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The Rugged Lunar Limb

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The Rugged Lunar Limb Ch04.qxd 7/4/07 12:03 PM Page 39 Chapter 4 The Rugged Lunar Limb The Moon is not a perfectly smooth sphere. The mean equatorial diameter is 3,476 km and the mean polar diameter is 3,470 km. But the actual surface, although the lunar maria are relatively smooth, contains some very rugged terrain. Indeed, at the lunar limb, as viewed from the Earth, there is precious little in the way of smooth plains. Most of the maria regions are directly facing the Earth. Also, due to the so-called “librations”, the limb of the Moon never presents the same jagged outline to us. Librations Libration is a phenomenon by which we are able to peer around the lunar limb and see, at a painfully shallow angle, the edges of the Moon’s far side. In fact, we can theoretically see 59% of the lunar surface, not just 50%, by using libration tilts. As we saw earlier the Moon rotates around the Earth every 29.5 days (from new Moon to new Moon) and every 27.3 days, with respect to the stars. However, it is con- stantly rotating on its axis such that the same face always points towards the Earth well, almost the same face. Imagine you are talking to someone, but occasionally they lower their head, so you see more of their badly fitting wig, or raise their head so you see more of their ludicrous goatee beard. Now and again they shake their head too, so you see a bit more of one ridiculous earring and then the other. This is analogous to what librations do to our view of the Moon. Because the Moon’s orbit is elliptical its angular position with respect to the Earth does not vary con- stantly, even though its axial rotation is always the same. The velocity of the Moon around the Earth is faster at perigee than apogee. Because of this, we can some- times peer around either the eastern or western limbs and see almost 8° more Moon (7°54′ to be precise). This is called a libration in longitude. There is an additional effect called diurnal libration, caused by the fact that the Earth has a radius of over 6,000 km and so, depending on whether the Moon is rising or setting (or if you are at the north or south poles for that matter) you are standing on a platform which gives you an extra ability to peer round the limb. However, most observers will view an eclipse when it is near their meridian. The Rugged Lunar Limb The main librations in latitude (excluding travelling to the poles of the Earth) are caused by the fact that the lunar equator is tilted with respect to the lunar orbital plane, much as the Earth’s equator/axis is tilted with respect to the 39 Ch04.qxd 7/4/07 12:03 PM Page 40 ecliptic/ecliptic pole. Thus, as the Moon orbits the Earth, first one pole and then the other tilts by 6°41′ towards the Earth (the absolute extreme librations are actually 6°50′). In practice, these monthly librations in latitude and longitude form a vector sum, peaking in a maximum libration effect of 10° when latitude and longitude librations peak together and swing a feature on the NE, SE, SW or NW limb towards Earth. Of course, that is not much use if the feature is in darkness, but it is highly exciting when a favourable Sun angle picks out the feature well and the sky is clear. Watts Charts Predictions As you can imagine, predicting just how rugged the lunar limb will be, from your location at a particular eclipse, is not a trivial task. However, a considerable amount of information is available for determining which peaks and valleys will be in silhouette at totality. For hybrid eclipses, which are on the borderline of the total/annular condition, this information is obviously crucial. But even for non- hybrid cases eclipse chasers always like to know if there is a good chance of some spectacular Baily’s Beads appearing at second and third contacts. Named after Francis Baily (1774–1844), the British astronomer, these are the glistening beads that are literally the last shafts of sunlight to get through the lunar valleys at the start of totality, and the first shafts of light at the end of totality. (Incidentally, to my knowledge there is nothing to link Mr Francis Baily and the equally famous Mr Robert Francis Bailey. The latter gentleman famously “spontaneously combusted” in Lambeth, London, after drinking meths, in 1967.) Despite the seemingly depressing and intimidating mountain (pun intended!) of work required to predict the lunar limb profile this has, essentially, already been done. In 1963, Watts