest showers could it benefit to center your view somewhat
below the zenith, certainly not near the horizon. For average or
fainter showers the best results will be observed at the zenith.
Sincerely,
Mike Linnolt
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