следует заметить, что при обсуждении метода лунных дистанций vs хронометр забывается одна важная деталь — для определения долготы по методу лунных дистанций тоже нужны приличные часы, которые не сильно врут хотя бы в течение суток, так как определение местного и стандартного времени производиься обычно в разные моменты суток. А поскольку часы все равно нужны, то, зная, как их сделать точными (это в первую очередь температурная компенсация, остальное мелочи), логично именно так и поступить. Метод же галиллеевых лун в этом случае подойдет в качестве резервного, для периодической поверки хронометра на суше или просто при тихой погоде.

Иные люди видят фазы Венеры

> Изредка встречаются люди с фантастически острым зрением. Таким обладал, например, Аристотель, описывавший столь детальные подробности строения насекомых, которые видны только в микроскоп. Считается, что на это способен один человек из миллиона. Правда, до нас не дошли сведения о том, насколько пристально великий грек приглядывался к Венере. Но утверждают, что мать Кеплера, которой сын показал Венеру в телескоп, первым делом спросила, почему «рога» у нее повернуты не в ту сторону.

Уже после открытия оптических пульсаций нейтронной звезды в Крабовидной туманности астрономы вспомнили что по меньшей мере один посетитель говорил про мигание этой звезды в телескопе, при том что она мигает емнип на 30ти герцах.

(вообще задача демонстрации этих пульсаций банальна для попаданца в 1850е и позже, забавно будет потом когда астрономы ничего подобного не найдут — другие известные оптические пульсары минимум на 8 звездных величин слабее)

С Ганимедом насколько я понимаю проблема чтобы увидеть его несмотря на блеск самого Юпитера, те же китайцы на это претендуют

> По данным китайских астрономических записей, в 365 году до н. э. Гань Дэ обнаружил спутник Юпитера невооружённым глазом (вероятно, это был Ганимед)

крутое зрение, учитывая, что угловой размер галилеевых лун около 2 секунд дуги, а самого Юпитера — около половины минуты. Хотя с учетом излучения (отражения) света картина несколько сложнее

https://www.youtube.com/watch?v=va05TlR7fsI&t=425s

с более-менее приличной оптикой (ахроматы и призматическая система) вместо галлилеевой трубы и метод спутников Юпитера мог бы вполне быть работоспособным

Одиночное покрытие наблюдается на ~ одной тридцатой территории

http://edu.zelenogorsk.ru/astron/moon/occ/antares/20051201.gif
http://edu.zelenogorsk.ru/astron/moon/occ/antares/20050426.gif

величина число_звезд
7 990
8 1876
9 5252
10 15625
11 ~44,000

Но смысла расчета выше это особо не меняет — он справедлив для любой конкретной точки, просто в разных местах будут разные события.

Но уж если просто движение луны считало два человека, тут тут еще надо составить точный каталог десятка тысяч звезд…

За сутки Луна проходит 12 градусов, при угловом диаметре в полградуса — итого покрывает 6 градусов. Угловая площадь неба 40 000 гр2, итого примерно единица деленная на 6-7 тысяч. Невооруженным глазом видно до 6 тыс звезд. Итого в среднем покрытие каждые сутки.

Понятно что половина покрытий происходит днем, а звезды 6 величины невооруженным глазом «видны» настолько плохо что поймать момент покрытия непросто даже если оно происходит на темной стороне.

Но добавим трубу в 60-90 мм с нулевым увеличением — цель просто собрать больше света в глаз. Мы увеличили количество поступающего света на два порядка — +5 звездных величин. Уж теперь точно найдется покрытие каждую ночь и звезду бу

Увеличение нулевое, значит влияние качки на наблюдения не меняется.

Недостаток метода — надо ждать события, наблюдения отнимут у офицеров больше времени. Надо идентифицировать звезду — не одну из пары десяток самых ярких, а одну из десятка тысяч. Возможно метод плохо работает во время полной Луны.

Имхо при наличии компа и трубы метод куда проще повторить чем лунные дистанции. А организация материала позволит легче идентифицировать звезды.

—

https://www.narit.or.th/files/JAHH/2020JAHHvol23/2020JAHH…23..495D.pdf
тут упирают на проблему распознания
Halley
… he had found it needed only a little
practice to be able to manage a five or six
foot telescope capable of shewing the ap-
pulses or occultations of the fixed stars by
the moon on ship-board in moderate weath-
er, especially in the first and last quarter of
the moon’s age, when her weaker light
does not so much efface that of the stars
…
Unfortunately, the occultation method turn-
ed out to be too cumbersome for practical ap-
plication given the scarcity of bright stars and
their infrequent lunar occultations.7 It was
deemed impractical to train maritime navigat-
ors to recognise a useful set of dimmer stars.

