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Re: (meteorobs) Distance for simultaneous meteor observation
birger.andresen@fesil.no wrote:
>
> Definitions :
> s = distance [km] ALONG the earth surface from where
> the meteor is at zenith (the "zenith location").
>
> h = height [km] of the meteor (typical 80-120 km) at the
> "zenith location".
>
> r = earth radius (approx 6378 km)
>
> A(rad) = Angel [radians] above the horizon at which you see
> the meteor at s km away from the "zenith location".
>
> A(deg) = Same as A(rad), but in degrees (360 deg = full circle)
>
> Calculations :
>
> h cos(B) - (r - r cos(B))
> A(rad) = arctan ---------------------------------------
> r sin(B) + h sin(B)
>
> where B = s / r
>
> A(deg) = A(rad) * 260 / (2 Pi) ; Pi = 3.141592
>
> Examples :
>
> Meteor height = h = 80 km :
> In the horizon at s = 1000 km,
> 30 deg above the horizon at s = 135 km
> 45 deg above the horizon at s = 80 km
>
> Meteor height = h = 100 km :
> In the horizon at s = 1120 km,
> 30 deg above the horizon at s = 166 km
> 45 deg above the horizon at s = 97 km
>
> Meteor height = h = 120 km :
> In the horizon at s = 1225 km,
> 30 deg above the horizon at s = 200 km
> 45 deg above the horizon at s = 116 km
>
Birger,
The formula you present seems to be a trigonometric identity to my
formula. The difference is my formula (reproduced again, below) shows
the distance of the meteor, "s" (which = my 'd') as a function of the
observed altitude angle "A", rather than the other way around, as in
your formula.
Also, I use the earth radius r=6367km, as the mean of the equatorial and
polar radii. 6378km is the equatorial radius only.
Mike.
--------------------------distance formula------------------------------
d = distance from observer to meteor sub-earth point (which is the point
on the earth directly below the meteor). (d is measured along the earth
surface in km)
A = altitude of meteor as seen by observer (degrees).
h = height of meteor above the earth surface (km).
R = radius of the earth (km).
we get:
d = (pi/180) * R * [ARCCOS(COS(A)/(1+h/R)) - A]
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