Zenithal hourly rate: Difference between revisions

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In astronomy, the zenithal hourly rate (ZHR) of a meteor shower is the number of meteors a single observer would see in an hour of peak activity if the radiant was at the zenith, assuming the seeing conditions are perfect^[1] (when and where stars with apparent magnitudes up to 6.5 are visible to the naked eye^[2]). The rate that can effectively be seen is nearly always lower and decreases the closer the radiant is to the horizon.

Calculation

The formula to calculate the ZHR is:

$ZHR={\cfrac {{\overline {HR}}\cdot F\cdot r^{6.5-lm}}{\sin(h_{R})}}$

where

${\overline {HR}}={\cfrac {N}{T_{eff}}}$

represents the hourly rate of the observer. N is the number of meteors observed, and T_eff 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).

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

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 multiply by F = 1.25.

$r^{6.5-lm}$

This represents the limiting magnitude correction factor (Population index). 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, this must be taken into account.

Example: If r is 2, and the observer's limiting magnitude is 5.5, the hourly rate is multiplied 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.

$\sin(h_{R})$

This represents the correction factor for the altitude of the radiant above the horizon (h_R). The number of meteors seen by an observer changes as the sine of the radiant height. ^{[dubious – discuss]}

Example: If the radiant was at an average altitude of 30° during the observation period, the observer's hourly rate will need to be divided by 0.5 (sin 30°) to know how many meteors they would have seen if the radiant was at the zenith.

References

^ Cooke, Bill (19 Nov 2019). "About the Upcoming (maybe) Alpha Monocerotid Meteor Shower Outburst". NASA Blogs.
^ Beech, Martin (2006). Meteors and Meteorites: Origins and Observations. United Kingdom: Crowood Press. pp. 80–81. ISBN 9781861268259.

External links

North American Meteor Network (NAMN)

[1] Cooke, Bill (19 Nov 2019). "About the Upcoming (maybe) Alpha Monocerotid Meteor Shower Outburst". NASA Blogs.

[2] Beech, Martin (2006). Meteors and Meteorites: Origins and Observations. United Kingdom: Crowood Press. pp. 80–81. ISBN 9781861268259.

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+{{More citations needed|date=September 2023}}[[File:AGOModra Leonids98.jpg|thumb|All-sky view of the 1998 [[Leonids]] shower. 156 meteors were captured in this 4-hour image.|216x216px]]
-{{unreferenced|date=April 2012}}
-[[File:AGOModra Leonids98.jpg|thumb|right|All-sky view of the 1998 [[Leonids]] shower. 156 meteors were captured in this 4 hour image.]]
-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 (meteor shower)|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]].
+In [[astronomy]], the '''zenithal hourly rate''' ('''ZHR''') of a [[meteor shower]] is the number of [[meteoroid|meteors]] a single observer would see in an hour of peak activity if the radiant was at the [[zenith]], assuming the [[astronomical seeing|seeing]] conditions are perfect<ref>{{Cite web |last=Cooke |first=Bill |date=19 Nov 2019 |title=About the Upcoming (maybe) Alpha Monocerotid Meteor Shower Outburst |url=https://blogs.nasa.gov/Watch_the_Skies/2019/11/ |website=NASA Blogs}}</ref> (when and where stars with [[apparent magnitude]]s up to 6.5 are visible to the [[naked eye]]<ref>{{Cite book |last=Beech |first=Martin |title=Meteors and Meteorites: Origins and Observations |publisher=Crowood Press |year=2006 |isbn=9781861268259 |location=United Kingdom |pages=80–81 |language=English}}</ref>). The rate that can effectively be seen is nearly always lower and decreases the closer the radiant is to the [[horizon]].
+== Calculation ==
 The formula to calculate the ZHR is:
-<math> ZHR = \cfrac{\overline{HR} \cdot F \cdot r^{6.5-lm}}{\sin(hR)} </math>
+<math> ZHR = \cfrac{\overline{HR} \cdot F \cdot r^{6.5-lm}}{\sin(h_R)} </math>
 where
 <math>\overline{HR} = \cfrac{N}{T_{eff}} </math>
-represents the hourly rate of the observer.  N is the number of meteors observed, and T<sub>eff</sub> is the effective observation time of the observer.
+represents the hourly rate of the observer. N is the number of meteors observed, and T<sub>eff</sub> 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).
+Example: If the observer detected 12 meteors in 15 minutes, their hourly rate was 48 (12 divided by 0.25 hours).
 <math> F = \cfrac{1}{1-k}</math>
+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).
-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 multiply by F = 1.25.
-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.
 <math> r^{6.5-lm} </math>
-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.
+This represents the limiting magnitude correction factor ([[Population index]]). 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, this must be taken into account.
+Example: If r is 2, and the observer's limiting magnitude is 5.5, the hourly rate is multiplied 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.
+<math> \sin(h_R) </math>
-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 the altitude of the radiant above the horizon (h<sub>R</sub>). The number of meteors seen by an observer changes as the sine of the radiant height. {{Dubious |Talk section sin(hR) dependence|reason=Using this definition, no meteors would be seen by an observer at sea level if radiant is on the horizon. Clearly rubbish, as the meteors radiate in multiple directions, and some would go above the horizon date=August 2018|date=August 2018}}
+Example: If the radiant was at an average altitude of 30° during the observation period, the observer's hourly rate will need to be divided by 0.5 (sin 30°) to know how many meteors they would have seen if the radiant was at the zenith.
-<math> \sin(hR) </math>
-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&deg; during the observation period, we will have to divide the observer's hourly rate by 0.5 (sin 30&deg;) to know how many meteors they would have seen if the radiant was at the zenith.
 ==See also==
 *[[List of meteor showers]]
+==References==
+{{Reflist}}
 ==External links==
 *[http://www.namnmeteors.org/guidechap8.html North American Meteor Network] (NAMN)
+{{Meteor showers}}
 [[Category:Meteoroids]]
 [[Category:Observational astronomy]]
-[[bg:Зенитно часово число]]
-[[ca:Taxa horària zenital]]
-[[de:Zenithal Hourly Rate]]
-[[es:Tasa Horaria Zenital]]
-[[fa:نرخ ساعتی سرسویی]]
-[[fr:Taux horaire zénithal]]
-[[gl:Taxa Horaria Zenital]]
-[[ko:정점 시율]]
-[[it:Tasso orario zenitale]]
-[[he:קצב זניתי לשעה]]
-[[lb:Zenithal Hourly Rate]]
-[[ms:Kadar Kemuncak Sejam]]
-[[nl:Zenithal hourly rate]]
-[[ja:天頂出現数]]
-[[pl:Zenitalna liczba godzinna]]
-[[pt:Taxa horária zenital]]
-[[ru:Зенитное часовое число]]
-[[sk:Zenitová hodinová frekvencia]]
-[[sl:Zenitna urna frekvenca]]
-[[sr:Зенитна часовна активност]]
-[[zh:每小時天頂流星數]]

