Letting some of it trickle out while trying to soak it all in

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.


  1. Ben says he won't read my comment until I post it here on the blog. So here we go.

    I'm not certain that your reasoning gets you exactly what you are looking for. I'm going to make a few simplifying assumptions, so please let me know if I'm assuming something I shouldn't as it concerns your argument.

    Let's assume that the moon lies in the ecliptic (it's quite an assumption, actually, because lunar apsidal precession has a period of something like 8 years, so you'd have years during which perigee full moons would be wasted on summer months, leaving you cold, small apogee full moons for your winter; of course, you'd have other years with winter perigee full moons and summer apogee moons--here, as elsewhere, the high latitudes take it lumpy; also, I'm not certain if your argument was making use of the fact that the moon's orbit was close to the ecliptic, but not exactly there, because there might be something to that); and let's also ignore anything else which might come from ecliptic orbits (the "earliest sunrise doesn't occur on the solstice" thing, for example).

    Additionally, let's assume that the lunar cycle is in sync with the solar cycle (otherwise we might have fluctuation from year to year simply due to when the full moons occurred with respect to the solar year).

    Further, let's simplify things by ignoring lunar orbital movement during a night (I don't think this one matters, but who knows, you might be able to make something out of the moon's apparent "slowness"--your long winter full moons are correspondingly an hour or so longer still, with the moon rising just before sunset and setting just after sunrise).

    So let's imagine twelve full moons spaced evenly throughout the circular year. The moon rises just as the sun sets, and for each day-night pair of lengths (x, y), there is a corresponding day-night pair of lengths (y, x). So, by the symmetry of the situation we find that no matter your lattitude, you enjoy the same amount of full moon time. The same argument applies, mutatis mutandis, to waxing gibbous time, new moon time, etc.

    Essentially, what I'm saying is that your example of the 21-hour winter full moon would be fully offset by the 3-hour summer full moon which occurs 6 months later.

    But then, I might be missing some relevant details myself.

  2. Thanks for bringing this conversation out into the light (moon or sun) where it belongs.

    I think all your assumptions are sound and are similar to the ones I made (though my assumptions were more complete because I didn't even know about the mutant gibbons).

    You are right about the full moon giving no advantage annually (if it fell on the solstice at least), it is the partially illuminated moons that spend less of their flytime in the sky at the same time as the sun that leads to the difference. Regardless of latitude the moon spends the same amount of time in view (assuming that all its wobbles cancel out--which they probably don't annually but probably do on decadal scales). But to a high latitude observer, more nighttime is spent during the illuminated phases of the moon when we are tipped towards the ecliptic.

    To hedge my bets I'll bring in another solar phenomenon that contributes to effectively enhanced moonlight. During the hypothetical three hour moonless summer solstice, the nightime isn't completely dark since the sun is only a few degrees below the horizon.

    To resolve this we need to crunch the numbers for a year. Time in the sky without the sun x % illumination = annual moontime. Data for rises and sets is here (http://aa.usno.navy.mil/data/docs/RS_OneYear.php) but there may be a better site that also provides % illumination. We should pick a latitudinal transect of at least three flat places and see if there is a pattern.

    Love you.

  3. How about the refracting effect that gives us a few more minutes of sun at dawn and dusk? this is the idea that the suns rays are bent because of the atmosphere and we see the sun a few minutes after it has actually set. Are you sure this is uniform at all latitudes? and there is no such refracting effect when you have 24 hours of sunlight (can't get more than 24) so I still say we are being cheated in Alaska.

    1. That's only true north of the Arctic Circle (where you have at least one day with 24 hours of sunlight). If anything, our long sunrises and sunsets magnify that effect spoiling us with sun. Love you.

  4. https://www.youtube.com/watch?annotation_id=annotation_3944063881&feature=iv&src_vid=tmNXKqeUtJM&v=T3gacnHb9TI

    reminds me of this