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Hi Duncan,
Interesting! I experienced exactly the same problem when I tried to edit a reply. Like yours, it just vanished. Maybe something to report to “the powers that be”?
Anyway – I agree with your “error bars”. Probably the only practical way to improve the accuracy and precision of the observations would be to increase the resolution of the image (mine was 1920×1920 pixels, cropped from 3264×2448 to centre it) and to use a better filter so the image was sharper. Mine was just a home-made item, constructed by inserting a small piece of Mylar sheet – formerly a lens from a pair of eclipse specs! – into the top of a closed cardboard cylinder sized to fit over my camera barrel. Cheap, but not exactly high quality! Then of course one would have to re-do the calculations to take account of the possibly differing apparent sizes of Sun & Moon. I’ve seen the required analysis on the Internet, but the result is by no means as simple as your “one-liner” formula! One must also consider the accuracy of the predictions themselves – do they assume a spherical Earth and Moon, for example, or use a “true geoid” and reliable limb profiles? At the level we are considering, such things become important.
I shall certainly be repeating these calculations the next time round though, on 29th March 2025!
Steve
Oddly, although before I made this reply the front page of the website said the latest reply was from Duncan, and the total number of replies before this one was given as 23 with the last made by Duncan 5 hrs 57 mins ago (at time of typing), the number of actual posts was shown as only 22 with nothing visible from Duncan. An aborted reply, or a glitch somewhere?
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
And hello to Duncan again!
I didn’t have my BAA Handbook at hand when typing my previous replies last last night but now I have I can perhaps shed some light on the eclipse diagram to which you refer.
Diagrams such as these are taken from the NASA eclipses website rather than being generated by the BAA, and there is an explanatory page about them at https://eclipse.gsfc.nasa.gov/SEplot/SEplotkey.html which might help you. It is, unfortunately, worded in very technical terms but the last part should help you understand the various numbers and times around the map. But basically the blue lines are lines of equal eclipse magnitude and the green lines join places where maximum eclipse for that place occurs at the same time. A larger and clearer version of the magnitude/time plot for the UK appears on page 273 of the current version of the Journal, where the text clearly says that the numbers are magnitudes rather than obscurations.
Hope that helps!
Hi Nick,
And here’s another animation I constructed showing that, although it appears to “roll” in an arc across the Sun in the previous animation, the Moon’s track across the Sun is indeed a straight line. Made by not removing previous frames when adding a new one until the straight line position is reached, and then successively removing early frames until last contact.
Hi Duncan,
Inspired by your remarks, I derived a series of formulae to calculate the obscuration from the chord length but “did it the hard way” i.e. by using just basic trigonometry, in order to get a completely different method from yours. Comparing my result with yours, for the chord length and sun diameter you quote, I found that the two answers are precisely the same. I think we may therefore conclude that your equation is correct (and very much simpler than my deliberately straightforward but multi-step derivation!).
I then applied the formulae to the observations I had made. I was fortunate to be able to take an image within seconds of maximum eclipse at my location, and as it was captured with a camera using a “hyper-zoom” lens the image was much larger than your projected image, enabling me to get a greater precision in the lengths involved. I found that the chord length was 846px and the Sun’s diameter was 1200px, resulting in an obscuration of 17.98%. I also calculated the magnitude using the same lengths, which was 0.2908. These numbers should be compared to the predicted values of 17.96% and 0.2910 given by the eclipse circumstances predictor written by the well-known “computer” Xavier Jubier. Pretty good result, I thought!
And now addressing myself to Nick James, concerning his message about the eclipse video above:-
Hi Nick!
I was quite lucky here in north Suffolk as although I had patchy cloud cover I was able to capture images between the clouds about every 5 mins, and from them assemble not a video as such but rather a “video animation”. This was after quite a lot of processing to get the images consistent of course! It shows the entire eclipse in just 25secs, as per the attachment.
It is certainly true that Jean has done many calculations of this type but not, as far as I am aware, about this specific topic.
I also analysed this situation in some detail, having seen many reports on the Internet about “nearest for 59 years”, with some claimimng 70 years. I came to the same general conclusions as Dominic and John – that this year’s opposition was closer than those dating back to 1963 / 1951 because although the perihelion to opposition interval was slightly greater than average (when the average is taken over the most recent cycle) and perihelion itself was very close to average, the combination of the two parameters was the most favourable overall during this period. This is because of the phase difference between the ~83yr cycle of perihelion-opposition intervals and the 59-yr cycle of closer perihelions.
