Sunday, March 16, 2014

Just our share of sun and more than our share of moon

As we approach the equinox, I am reminded about the only fair thing on earth. Whatever latitude you live at, you receive the same duration of illumination from the sun annually: 4,380 hours. Whether you live on the north pole where the sun rises and sets once a year or on the equator where the length of day is interesting as American Idol, half the time the sun is up, half it is down averaged over a year. This justice is afforded by the passionless geometry of a tilted sphere*.

Thanks Cornell for the diagram. I don't agree with all their 
scaling and color choices but it gets the point across.

Here in Fairbanks we take our sunshine lumpy. We are two degrees shy of the Arctic Circle which is defined as the lowest latitude that experiences at least one day a year without sunset. But we get reasonably close with almost 21 hours of sunlight on June 21st and just over three hours of low-slung sun on December 21st (that is literally a dark day here in Alaska).

Though our annual allotment of sunshine is completely fair (in a Solomon sort of way), it doesn't agree with everyone who lives here. That's why I'm here today to tell those who live at high latitude that there is an important, and as far as I can tell, completely overlooked luminous advantage to living in the far north (or south). Because the moon is more closely aligned with the earth-sun axis rather than with earth's equator, during the darkest months, the farther north you are, the more moon-time you get.

Long haired-man and the three wolves of justice bearing news 
that the moon spends more time looking at high latitudes.

Since the moon is illuminated when it is on the opposite side of the earth from the sun, and because during winter the earth is tilted in that same direction, at high latitudes the moonlight is out more. Over the course of a year this results in high latitudes facing a larger proportion of illuminated moon than lower latitudes.
All made possible by the quirky moon being more closely aligned with 
the sun than the tilt of the earth (awesomely termed latitudinal libration).

To make this clearer we need to specify what we mean by the moon being out. The moon is technically "out" or in sight 50% of the time at all latitudes. But at high latitudes a larger portion of that "out" time occurs when the moon is illuminated, giving us less "wasted" new moon time. Consequently, we have less daytime moonlight than lower latitudes when the moon is out (and illuminated) at the same time as the sun. The farther from the equator you travel, the more illuminated and out time you get.

For example, on the shortest day of the year in Fairbanks, the full moon rises at 2:40 pm as the sun goes down. The frosty moon then follows the same arc across the sky that the midnight sun followed exactly six months before on the summer solstice, providing the brightness of the full moon for 21 hours until it sets the next morning at 11 when the sun rises.

Sorry if this post reads more like a word problem than a stimulating diversion, but hey, it's near midterms and this is good practice.

As a warning, I have never heard anyone talk about this phenomenon so there is a chance I am missing something in my reasoning and am wrong. Let me know if you figure that out, but until then here's to mood swings, seasonal affective disorder, and moonlight!


*While this is true at a continental level, local topography strongly affects actual length of direct sunlight. For those of you behind a mountain or hill, you might have hundreds of hours less than your allotted 4,380 hours of sunshine. And this even though the earth is relatively smoother and more spherical than a pool ball.