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Measuring Earth's shadow: 170 years of crater timings: a very long-running lunar eclipse project reaches fruition.

The last rim of the rayed crater Tycho (arrowed) was just about to cross the edge of Earth's umbra when Dennis di Cicco took this shot on the evening of November 8, 2003.

Maybe you have been one of them--a backyard astronomer, watch in hand, intently peering at a partially eclipsed Moon with a 2- to 8-inch telescope. You watch as a crater or small marking drifts up to, and then across, the edge of Earth's shadow. You note the time, realizing that you could be off by 20 or 30 seconds because the edge of the shadow is rather fuzzy. Crater timings may seem somewhat crude, but astronomers have made them this way for centuries. That's their beauty, and their potential value.

Last October, David Herald and I published a large database of these timings on the VizieR Service for Astronomical Catalogues operated in Strasbourg,

France. Our data set holds 22,539 records of 26,685 individual timings, all made visually with small telescopes, during 94 total and partial lunar eclipses from 1842 through 2011. This is by far the largest collection of such timings that has ever been assembled.

Sky & Telescope readers can take special pride in contributing roughly half of these timings, starting almost 60 years ago. Editor Joseph Ashbrook solicited them from 1956 until his death in 1980, at which point I took over the magazine's crater-timing project. The rest were collected by Australian amateur Byron Soulsby, who cultivated his own worldwide network of crater timers and gleaned more timings from older literature. Especially important was a long series made by the noted lunar observer J. F. Julius Schmidt from 1842 to 1879, first in Germany and later at Athens Observatory in Greece.

When Soulsby died in 2009, David Herald (of the International Occultation Timing Association) and I merged and reformatted all these records. This vast collection serves as a check on just when lunar eclipses begin and end. It also helps us to assess some quaint theories about the size and shape of Earth's shadow.

It's well established that Earth's atmosphere makes the umbra (the shadow's dark central portion) a little larger than would be expected for an airless Earth. So lunar eclipses always begin a few minutes early and end late. This effect was noticed as early as 1687 by French almanac maker Philippe de la Hire. To allow for it, modern publications such as the U. S. Naval Observatory's Astronomical Almanac routinely add 2 percent to the radius of Earth's umbra in their eclipse predictions.

But do careful timings by observers fully support this procedure? Is 2 percent the right value? No, in fact, as we'll see later in this article.

There are many further wrinkles. In a 1950 study of 33 lunar eclipses, Czech astronomers Jiri Bouska and Zdenek Svestka reported that the umbra was somewhat more swollen if an eclipse occurred within a few days after a meteor shower, presumably from extra meteoric dust in the upper atmosphere. Another 57 eclipses, studied in 1954 by Frantisek Link and Z. Linkova, appeared to confirm this finding. But Herald and I could find no such correlation in our much more extensive data.

We also checked to see if the umbra's size tracks the 11-year solar cycle in any way. That question suggested itself because, in a 1921 analysis of 150 eclipses by French astronomer Andre Danjon, the eclipsed Moon's brightness and color seemed to be tied to the solar cycle. In fact, Danjon devised his five-point L scale for rating an eclipsed Moon's brightness to aid further study of this effect. Alas, the database shows no solar-cycle correlation with the size of the umbra at all.

What about major volcanic eruptions? These can loft many cubic kilometers of dust into the Earth's stratosphere, where it spreads around the globe and persists for many months. Nine months after a huge eruption of Mount Agung on Bali, the Moon became as dim as a star of visual magnitude 4.1 during the legendary total eclipse of December 30, 1963. But the 615 crater timings Sky & Telescope received from that event show an umbra size quite typical of most other eclipses, bright or dark.

The Shape of the Umbra

The most enduring oddity claimed for the umbra relates not to its size, but to its shape. For example, crater timings led French astronomer Guillaume Joseph Le Gentil to announce in 1755 that the umbra was larger northsouth than it was east-west. But how could that be, given that Earth itself is "squashed" at the poles?

Then in the 20th century, a contrary supposed flattening of the umbra caught on. At various times Bouska, Link, Ashbrook, and Soulsby all reported the umbra to be wider east-west than it ought to be, even allowing for Earth's slight spread at the equator and the geometrical distortion in a converging light cone at the Moon's distance.

Following their lead, G. F. Schilling (Rand Corporation) wrote in the March 1965 Journal of the Atmospheric Sciences that a variation in the height of Earth's mesosphere (a zone from roughly 50 to 100 kilometers up) by latitude could explain the added oblateness of the shadow. Using measurements of noctilucent clouds as a guide, Schilling suggested that the mesosphere's height might vary from roughly 100 km at the equator down to 82 km at latitude 60[degrees] north or south.

Once again, however, the new database fails to agree. On average, the umbra appears as if an occulting layer 87 km thick uniformly surrounds the (oblate) Earth. This thickness, deduced from timings, does not vary in a predictable way with the position angle around the umbra--which is closely related to the latitude on Earth that accounts for a given piece of the shadow's edge.