During the period prior to the present, perihelion distances were smaller than average for the 2010 and 1999 oppositions but the perihelion-opposition intervals were greater, and then although the p-o interval in 1987 and 1975 was less than average the perihelion distance was greater. It was not until 1963 that near optimum conditions were reached again, with a minimum p-o interval and just above average perihelion distance. The situation in 1951 was then even better, with a much less than average p-o interval but a minimum perihelion distance. Things got steadily worse before that, with both the p-o interval and the perihelion distance steadily increasing.
However, it should be noted that the variation in Sun-Earth distance has a greater effect on the results over this period than might have been assumed from Dominic’s final paragraph. While it is of course true that the variation in Jupiter’s orbit is greater than that in the Earth’s, it is important to consider distances at opposition rather than at Jupiter’s perihelion, and because of the large changes in perihelion-opposition interval the opposition distances have a different “variation profile” from the perihelion distances alone. In fact, the Sun-Earth distance at opposition in 2022 was from 0.0077 to 0.0021AU greater than in all the oppositions from 1999 to 1951 while the Sun-Jupiter opposition distance varied from 0.0027AU greater to 0.0058AU smaller than 2022 over the same period. It can thus be seen that the two variations in distance actually had the same degree of influence on the final result.
A very interesting analysis to undertake, however!
Right then – here it is! “Hubble Tension Refuted” – without recourse to the consumption of orange flavoured cakes (sic!) or listening to famous bandleaders of the same name. However, even sticking to the salient points the discourse turned out to be quite long so I am presenting it as an attached PDF rather than “inline”. I hope this will not discourage interested members from reading it however – comments are welcomed and invited!
Superb! Thanks for bringing this item to the attention of a wider readership Jeremy. Understated humour and irony coupled with (apparent) scientific rigour is clearly a winner! And, most importantly, the correct conclusion is reached – which I would be celebrating with one of the famous cakes were it not for the fact that I currently do not have any in stock. A Digestive
cakebiscuit is thus having to suffice.Yes, it would be nice to think that (as you imply) this was simply a “Poisson d’Avril” but a quick literature search indicates that it’s not the first time that such an “explanation” has been put forward, apparently seriously, and of course (as current world affairs have shown only too shockingly) even the most outrageous mis-information will be believed, and spread, by somebody. The fact that in this case the mis-information is in the form of a scientific (or perhaps I should say pseudo-scientific) paper submitted to arxiv will tend to lead credence to the “research” even though it was published on 1st April and so I felt I should counter the arguments made so at least readers of the Forum who are not perhaps au fait with cosmological ideas will not be deceived.
As previously stated – watch this space!
An interesting paper but unfortunately total nonsense. I am preparing a detailed rebuttal but that is not top of my ToDo List currently – watch this space!
Very helpful Peter – thank you. I had “browsed” that paper in the Journal but clearly missed the vital bit which was of relevance to my recent sunspot adventures. Quite a difference between the two groups in Fig.24, is there not? Good to know that I wasn’t just doing something silly with my analysis though and that at least smaller sunspots really do move around. Maybe fortunate that my second subject for analysis (2835) was exactly as per your description of the ideal candidate else I really would have been puzzled!
A good learning experience though, so definitely worth investigating.
Thanks for the link to that Bulletin – very interesting (though I would note that the last bit should be “WeeklyPDF” rather than “Weekly/PDF”). However, it shows that whereas 2836 does indeed move from 57 to 62 degrees, 2835 also moves – if a little less. This might be a reflection of the changing shape of the entire 2835 group though (and hence a shift of its “centre of gravity”) rather than proper motion as such. The situation with 2836 is much more clear-cut though so I think we can say it truly does exhibit proper motion. Just my luck to choose to follow a small spot on the basis that it would be easier to measure!
Yes, after a near miss in Cherbourg in 1999 I was in Africa too – in a field full of maize stubble just off the Great North Road out of Lusaka, the capital of Zambia. My equipment was a Minolta 7000i SLR 35mm film camera (remember those?) fitted with a 600mm mirror lens plus x2 doubler and loaded with 400ASA slide film. A home-made solar filter constructed from one (mylar) lens of a pair of eclipse specs was inserted into the focal point filter-holder of the mirror lens – not quite sure how it failed to melt! – and this lot was mounted on a standard alt-az photographic tripod weighted against the wind by a thermos flask of water tied to the tripod head with a piece of string! Finding the Sun was very difficult (small field of view and no finder) and even when it swam into view the tripod’s elevation clamp was not quite strong enough to hold the extra weight and so a degree of “droop” had to be allowed for. The fact that I was able to get quite a reasonable set of images was thus little short of a miracle! Here’s a few:-
The tour group sits in the shade, watching the early partial phase through eclipse specs.
The crescent Sun, as viewed through the mylar filter somewhat before totality, presages things to come!