v t e Meteor showers
By name	Andromedids Antihelion Source Aquariids eta Aquariids kappa Aquariids North delta Aquariids North iota Aquariids South iota Aquariids Southern Delta Aquariids tau Aquariids Aquilids South June Aquilids Arietids Daytime eps. Arietids Daytime May Arietids Aurigids alpha Aurigids delta Aurigids Nov. iota Aurigids Bootids (June Bootids) Canis-Minorids Cancrids (delta Cancrids) Capricornids alpha Capricornids Daytime Capri.-Sagitt. Carinids (eta Carinids) Cassiopeids (beta Cassiopeids) Centaurids alpha Centaurids theta Centaurids omicron Centaurids Cetids omega Cetids pi Cetids Comae Berenicids Cygnids (kappa Cygnids) Doradids (gamma Doradids) Draconids Eridanids (eta Eridanids) Geminids (epsilon Geminids) Herculids (tau Herculids) Hydrids (sigma Hydrids) Leonids Leonis Minorids (Dec. Leonis Minorids) Lyrids eta Lyrids June Lyrids Monocerotids alpha Monocerotids Normids (gamma Normids) Orionids Pegasids Perseids Daytime zeta Perseids September epsilon Perseids Phoenicids (July Phoenicids) Piscis Austrinids Puppids (pi Puppids) Puppid-Velids Quadrantids Scorpiids alpha Scorpiids North omega Scorpiids South omega Scorpiids Serpentids (kappa Serpentids) Sextantids (Daytime Sextantids) Taurids Daytime beta Taurids Northern Taurids Southern Taurids Ursids Virginids alpha Virginids gamma Virginids eta Virginids theta Virginids iota Virginids lambda Virginids mu Virginids pi Virginids psi Virginids March Virginids
By peak date	January 4 February 8 February 10 March 14 April 17 April 22–23 April 26 May 6 June 7 June 27 July 13 July 28–29 July 30 July 31 – August 1 August 13 September 1 October 8 October 10 October 21 October 22 November 9 November 12 November 18 November 21–22 December 5–6 December 13–14 December 15 December 22
Related topics	American Meteor Society Earth-grazing fireball International Meteor Organization Meteor procession North American Meteor Network Population index Radiant Zenithal Hourly Rate
See also List of meteor showers