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Re: (meteorobs) The formulae of ZHR
Hello Sirko,
Many thanks for your explanation for these two formulae.
But in your explanation,
> cos (z) = sin (h).
> z is the zenith distance, h is the altitude.
> So z = Pi - h, and
> cos (-x) = cos (x) = sin (x+Pi)
I think the "Pi" should be "Pi/2" in these formulae, as z+h=90 degree, but
Pi=180 degree.
And at the end of your mail, if I have a right understanding, it seemed you
wanted to tell us that the ZHR of any shower activity has a lowest limit.
Then, what's number of the lowest limit? And can it be zero?
All best wishes and Clear skies!
Huan Meng meteorobs@263dot net
----- Original Message -----
From: Sirko Molau <molau@informatik.rwth-aachendot de>
To: <meteorobs@jovian.com>
Sent: Monday, June 11, 2001 8:56 PM
Subject: Re: (meteorobs) The formulae of ZHR
> Hello Huan Meng,
>
> > ZHR=HR/[r^(Lm-6.5)*cos(z)^1.47] (in the calendar, and it was said it's
from
> > IMO)
> >
> > or
> >
> > ZHR=(1+sum n)/sum(Teff/C)
> > C=r^(6.5-Lm)*F/sin(h) (in nearly all the IMO shower circular)
>
> both formulaes are in a sense "correct", even though there are two
> differences that require some explanation.
>
> First of all, cos (z) = sin (h).
> z is the zenith distance, h is the altitude. So z = Pi - h, and
> cos (-x) = cos (x) = sin (x+Pi)
>
> You are right the the field obstruction factor F was left out in the
> first formula, you in general you should try to avoid obstruction, anyway.
>
> The first real difference is the so-called zenith correction exponent,
> which is assumed to be gamma=1.47 in the first formula (cos(z)^1.47) and
> gamma=1.0 in the second (sin(h)^1.0=sin(h)). This exponent gamma has been
> discussed for many years in a number of publications. Some people favour a
> value of 1.47, whereas other investigations came up with a value close to
> one. This is why in all IMO Shower Reports the old "standard value" 1.0 is
> used. When publishing ZHR figures you should always state which gamma you
> applied, as the difference in the computed ZHR will usually be quite
> large.
>
> The second difference comes from the statistics of small numbers. In the
> upper formula there is simply written HR, which is HR=(sum n)/sum(Teff).
> However, statistics teaches us that the correct expectation value for HR
> is (1+sum n)/sum(Teff). There was an article by Janko Richter in WGN a
> few years ago (?) which pointed to this little inconsistency in the
> standard ZHR formula(*), and since then the correct formula (with +1) has
> been used in all shower reports. The impact on the computed ZHR is
> neglectible for major showers, but noticable for minor showers with ZHRs
> well below 10.
>
> So for your own calculations I suggest you use the second formula.
>
> Best wishes,
> Sirko
>
> PS: I explained the stuff above to the best of my knowledge - don't
> hesitate to correct me if I'm wrong in some point! :-)
>
> (*) It may look strange that the expected HR value is >0 when you
> observed 0 meteors in a given time interval, but consinder the extreme
> case that you observed only one minute. Even when watching in August you
> will probably have seen no meteor in that minute, but the expected HR
> value is certainly not zero during the Perseids. If you add 1 as tough by
> statistics this does not happen. The expectation value for HR will be 1,
> for example, if you watch for a full hour but see no meteor, and will
> converge to zero the longer you observe without success.
>
> --
> **************************************************************************
> * Dipl.-Inform. Sirko Molau * *
> * RWTH Aachen, Lehrstuhl fuer Informatik VI * __ *
> * Ahornstr. 55, D-52056 Aachen, Germany * " 2B v 2B " *
> * * *
> * phone: +49-241-8021615 * Shakespeare *
> * fax : +49-241-8888219 * *
> * email: molau@informatik.rwth-aachendot de * *
> **************************************************************************
> * www : http://www-i6.informatik.rwth-aachendot de/Colleagues/molau *
> **************************************************************************
>
>
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