Baily’s Beads shine out between the lunar mountains.
As totality arrives, the inner corona becomes visible together with more prominences.
A composite of eight pictures shows the delicate beauty of the full corona.
The beginning of the end: the chromosphere is briefly visible as the Sun’s brightness re-appears.
As the Moon retreats, sunspots are revealed (again through the filter).
I was actually rather pleased with my efforts, given the circumstances. Not quite such a struggle these days, what with digital imaging and stable EQ tripods, but “doing it the hard way” was certainly a good learning experience!
Many thanks for that most helpful and instructive set of replies Robin! And for taking the time to search out the other spectra & spectrum comparisons and construct links to them. Given the several places within the website that observations can appear, it can be difficult to keep track of developments and thus find the most relevant post.
It was interesting to learn that prism and grating spectroscopes give fundamentally different outputs and that therefore the Harlow and Hugh spectra are incompatible by definition. I don’t think this important aspect was covered in the A-Level syllabus so many years ago! Perhaps I should mention at this point that when I referred to the great differences in spectrum linearity I was not implying any fault in the instruments or technique but merely commenting on what I could see before me – apologies if anyone thought otherwise. It’s comforting to know that my deduction of a “stretched violet” for prismatic spectra was accurate though! I will now have to carefully study the information in the links Robin gave me, and the more recent posts on the Nova Cas topic, so I can get a better idea of this facinating subject.
So – keep up the good work you spectrographers, as your results are being followed not just by the “experts” but also by those with a rather less detailed knowledge of the subject!
Although Roger is unable to update the postings on this topic himself, he has been keeping a keen eye on the lively discussions in “read only mode”, as it were, and advising me on possible responses. However, now that things seem to have quietened down he has suggested that the topic be brought to an end.
Accordingly, he has asked me to forward his thanks to all those who took the time to suggest possible hardware solutions which embody similar functionality to his prototype device even if, in several cases, they sit at a much higher price point or, in the case of the 9×50 finder purely optical solution proposed by Jeremy, lack a number of distinctive features which can only be provided “electronically”. He remarked that he is actually encouraged by the fact that no-one has come up with an electro-optical device which has all the functionality required by a “beginner improver”, and no more (no need for focusers, replaceable eyepieces, filters, multi-element optics etc.), which might perhaps indicate that there is a gap in the market for a device such as his if it can be manufactured at a reasonable price. Proving it might be more of a problem though!
In closing, we both wish everyone “Clear Skies” and good observing.
Thanks for the new information Jeremy, and the link to the Astro Essentials finder. I had in fact come across this device when I did a search for 9×50 finders after your last post but was unsure of the quality of such a device at this price point. It’s thus reassuring to hear that “beginners speak well of this kind of finder scope”.
On the downside however, one reviewer does mention the “weight” issue which Roger encountered with the 9×50 he tried. And while the erecting prism will give a corrected view, this is only true for one orientation of the optics. If the prism is removed or rotated (for “observational convenience”), the view will change in a way which might be confusing to a beginner (as I previously noted). Also, an optical device lacks the other advantages of an electronic device which I mentioned in a previous post.
In the end though, it will probably come down to a price/performance trade-off – even at this level of cost. A beginner just starting out or one not wishing to become involved with the “paraphernalia” you mention would undoubtedly find the Astro Essentials device a good fit for their needs. It is unlikely that a device such as Roger has built could be commercially constructed for a similar price to this optical finder, but a beginner wishing to take the next step in imaging might well be prepared to pay a little more for the extra advantages an electronic finder confers while still keeping things well below the price of the sort of finder/guiders mentioned at the beginning of this topic. In other words, there might well be a gap in the market which Roger’s device could fill.
Ah, yes, quite right! It’s a big “mea culpa” from this end, I’m afraid. Apologies for this “terminological inexactitude” but when one has recently spent some time reviewing and assessing webcams for Skype & Zoom compatibility and usability as outdoor observation devices the term does eventually attain a sort of generic applicability!
However, whatever one calls them, I feel that the retail cost of a complete astrocamera unit (whether in the past with the 034 or currently with the 120) is perhaps peripheral to the issue in hand. As you yourself imply, it would clearly be uneconomic for a manufacturer wishing to duplicate Roger’s device to buy a complete unit and install it in a housing of his construction. Given the presumed ready availability of “bare” sensor modules nowadays (led by the revolution in the quality of smartphone imaging systems), a manufacturer would clearly only have to buy a module, not all the associated mounting and focus gubbins, at a wholesale price very much less than that of a complete unit. Hence Roger’s assumption that an all-in price of £100 or less is entirely feasible, given also the simplified nature of the mounting housing.
