A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2017 Aug 18, 12:53 -0700
Start simple. You could shoot an ordinary Sun-Moon fix, though you'll have to separate the sights in time, like a running fix, to get enough azimuth spread. For example, here in New England I could shoot the altitude of the Sun just after the beginning of the eclipse around 1:30 when its azimuth is around 200°. Then I could shoot the altitude of the Moon's upper limb (in front of the Sun!) at mid-eclipse about 2:45 when the azimuth of both bodies is nearly 230°, far enough from the first sight to cross the lines of position. And I could shoot the Sun's altitude again just before the end of the eclipse. Needless to say, I could skip the Moon entirely and shoot a Sun upper limb in the middle, but where's the fun in that? This is strictly for the amusement value of getting a line of position from the New Moon, which is otherwise impossible.
For lunars-style sights, you could estimate the times of first and last contact. This is not actually easy, but we can use our sextants to make it more accurate. The two cusps at the Moon's limb crossing the Sun's face move quite rapidly under some geometric conditions. Just after the Moon begins to cross onto the Sun's face, and you detect that little bite taken out, measure the angle between the two cusps. Do this repeatedly, maybe once a minute for ten minutes, and then plot the results on a graph. You'll see that the rate of increase of the angle is high at the beginning and then rapidly slows down. If the limbs of both bodies were perfect circles, the rate at the beginning would be formally infinite. Can you extrapolate back to get the time to the second when the eclipse began? Reverse the process at the end of the eclipse. You could also get those times by measuring the angle from the inside limb to the Sun's opposing limb (like the phase as described) and extrapolate more-or-less linearly to the time when that angle would be equal to the Sun's diameter (from tables or measured before and after the eclipse). Those times correspond to instants of zero apparent lunar distance, and you can reduce them as lunar distance sights with the usual caveats about very short distances.
For observers relatively close to the path of totality, try measuring the altitudes of the cusps near the time of maximum eclipse. They will change rapidly and at different rates. Can you do anything with that??
Yet another lunar-like observation: measure the minimum angle during the eclipse between the Moon's limb on the face of the Sun and the limb of the Sun parallel to it. This is a measure of the maximum "phase" of the eclipse and provides a nice line of position without measured altitudes. This is very similar to getting a fix by observing artificial satellites against background stars though the potential accuracy is only about 5-10 nautical miles since the Moon is so far away. When using artificial satellites, since they are typically a thousand times closer, you can get results as much as 1000 times more accurate which is near GPS accuracy.