Tuesday, March 22, 2011

Supermoon still beautiful

kw: astronomy, moon, sun, eclipses

The Super Moon of 2011 occurred just three nights ago. I was out earlier this morning to get the newspaper, and the gibbous moon is still a lovely sight. But then, I love to see the moon no matter what its phase or distance from Earth. There are tons of websites explaining this super moon, but most of them leave out a crucial detail.

The diagram below, from a NASA Science News video (also found on YouTube), shows the basic phenomenon. The range of distance between apogee and perigee (apo- means "far" and peri- means "near") is about 14%. The apparent area of an object 14% closer and thus 14% larger, in an angular sense, is 1.14x1.14 = 1.30, so a perigee full moon is 30% brighter than an apogee full moon.

As it happens, this is a Super Moon not just because the full moon occurs the same day as perigee. It is doubly super because this is the closest perigee of the year. In 2011, perigee distances range from 356,577 km to 369,565 km, and apogee distances range from 404,274 km to 406,655 km. The "average" perigee is about 363,000 km and the "average" apogee is about 405,000 km. 405/363 = 1.116, but dividing largest apogee by smallest perigee, we get 406,655/356,577 = 1.140. See Lunar Perigee and Apogee Calculator to calculate these figures for any year.

Another way to state it is angular size. The moon's diameter is 3,476 km. The minimum angular diameter of the moon in 2011 will be 3,476/406,655 = 1/117.0, which is 0.4896 degrees or 29.4 arc minutes. Its angular diameter on the 19th was 3,476/356,577 = 1/102.6, which is 0.5585 degrees or 33.5 arc minutes.

Now, to take a side run, this helps explain why some total Solar eclipses are more "total" than others. I have been privileged to view several solar eclipses in the past fifty years, and one of these was annular. That is, at mid-eclipse, the moon did not cover the sun, but formed a central block, with the sun showing all around. The following diagram, from Spaceweather.com, shows the range of solar distances for 2005.

The Earth's distance from the sun varies from about 147 million km to about 152 million km. The sun's diameter is 1,392,000 km, so the range of angular diameter is as shown in this image, from 31.46 arc minutes to 32.53 arc minutes. This is a narrower range than that of the moon. This is fortunate for us. 152.1/147.1 = 1.034, and the square of this is 1.069. This, the sun's radiation varies only 7% over a year. Just by the way, this seven percent can either enhance or detract from the brightness of a super moon. A super perigee moon that occurred when earth was at perihelion would be 37% brighter than a super apogee moon at aphelion.

But the main point here is the ranges of angular diameter. When the moon is farther than 379,800 km, about halfway to apogee, it cannot cover the sun, even when the sun's angular size is at its smallest. A central solar eclipse that occurs when the moon is in the apogee half of its orbit will thus be annular. Now, I wonder if it ever occurs that there is an "exactly total" solar eclipse, such that, for observers in just the right place, Bailey's beads will be seen all the way around the moon for just a second (Bailey's beads are the bits of sunshine that pass through mountain valleys on the rim of the moon just as the totality begins and ends, or second contact and third contact. A single bright BB is called a "diamond ring"). Now, that would be a sight for a millennium!

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