A night under the stars — and haze

Posted by Rich Talcott
on Thursday, December 14, 2006

Mathematicians like me find numbers in almost everything we do. Last night, the key number was 11 — a simple count of the number of Geminid meteors I saw while observing for 1 hour centered around the shower's predicted peak at 2:45 A.M. CST.

At first glance, that doesn't sound like many. Meteor expert Peter Jenniskens of the SETI Institute predicted the Geminid shower would peak at a zenithal hourly rate (ZHR) of 130 +/- 20 meteors per hour. But bear with me — you'll see the numbers matched almost perfectly.

First, some other important numbers: The temperature was a balmy 33° F (this is Wisconsin in mid-December, after all), but the humidity was a soggy 92%. The high moisture content meant I had less-than-ideal sky conditions, which were exacerbated by occasional high, thin clouds and a waning crescent Moon in the east.

My limiting magnitude averaged about 3.7. I could always see Lambda Orionis, at magnitude 3.5, but rarely glimpsed Zeta (ζ) Aurigae, at magnitude 3.8. That's what really killed me. The ZHR is defined as the number of meteors an average observer would see under a transparent sky if the shower's radiant appears directly overhead and the faintest stars visible glow at magnitude 6.5.

You can calculate a shower's ZHR from observations by taking into account clouds or other obstructions, the limiting magnitude, and the radiant's altitude. I really wasn't bothered by the clouds or any obstructions - the key for me was limiting magnitude. The Geminids have a "population index" of 2.3, which means there are 2.3 times as many meteors visible for each magnitude fainter you go. So, for every 10 Geminid meteors of magnitude 3, there should be 23 meteors of magnitude 4, 53 of magnitude 5, and 122 of magnitude 6. To calculate how many more meteors I would have seen under perfect conditions, I have to multiply by the population index raised to a power of 6.5 minus the limiting magnitude, or 2.32.8 = 10.3.

I also have to adjust for the radiant's altitude at the time of my observations, but that's a minor effect because Gemini was high in the sky. Around 3 A.M. local time, the radiant lies 20° from the zenith, giving an additional factor of 1/cos (20°) = 1.06.

Putting it all together, my ZHR last night was 11x10.3x1.06 = 120, within the margin of error predicted by Jenniskens. (For other Geminid observations, visit the International Meteor Organization's web site.

But the key number last night was 1: A single bright, long, and beautiful meteor trail that cut through Auriga, Taurus, and Aries. It made the whole night worthwhile.

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