Zenithal Hourly Rate

by Dominic Ford, Editor
Last updated: 12 May 2020
Zenithal Hourly Rate

An artistic depiction of the Leonid meteor storm seen over North America on the night of November 12-13 by Edmund Weiss (1833).

The zenithal hourly rate (ZHR) of a meteor shower. is a measure of the rate at which it produces meteors, expressed as the number of meteors seen per hour.

In practice, the number of meteors actually seen will by significantly less than the ZHR, which is the theoretical number of meteors which would be seen under perfect conditions. The observed number will depend on many factors, including sky conditions, the degree of light pollution in the observer's neighbourhood, and the altitude of the meteor shower's radiant in the night sky.

Even when looking at the same meteor shower, these factors will vary from one observer to another. For example, the altitude of the meteor shower's radiant will depend on the observer's geographic latitude.

The number of meteors you are actually likely see to see is given by the formula

\[ \text{Number of meteors}= \frac{\text{ZHR}\times \sin(\theta)}{F \times r^{6.5-m}}. \]

The terms in this equation are as follows:

ZHR is the zenithal hourly rate,

\( \theta \) is the altitude of the radiant of the meteor shower above the horizon,

\( F \) is a correction factor for the amount of sky you're looking at,

\( m \) is the limiting magnitude, and

\( r \) is a constant, typically equal to 2.

The factor \( F \) is calculated using the formula:

\[ F = \frac{1}{1-k} \]

where \( k \) is the fraction of the sky which is which you cannot see, because it is obscured by cloud or other obstructions such as trees.

As an example, if the radiant of a meteor shower appeared 30° above your horizon, the maximum number of meteors you might expect to see is half the ZHR, since \( \theta=30^\circ \) and \( \sin(30^\circ)=0.5 \).

If you were observing from from a town, and the faintest stars you could see were magnitude 4.5, the rate of meteors might be further reduced by a factor of four, since \( r^{6.5-m} \) would equal 4.


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