Nor does it show any periodic or long-term trend over 170 years, despite the slow global warming that has happened during the last 100 years and especially the last 40. The timings do show the umbra to be oblate, but only to the extent expected from the known oblateness of Earth and the geometry of the shadow cone.

We call this atmospheric add-on to Earth's radius the "notional eclipse-forming layer" or NEL. We stress that this does not mean the atmosphere up to 87 km literally blocks sunlight traveling in a straight line past Earth toward the Moon. A combination of scattering, absorption, and refractive effects at many levels must be involved. The NEL is just a convenient concept for comparing, or predicting, lunar eclipses.

Should Predictions Be Revised?

A key finding from the new database is that crater timings disagree with the way in which contact times for lunar eclipses are predicted in the annual Astronomical Almanac (jointly published by the nautical almanac offices at the U.S. Naval Observatory and in the United Kingdom). Contact times are when the edge of Earth's umbra touches the Moon's edge, marking the start and end of the partial and total phases of a lunar eclipse. The Astronomical Almanac uses the 2-percent rule mentioned earlier, which goes back to a recommendation by American astronomer William Chauvenet in 1863.

Applying any constant percentage increase to the umbra's size overlooks, however, the fact that at some eclipses the Moon is near the far point of its orbit (apogee), while other eclipses occur with the Moon closer to Earth (perigee). As seen in the middle diagram on the facing page, crater timings "detect" this percentage problem, while the NEL method works equally well no matter where the Moon is in its orbit. Depending on which method is used, limb-contact predictions could easily differ by a minute or more.

Unlike the Astronomical Almanac, the French Connaissance des Temps uses a better prediction method recommended by Danjon in 1951. In effect, he adopted an NEL height of about 75 km. But his method, too, could be improved by a switch to the 87 km implied by the new database.

Keep in mind that our 87 km is the average for the 94 eclipses in our analysis. Certain well-observed eclipses have deviated from it--maybe not for the reasons suggested by past investigators, but deviated nonetheless.

For example, the 1,164 timings from the July 6,1982, eclipse imply a height of 91 [+ or -] 1 km, while the 1,119 timings made on August 16-17,1989, yield 82 [+ or -] 1 (where the uncertainties are one standard deviation from the mean; the 68% confidence level). These differences are statistically robust, but their cause remains unexplained.

Shortcomings

As with any crowdsourced inquiry, there are benefits in the sheer quantity of observations we received from dedicated volunteers, but there are caveats, too.

Observers have been asked on some occasions to use the steepest brightness gradient in the umbra's edge for making their timings (our preferred method), and at other times to use the mid-brightness between the umbra and penumbra on either side of the edge. The second method is especially problematic when one tries to time not craters, but the umbra's contacts with the Moon's limb. At first and last contact the Moon is wholly outside the umbra, while at second and third contact it is wholly inside. So an observer can't see the two brightness levels to judge their midpoint.

Observers agree more closely when timing the passage of small craters or spots across the umbra's edge. (Happily, 91% of the database timings are this type.) But even then, twilight or haze might throw timers off.

If the aim is to characterize the umbra at a particular lunar eclipse in hopes of understanding what makes the edge fuzzy, a specialized photometer or digital imaging technique would provide fodder for serious research. But if our interest lies, instead, in the visual response of the typical human eye, or in checking for possible cycles or long-term changes in the umbra--a fascination of past investigators--there's no substitute for visual timings spanning many decades or even centuries.

On September 27, 1996, a total eclipse of the Moon yielded 302 crater and contact timings sent in by readers. They indicate a higher than average eclipsing layer at that time, 92 [+ or -] 2 km.

This September 27th, one Metonic cycle later, a very similar total lunar eclipse will be widely seen during the evening throughout the Americas. The Moon may look dark, bright, or especially colorful as eclipses go. And no one knows if the umbra's size will correspond to the typical 87 km or something else. Only timings will tell.

Senior Contributing Editor Roger W. Sinnott, who joined the S&T staff in 1971, was amazed to see the Moon almost vanish from the sky during the predawn eclipse of December 30, 1963.

The Online Data

The new crater-timing catalog is publicly available at vizier.u-strasbg.fr/viz-bin/VizieR, with the designation VI/140. It includes timings for the umbra contacting the Moon's limb as well as the ingress or egress of individual spots and craters. Each of the 22,539 records is accompanied by two calculated quantities: the percent enlargement of the umbra, and the NEL height that the timing implies for that point on the umbra's edge at that time.

Each record also shows the name of the individual or group who submitted it (a few are unknown). There are 764 names in all, including some people who made timings in their youth and went on to become well-known professional astronomers.

For a more detailed report on the database and the conclusions we draw from it, see "Analysis of Lunar Crater Timings, 1842-2011" by David Herald and Roger W. Sinnott in the October 2014 Journal of the British Astronomical Association, pages 247-253.
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Title Annotation:The Size and Shape of Earth's Umbra
Author:Sinnott, Roger W.
Publication:Sky & Telescope
Date:Jun 1, 2015
Words:1938
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