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This is probably important only if you are a werewolf - Mark Atwood
This is probably important only if you are a werewolf
In a geeky discussion in a chat, the conversation turned computing the phases of the Moon, I wondered if the POM calculator in emacs needed the observer's lat/lon numbers.

someone: Phases of the moon don't depend noticeably on lat/long - the moon is far enough away compared to the diameter of the earth that to all intents and purposes you see the same hemisphere of the moon no matter where you are on earth. I think they're ususually just calculated wrt the centre of the earth. http://aa.usno.navy.mil/faq/docs/moon_phases.php says "For practical purposes, phases of the Moon and the percent of the Moon illuminated are independent of the location on the Earth from where the Moon is observed."
mra: (looks up numbers, does trig)
mra: the sin of the max angle of view is (12750km / 2) / (384403km / 2)
mra: so the max angle of divergence from plumb is 0.0331743996 radians
mra: which is .005282547 of the full circle, 3.46 hours of the lunar orbit
mra: so the apparent phase can be 3.5 hours early or late, depending on where you are standing on the earth
mra: when something is computing the time of the phase to the closest minute, it looks like your lat/long is significant

Did I get my math right?

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3 comments or Leave a comment
whl From: whl Date: September 25th, 2007 09:44 pm (UTC) (Link)
I think if it only mattered to the Werewolf exactly when the moon was full (within a minute or so), the problem would be more managable.

In their case, the error bars seem much larger...
loganb From: loganb Date: September 25th, 2007 10:29 pm (UTC) (Link)
When you say "to the closest minute," do you mean arc-minute or time-of-day?

Also should the angle be arctan(Re/Dm) where Re is the radius of the earth and Dm is the distance to the moon? I then get 0.01 radians which is significantly less. It is certainly not relevant for any practical application, but merely highlights a bug in the POM app where it yields insignificant digits.

From: wnoise Date: September 28th, 2007 07:59 am (UTC) (Link)
I think so.

If I'm following what you did, you divided earth's radius (diameter / 2) by the moon's orbital radius / 2, so your angle is the full angle not, maximum displacement from the assumed mean. I'd divide by two to find out how far off things are.

In the werewolf literature I've seen, a few hours don't matter. Nights of the full moon (and nearby nights, sometimes) matter. A few hours off is basically not noticeable by eye when looking at the moon, either.
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