Hi Duncan,
Happy to hear you liked my video animations. Given the “rather variable” (!) conditions I experienced during the eclipse; the need to take several shots on different exposures each time to combat the variable cloud cover, as well as experimenting with two different density filters for the same reason, and the problem of taking shots at the required 5 minute interval if clouds decided to intrude meant that the individual frames needed A LOT of processing to get them consistent enough to be assembled into the animations. I’m thus glad to know that my efforts have been appreciated! The second one is particularly intriguing, as you say – I haven’t seen anything similar on the Internet so I was rather pleased it came out so well.
I also found equations of the form you derived on the Internet but wanted to explicitly avoid that approach so I could get my results via an entirely different route and thus be confident in the comparison between the two methods. Doing it “the hard way” also enabled me to sort of work backwards from the answer and derive an again multi-step process for converting from magnitude to obscuration, which I’m sure will prove useful.
In terms of the measurement and calculation errors which might be expected, the fact that I was able to use a much larger image gave me advantages in both precision and accuracy. More precise as I was working at the 1 in 1000 level whereas you were at 1 in 250, and potentially more accurate as, because of the greater precision, I could determine my measurements at a smaller “step length”. That is, in my case a 1 pixel step hardly moved the “marquee” lines I was using to measure distances, and so the lines could be more closely aligned with the Sun, whereas your 1 pixel change will have moved the measurement point by four times as much so you might not have been able to line things up exactly. I still had the problem of estimating the correct points to measure from of course, given that my image was not sharp (because of the limitations of the home-made filters I was using), but even so I believe that my distances were probably correct to +/- 1 pixel. Translated to the difference this would make to the final result, as compared to the nominal 1200 by 846 figures, the maximum difference (in the cases 1201 / 845 and 1199 / 847) was just less than 0.5% which is still pretty acceptable.
The same website I used to determine the theoretical magnitude and obscuration also gave the ratio of the diameters at my maximum eclipse, which was 0.99253. The assumption of equal sizes is thus highly reasonable, involving potential errors of only the same order of magnitude as those involved in taking the measurements and probably less as the radii are used as part of more complex equations rather than as direct parameters. The SD values on the NASA chart are of course those relating to the point of absolute greatest magnitude (over eastern Siberia) so, while indicative of the situation, will not be applicable to the UK as the Moon will have moved along its orbit during the eclipse.
Steve