Zenithal Hourly Rate
Encyclopedia
In astronomy
, the Zenithal Hourly Rate (ZHR) of a meteor shower
is the number of meteors a single observer would see in one hour under a clear, dark sky (limiting apparent magnitude
of 6.5) if the radiant
of the shower were at the zenith
. The rate that can effectively be seen is nearly always lower and decreases the closer the radiant is to the horizon
.
The formula to calculate the ZHR is:
where
represents the hourly rate of the observer. N is the number of meteors observed, and Teff is the effective observation time of the observer.
Example: If the observer detected 12 meteors in 15 minutes, their hourly rate was 48. (12 divided by 0.25 hours).
This 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.
This represents the limiting magnitude correction factor. For every change of 1 magnitude in the limiting magnitude of the observer, the number of meteors observed changes by a factor of r. Therefore we must take this into account.
Example: If r is 2, and the observer's limiting magnitude is 5.5, we will have to multiply their hourly rate by 2 (2 to the power 6.5-5.5), to know how many meteors they would have seen if their limiting magnitude was 6.5.
This represents the correction factor for altitude of the radiant above the horizon (hR). The number of meteors seen by an observer changes as the sine of the radiant height in radians.
Example: If the radiant was at an average altitude of 30° during the observation period, we will have to divide the observer's hourly rate by 0.5 (sin 30°) to know how many meteors they would have seen if the radiant was at the zenith.
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
, the Zenithal Hourly Rate (ZHR) of a meteor shower
Meteor shower
A meteor shower is a celestial event in which a number of meteors are observed to radiate from one point in the night sky. These meteors are caused by streams of cosmic debris called meteoroids entering Earth's atmosphere at extremely high speeds on parallel trajectories. Most meteors are smaller...
is the number of meteors a single observer would see in one hour under a clear, dark sky (limiting apparent magnitude
Apparent magnitude
The apparent magnitude of a celestial body is a measure of its brightness as seen by an observer on Earth, adjusted to the value it would have in the absence of the atmosphere...
of 6.5) if the radiant
Radiant (meteor shower)
The radiant or apparent radiant of a meteor shower is the point in the sky, from which meteors appear to originate. The Perseids, for example, are meteors which appear to come from a point within the constellation of Perseus....
of the shower were at the zenith
Zenith
The zenith is an imaginary point directly "above" a particular location, on the imaginary celestial sphere. "Above" means in the vertical direction opposite to the apparent gravitational force at that location. The opposite direction, i.e...
. The rate that can effectively be seen is nearly always lower and decreases the closer the radiant is to the horizon
Horizon
The horizon is the apparent line that separates earth from sky, the line that divides all visible directions into two categories: those that intersect the Earth's surface, and those that do not. At many locations, the true horizon is obscured by trees, buildings, mountains, etc., and the resulting...
.
The formula to calculate the ZHR is:
where
represents the hourly rate of the observer. N is the number of meteors observed, and Teff is the effective observation time of the observer.
Example: If the observer detected 12 meteors in 15 minutes, their hourly rate was 48. (12 divided by 0.25 hours).
This 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.
This represents the limiting magnitude correction factor. For every change of 1 magnitude in the limiting magnitude of the observer, the number of meteors observed changes by a factor of r. Therefore we must take this into account.
Example: If r is 2, and the observer's limiting magnitude is 5.5, we will have to multiply their hourly rate by 2 (2 to the power 6.5-5.5), to know how many meteors they would have seen if their limiting magnitude was 6.5.
This represents the correction factor for altitude of the radiant above the horizon (hR). The number of meteors seen by an observer changes as the sine of the radiant height in radians.
Example: If the radiant was at an average altitude of 30° during the observation period, we will have to divide the observer's hourly rate by 0.5 (sin 30°) to know how many meteors they would have seen if the radiant was at the zenith.