R G B W

Calculate the Zenithal Hourly Rate for a meteor shower

ZHR (Zenithal Hourly Rate) is the value used by astronomers to define the number of meteors that can be spotted by the human eye in one hour if the radiant of the meteor shower is seen at zenith. You find these values pre-calculated in astronomy books and on the internet.

Following is the formula used to determine the ZHR-value. Use it to calculate the ZHR of a meteor shower based on your own personal meteor observations. Since every observer around the earth don't have the same observing conditions, it is a bit more complicated than just go out and count meteors.

The formula is: ZHR = 1/sin L * R^(6.5 - m) * b * n.

where:

L = the height of the shower center on the sky
R = a special value for each meteor shower
m = the limiting magnitude
b = a number that depends on how many that observed
n = number of meteors seen in an hour
Explanation

First of all you have to know how many observers are watching. When there are more than just one, the easiest way is to assign different parts of the sky to different observers. Let everybody watch for about a quarter of an hour and write down the number of meteor this person have seen.

When you have completed the observing session, sum up the values. Here is a little example where 12 meteors were seen in 15 minutes.

One of the first things you have to compensate for is the radiants altitude in the sky. It may change because the earth moves through space so remember to use the average height.

1/sin 40° * 12 = 18.67 ......................where the height of the meteor shower is 40°

Then you have to consider the limiting magnitude. To do this you must estimate which magnitude the faintest star you can see in zenith has. Many amateur astronomers use the stars in Ursa Minor to compare with. Here is a star map to compare to.

Now use the following formula. R^(6.5 - m)

R is a value that is different for each meteor showers and compensates for the shape of the meteor shower relative to it's magnitude. In this example we're looking at Perseid meteors so the R-value is 2.6.

On IMO:s (International Meteor Organization) homepage there are calenders and lists with the meteor showers respective R-values.

Let's say you have estimated the limiting magnitude to 5.8. When multiplying this to the number you got before, it gives you 2.6^(6.5 - 5.8) * 18.67 = 2.6^0.7 * 18.67 = 36.44

You must also take into consideration the number of observers. Here is a list that will give you a number depending on how many were out watching.

1 observer = 1.00 

2 observers = 0.56 

3 observers = 0.41 

4 observers = 0.36 

5 observers = 0.32 

6 observers = 0.28 

7 observers = 0.25 

8 observers = 0.22

In this example we were two observers so we will use the number 0.56. Multiply the result from the previous calculation with 0.56 and it gives you:

0.56 * 36.44 = 20.41

Finally multiply the number with 4 to make up for the missing quarters. Remember that the ZHR value stands for the number of meteors seen during a whole hour.

20.41 * 4 = 81.63

ZHR=81.63

This is the Zenithal Hourly Rate, 81.63.

The accuracy can also be calculated and this is done with the formula ZHR/sqrt(N). N is the number of meteors seen in an hour and in our case that would be 4*12 since we were just observing for a quarter of an hour.

81.63/ sqrt(4*12) = 11.78

The result of our observing session would be that the Zenithal Hourly Rate is 81.63 ± 11.78.

Edit..

Text and photographs copyleft Olle Eriksson unless otherwise noted. All rights reversed.

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