Contributed By: George Zay, IMO Member

The zenithal hourly rate is a means by which different observers can convey their results to each other. Of course, this is the ideal condition to observe meteors under. However, conditions are not always perfect. To make matters worse, the human factor is a variable that makes ZHR results less precise. There are several methods to finding a ZHR. Some are more accurate than others and are quite involved in calculations. Variables to consider include clouds, limiting magnitudes, observing periods, the radiant's zenith distance, geographical latitude of the observer, and the observer's own perception. The following method does not take all of these variables into account. But this method from Neil Bone's book, Meteors will serve our purposes here as an introduction to the subject.

HR = observed hourly rate; r = population index; LM = your average limiting magnitude; and A = altitude of the shower's radiant above the horizon in degrees

a) Formula with an LM above 6.5

      (HR) (r)^1-(LM - 6.5)
ZHR = ----------------------   
             Sine A 

b) Formula with an LM below 6.5

       (HR) (r)^6.5-LM
ZHR = -------------------  
            Sine A

Example: Geminids with clear skies and no obstructions.

HR = 57 meteors seen for 1 hour
r = population index for Geminids is 2.6
LM = average limiting magnitude for that hour is 5.7
A = the shower's radiant above the horizon for that hour is 60 degrees

       (HR) (r)6.5 - LM
ZHR = -----------------------
           Sine A

      (57) (2.6)6.5 - 5.7
    = -----------------------
        Sine 60 degrees

          (57) (2.6).8
    = -----------------------

            57 X 2.14
    = -----------------------

    =   ---------------------

    =    140 ZHR

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