of the US Naval Observatory produced a mass of data based on analysis of photographs of the lunar limb regions. Although these contained less than complete data near the poles, they still, four decades later, provide the basis for eclipse predictions. The charts are known simply as “Watts Charts”. Since 1963 extra data on the polar limb regions has been added and, even today, the Tokyo National Observatory refines the Watts Charts data based on the timings of thousands of lunar occultations (stars timed disappearing behind the Moon). In 1970 and 1979, respectively, Van Flandern and Morrison proved that the lunar profile based on Watts analysis was slightly elliptical and the lunar centre implied by Watts was not exactly at the centre of the lunar mass. Morrison and Appleby, in 1981, further showed that there were tiny errors due to the average Watts radius varying with lunar librations. However, these only amounted to about 0.4 arcsec in the worst cases. This is equivalent to about 700 m on the lunar surface. Watts charts, which are provided for each eclipse typically by Fred Espenak of NASA, show a Moon in which the limb irregularities have been enormously exaggerated to allow easy interpretation of what is happening (see Fig. 4.1). If the Watts charts The Rugged Lunar Limb were reproduced without exaggeration of the limb irregularities, a 200 mm diam- eter Moon disc would have mountains and valleys only tenths of a millimeter above and below the perfect circle. 40 Ch04.qxd 7/4/07 12:03 PM Page 41 N True Limb Mean Limb 00Њ Zenith (Center of Figure) 3 2 Mean limb (Center of Mass) Second 1 Contact 0 Moon North −1 −2 −3 Second Contact Contact Time Time Correction Curve Correction Scale E 090Њ 2 1 0 −1 −2 Seconds Fig. 4.1. Watts charts can be used to predict the precise timings of second and third contacts at total solar eclipses by taking into account the mountains and valleys on the lunar limb. The Watts data for the northeast quadrant of the Moon at the 29 March total solar eclipse is shown here, specifically for 10:30 U.T. and a geographic position of 28°38′47.9′′N 21°53′39.9′′E. The jagged outer circle is the exaggerated (by about 60 ×) rocky lunar limb as it deviates from the mean limb (dotted line). The next inner circle is the mean limb radius based on the lunar mass rather than the mean lunar figure. The much smaller radius solid inner circle for this quadrant marks the contact time correction zero point and the wiggling curve shows, at a large scale, the second contact time correction curve. Image: NASA 2006 Eclipse Bulletin by Fred Espenak and Jay Anderson Hybrids and the Lunar Radius During an eclipse, if the last or first part of the Sun disappears or reappears close to a very deep set of lunar valleys, the Baily’s beads can literally sparkle, momen- tarily, like diamonds at the limb. The radii of the Sun and Moon during total solar eclipses are, of course, fairly similar (see Fig. 4.2). In the hybrid case the radii are essentially the same, whereas in the longest total solar eclipses the lunar radius is roughly 7% greater than the solar radius. In the former case, or at least in very short total eclipses, as the last chink of the solar photosphere disappears at the “diamond ring” position angle, Baily’s beads may sparkle over a considerable arc of the lunar limb. Indeed, in the exact hybrid case, if the observer is close to the point on the track where annularity changes into totality, it may feel as if the Sun The Rugged Lunar Limb never disappeared, as the chromospheric glow on the second contact side will barely have disappeared before it reappears on the third contact side, swiftly 41 Ch04.qxd 7/4/07 12:03 PM Page 42 Fig. 4.2. Second contact at the 3 October 2005 Annular Eclipse, clearly showing the rugged lunar limb. Image: Damian Peach Fig. 4.3. The rugged lunar terrain and limb near the crater Demonax on 19 April 2005. Image by Damian Peach using a Celestron C 9.25 and Lumenera LU 075M camera. followed by the emergent Baily’s beads and the third contact diamond ring. As discussed earlier, the 3 October 1986 hybrid is, perhaps, the ultimate example in modern times. Predicting where an eclipse will be total along such a track requires precise attention to detail. A total eclipse is only total if the Sun is smaller than a mean lunar radius that accounts for the deepest valleys. If any photospheric light seeps through any valley at the deepest part of the eclipse, then totality has not been achieved from that viewing site.
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