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# Zenithal Hourly Rate

In astronomy, the Zenithal Hourly Rate (ZHR) of a meteor shower is the number of meteors an observer would see in one hour under a clear, dark sky (limiting apparent magnitude of 6.5) and if the radiant of the shower were in the zenith. The rate that can effectively be seen is nearly always lower and decreases as the radiant is closer to the horizon.

The formula for calculation of the ZHR:

$ZHR = cfrac\left\{overline\left\{HR\right\} cdot F cdot r^\left\{6.5-lm\right\}\right\}\left\{sin\left(hR\right)\right\}$

when

$overline\left\{HR\right\} = cfrac\left\{N\right\}\left\{Teff\right\}$

Represents the hourly rate of the observer, N, number of meteors observed, divided by Teff, effective observation time of the observer. Example: If the observer detected 12 meteors in 15 minutes, his hourly rate was 48. (12 divided by 0.25 hours).

$F = cfrac\left\{1\right\}\left\{1-k\right\}$

Represents the field of view correction factor, where k is the percentage of the observer's field of view which is obstructed (by clouds, for example). Example: If 20% of the observer's field of view were covered by clouds, k would be 0.2 and F would be 1.25. The observer should have seen 25% more meteors, therefore we multiply by F = 1.25.

$r^\left\{6.5-lm\right\}$

Represents the limiting magnitude correction factor. For every change of 1 magnitude in the limiting magnitude of the observer, the number of meteors observer changes by a factor of r. Therefore we must take this into account. Example: If r is 2, and the observer's limiting magnitude was 5.5, we will have to multiply his hourly rater by 2 (2 in the power of 6.5-5.5), to know how many meteors he would have seen if his limiting magnitude was 6.5.

$sin\left(hR\right)$

Represents the correction factor for height of the radiant over the horizon(hR). The number of meteors seen by an observer changes with the sinus function of the radiant height in degrees. Example: If the radiant was on average at a height of 30 in the sky during the observation, we will have to divide his hourly rater by 0.5 (sin(30)) to know how many meteors he would have seen if the meteor was in the Zenith.