Timing the Shadow

Sharp-eyed readers may notice that eclipse timings given on the UK Track page differ slightly from those given in the the NASA SDAC bulletin. How come?

Same Difference

The total eclipse times and durations on my UK page are taken from the Royal Greenwich Observatory publication The RGO Guide to the 1999 Total Eclipse of the Sun. This provides slightly longer total eclipse durations for towns in the total eclipse path than the "raw" data given in the NASA SDAC bulletin. These are the differences for towns listed in both guides:

Size Counts -- but So Does Shape

So, who's right? The answer is, both, kind of. The width of the path of total eclipse, and the duration of total eclipse seen, depend, of course, on the size of the Moon -- the bigger it is, the bigger its shadow, and hence the longer the duration of totality. So what's the big deal? Surely we know how big the Moon is, and it doesn't exactly change much?

Well, the problem is that the Moon is not exactly spherical, so there is no one "right" value for the diameter of the Moon. One factor is the angle from which the Moon obscures the Sun, for example; and the mountains and valleys on the Moon play a large part.

The RGO Approach

The International Astronomical Union (IAU) defined a "standard" value for the moon's diameter, which averages mountain peaks and low valleys around the Moon's rugged edge. The Royal Greenwich Observatory used this standard size in the production of their eclipse data, and it gives perfectly adeqaute results for the casual observer. (I used the RGO data in my UK Track page because it provides local circumstances for more UK towns than the SDAC data.)

The problem with calculating the total eclipse zone in this way is that near the edge of the calculated zone, the Sun may still be visible through lunar valleys, causing Baily's Beads to be seen; so areas calculated to get a total eclipse may not (although very nearly). Similarly, on the centreline of the eclipse, the duration calcuated by this method may not be accurate, due to irregularities in the shape of the Moon.

The SDAC Approach

Fred Espenak, the author of the NASA SDAC bulletin, takes the Moon's irregularity into account by using a smaller value for the Moon's size; this value is itself somewhat arbitrary, being a mean minimum radius of the Moon, without taking into account the angle at which the Moon approaches the Sun. The data produced with this method is presented in Table 3 and Table 7 of the SDAC bulletin.

He then calculates, for points along the centreline, the effects on the duration of the eclipse of the actual shape and orientation of the Moon at each point; adjustments to the durations are presented in Table 6, as described in Limb Profile Effects on the Duration of Totality. Also, he calculates the actual north and south limits of the path of totality in terms of "grazing zones"; areas just short of totality in which the Sun's crescent is broken into beads and fragments. The limits of the grazing zones are presented in Table 8, and described in Limb Corrections to the Path Limits: Graze Zones.

Results

The upshot of the SDAC calculations is that the centreline durations are just slightly shorter (a couple of seconds) than those predicted by the RGO; however, one interesting result of the Moon's odd shape is that locations in Cornwall south of the centreline, by around 3-5 miles, may see a longer total eclipse than those on the centreline -- by 2-3 seconds. (See Limb Profile Effects on the Duration of Totality.)

For observers on the limit of the total eclipse (in Cornwall/Devon, that means the north limit, of course) things are a little more complex. The RGO's eclipse limits and durations actually reflect the outer edges of the grazing zones; so towns shown as having a total eclipse may, in fact, see Baily's Beads shortening the eclipse durations below the values I've published.

One interesting case is Teignmouth: the "base" SDAC data predicts that it will not see a total eclipse, whereas RGO predicts 14 seconds of totality! In fact, I believe that the centre of Teignmouth (where the A381 meets the Dawlish road) is exactly on the northern limit of the eclipse given by the "base" SDAC data; but is, in fact, substantially within the zone of grazing eclipse as given by the SDAC graze zone data. Observers there should, therefore, see a near-total eclipse, with the crescent Sun broken up into Baily's Beads for a short while. (It's close, though; just across the Teign is totality, by my reckoning!)

I'd be interested to hear what people actually observe on the day. If you feel like taking a stopwatch, let me know the duration you measured (from the moment the Sun totally vanishes, Baily's Beads and all, to the moment it reappears) and where you were. If you're in Teignmouth, I'd be interested to hear what you saw, but really, you'd be better off getting down to Salcombe to see a decent eclipse!

Sources

Correspondance with Steve Bell, H.M. Nautical Almanac Office, 26 August 1998