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!

That was the day that was - 6 megahits

kw: book reviews, nonfiction, sun, moon, earth

I just Googled "that was the day that was" and got 5.9 million hits (Yes, I used quotes. Without them, it's 1.1 Billion(!) hits). Raconteur Michael Sims spends a day with us in Apollo's Fire: A Day on Earth in Nature and Imagination, and like all semi-fictional days, it is one packed day. Authors aplenty have written "day in the life of" novels and memoirs. This book is a day in the life of...a Day.

It is only recently, historically speaking, that people determined that the Sun is large and comparatively far away. How large? Its diameter is more than 100 times the Earth's, so its volume is greater than one million Earth volumes. How far? Whether you think in miles (93 million) or km (149 million), it is FAR: nearly 12,000 times Earth's diameter, or 3,700 times around, and around, and around...

But for thousands, perhaps hundreds of thousands, of years, since we had a thinker to think with, the Sun was thought of as a powerful but familiar Presence, perhaps the size of the next big town down the road, hung on a big bowl of a sky held up by the distant hills or mountains.

By turns didactic, lyrical, bare-bones factual, yet always engaging and witty, Sims takes us, not hour by hour, but event by event, through one day: pre-dawn darkness, dawn, morning, midday, afternoon and "brillig", sunset, twilight, and night. Here both science and mythology have a place.

Every culture bases its religion or mythology on daily events and the dominant players, the Sun and Moon. It could hardly be otherwise. Suppose that one side of Earth faced the sun perpetually, as the Moon's visible hemisphere always faces Earth. There would be no notion of "reliable as the sunrise". The Moon, which circles Earth monthly, would be the primary mobile item in a fixed Heaven, and would likely be the dominant deity; the Sun is "just there all the time, and does nothing". Subtler events like the slow orbits of Mars and Saturn take a people with plenty of leisure to puzzle out.

Many in the West know the Biblical formulation, "The Sun to rule the day, and the Moon to rule the night." But have you noticed the Moon in the daytime? This image from a spacecraft on its way to the outer planets captures an amazing view: Not only is the Moon at First Quarter, so is the Earth.

Those in Earth's nighttime see the half-moon high in the sky at sunset, rapidly descending to set about midnight. But consider those on the late afternoon portion of Earth. The Moon is (barring overcast skies) visible as a white half-cookie pasted on a blue sky, about halfway around the sky from the Sun's position. About half the time, the Moon is a daylight object, and near New Moon, it hardly appears after dark.

And that blue color? It is the blue sky seen from above. The air scatters light; even very pure air containing no dust will scatter light. Blue scatters more than red, because the short wavelength of blue light is more closely matched to the size of the molecules that make up the air. When you look at a mountain range such as the Rockies, seen from forty or fifty miles away, the blue, hazy effect is the blueness of the air between. Air is visible. Even after dark, if the moon is up, the sky appears grayish, not black. If our color vision were more sensitive, we would see that moonlit skies are also blue. Maybe lemurs, with their huge eyes see blue nighttime skies. But they are dark to us.

Darkness. What is the reason? The existence of a dark sky is visible proof that the Universe is finite, either in time, in extent, or probably both. Sims takes us rapidly through the wranglings of Galileo, Kepler, Olbers, and finally Slipher, as the puzzle of the dark sky was gradually solved...well, as solved as it can be at present. We still don't know for sure whether the expansion following the Big Bang is slowing down or, as many now contend, speeding up (My take: slowing down. The apparent anomaly in supernova brightness at very great distances is related to elemental evolution. The stars billions of years ago, having very low "metals" abundance, got bigger, burned brighter, and blew up more energetically than is the rule now. Type Ia supernovae in the early universe were genuinely brighter.).

By the end of the book, I felt like I'd been sitting with a comfortable, knowledgeable companion through a long, pleasant day.