Sunday, September 18, 2005

Harvest Moon

Something startled our dogs at around 3:30 am this morning, waking me up — and then something startled me: the very bright light streaming in our bedroom window. It appeared to be just a little bit too bright to be the moonlight. We live in a rural area with no artificial sources of light around, so my sleepy brain was scrambling for explanations. But when I got up and peered through the window, an amazing sight greeted me: it was moonlight, so bright that I could (just barely) make out colors and textures in my yard.

So I got dressed, let the dogs out into the yard, and went out myself to see what this brightly moonlit night might look like. Standing on our patio and looking to the north, I could see several unusual and surprising things. The muted greens and browns in the chapparal covering the low mountains about two miles to our north were clearly visible. The sky in the northeast quarter, opposite the full moon, was distinctly lighter and had tinges of blue. The Italian stone pines in my yard, about 10 meters high, were crisply lit — and green. The reddish flagstones of our patio were ... reddish. And when I turned to the southwest and looked at the moon itself, the darned thing was so big and bright that it put a hurt on my eyeballs!

This needed explaining. Why, on this particular night, was the moon so much brighter than usual?

My first thought was that perhaps the weather conditions were unusual. Looking at the sky, I could easily see that it was clear of clouds ... but I could also see a little backscatter (a background glow), indicating that there was at least a little haze in the air. Looking at my weather instruments showed it was 60°F and 25% relative humidity — beautiful weather, to be sure ... but not at all unusual here. The barometer was dropping, but only within normal and common range. Conclusion: nothing unusual enough about the weather to explain the brightness.

So I did what any amateur scientist would do in this situation. I fired up Google, and started looking for information about bright full moons.

And I got some answers (very quickly, actually). It's all about the perigee. It turns out that the moon's orbit around the Earth is not exactly circular — at apogee (or furthest point) it is about 406 thousand kilometers from Earth; at perigee (or nearest point) it is about 360 thousand kilometers from Earth. The photos at right show the moon at perigee (left) and apogee (right); the apparent size difference is obvious. That's roughly a 10% difference in distance, but from John Walker's Fourmilab we find out that makes about a 30% difference in brightness:

How Bright the Moonlight?

When the Moon is full near perigee, you'd expect it to be brighter than a full Moon near apogee and it is: lots brighter; let's figure out how much. Since the Moon shines by reflecting sunlight (not very well — it reflects only about 7% of the light that strikes it, comparable to a lump of coal) the following two factors determine the intensity of moonlight at the Earth:

1. The intensity of sunlight striking the Moon.
2. The distance reflected light travels from the Moon to the Earth.

Since the difference between the minimum and maximum distance of the Moon, 50345 km, is an insignificant fraction of the average distance from the Sun to the Earth and Moon, 149597870 km, the intensity of sunlight at the Moon can be considered constant and ignored in this calculation. (Sunlight intensity at the Moon does vary, of course, due to the eccentricity of the Earth's orbit around the Sun, but we'll ignore that smaller annual effect here since we're concentrating on lunar perigee and apogee.)

The intensity of light varies as the inverse square of the distance between a light source and the observer, so taking the ratio between the perigee and apogee distances in the photographs above as typical, the distance at apogee was 1.1363 times the perigee distance, and hence the Moon's intensity at perigee was the square of this quantity, 1.2912 times brighter--about 30%. Using the long-term extremes plotted in the drawing in the previous section yields only a slightly greater intensity difference: a distance variation of 1.1413, with the Moon shining 1.3026 times brighter at perigee.

But the full moon isn't always at perigee. The moon is at perigee once in each of its orbits (each 27.3 days); full moons occur every 29.5 days. The difference between the two is due to the Earth's rotation around the sun. The result is that the moon is at different distances from the Earth during each full moon, but those distances can be calculated easily (see here and here). And it turns out that for tonight, the full moon occurred very near perigee, which was just two days ago (on September 16th).

In addition to the distance of the moon from the Earth, it also turns out that the distance from the sun to the Earth makes a difference (as Mr. Walker mentions above), albeit a much smaller one. Perihelion is the closest approach of the Earth to the sun, and it occurs in early January each year. At perihelion the sun (and therefore the reflected sunlight of the full moon) is about 7% brighter than at aphelion (when the Earth is most distant from the sun, in early July). Currently we're just under halfway through that cycle, so the full moon is about 3% brighter than it would be under the same conditions in July.

So there you have it! The moon tonight was about a third (33%) brighter than at its dimmest — and this is a fairly unusual combination of events to make it this bright. Of course it didn't hurt a bit that our viewing conditions were near perfect!

I'll leave you with a few other interesting sites I found on bright moons: here, here, here, and here.

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