Leonhard Euler’s 1749 paper:
METHOD FOR DETERMINING THE LONGITUDE OF PLACES BY OBSERVING OCCULTATIONS OF FIXED STARS BY THE MOON
упирает на неточность расчетов?

если в хронометре использовать колесо баланса из инвара (например, железа 65% и никеля 35%), а пружину баланса из элинвара (железа 56%, никеля 36% и хрома 8%), то от всех устройств тепловой компенсации можно полностью отказаться. Одного-двух килограммов сплава хватит на сотни или даже тысячи хронометров.

//Several factors moulded Ramsden’s career as a scientist and scientific entrepreneur from the 1760s onwards. Pre-eminent among these factors was the development of the shipboard astronomical instrumentation whereby ‘lunars’ (i.e. the measurement of the changing angles between the moon and certain stars) could be practically determined for finding the longitude. The second was a fundamental change taking place in the research instrumentation of astronomical observatories, as the circle usurped the ancient quadrant as the fundamental angle-measuring device. The third, in order of scientific if not commercial importance, arose from the growing need for surveying and drawing instruments by architects, draughtsmen and canal engineers in the late eighteenth century. Jesse Ramsden ‘industrialized’ the first and third branches of instrumentation by mechanizing, in various ways, their process of manufacture, shifting reliance for accuracy from the artisan’s skill to the automatic action of a machine, and greatly speeding up production. The profits generated by this high-quality ‘bread and butter’ trade in
…
Devices for speeding up or regularizing specialized aspects of instrument manufacture had been in use a long time before Ramsden. The clock makers’ wheel-cutting engine dated from around 1670, while opticians had long since used lathes and tools intended to give relatively uniform focal lengths to batches of lenses. Yet all of these techniques operated within relatively stable conditions of supply and demand, simply to speed up or regularize an established product. Jesse Ramsden’s dividing engine in the 1770s, however, was invented to develop and manufacture what was, in practical terms, a new product, operating within new parameters of accuracy, to be used in conjunction with newly available astronomical data. While it is true that Bird had made a few large-radius hand- divided sextants with which to try out Mayer’s lunar tables at sea, both the instruments and the technique had been experimental in 1760.
…
It can be argued that the key to Ramsden’s achievement, and the factor which created the problems which his particular ingenuity first came to solve, was the production of reliable lunar tables by Tobias Mayer in the 1750s and their subsequent development for use at sea by Maskelyne in the Nautical Almanac after 1767. Before these tables could be of practical advantage in the finding of the longitude, however, it was necessary for navigators to possess a hand-held instrument which was sufficiently compact to be usable on the deck of a pitching vessel, yet accurate enough to read angles to 30 arc seconds or less: an accuracy level higher than that attainable with a rigidly mounted observatory quadrant of seven feet radius a century before. Equally important, moreover, it was necessary for the instrument to be as easy to use when measuring awkward angles between the moon and a star as it was in the vertical, while its scale had to possess a sufficient amplitude to allow the navigator to shoot angles of over 100 degrees to catch stars that were behind his back. In short, the finding of the longitude at sea by lunars demanded a shipboard instrument which was smaller and more compact than an old-fashioned sea quadrant, and yet ene still read to what was almost a land-based observatory standard of accuracy. Though we have long admired John Harrison for his painstaking analysis of the problems of marine chronometry, little attention has been paid to the equally important problems involved in developing a viable sextant for lunars, which was Ramsden’s achievement.
…
It was the marine octant, devised by John Hadley around 1731, which provided the principle from which the sextant developed. By using a 45-degree scale that was capable of reading to 90 degrees by reflection, the octant was a relatively compact and easily held instrument reading down to one arc minute on a 15- or 18-inch radius. But to produce an instrument which was light enough in weight to carry such a comparatively large radius at sea, the frame had to be made of thin wood and the scale of ivory. These materials inevitably limited the accuracy of the instrument, for they lacked the rigidity and thermal uniformity of brass. While a Hadley octant was sufficient in theory to take the sun’s noon altitude to a minute, it was still incapable of reliably taking sightings for lunar computations which demanded much higher levels of manoeuvrability and accuracy.”

Not only had the 90-degree scale of the octant to be increased to 120 degrees, but the radius had to be drastically reduced to around eight or ten inches to make it more compact and easily handled. At the same time, the graduations had to be twice or three times more accurately drawn at nine inches radius than had been customary on an octant of fifteen. In short, the instrument had to be miniaturized, made more rigid and much more finely divided, equipped with a telescopic sight for more precise alignment, and capable of being supported in the right hand while the left was free to make fine adjustments. This was a tall order in terms of design, and Ramsden perceived that everything hinged on the craftsman’s capacity to produce impeccably accurate divisions at ten or twelve inches radius.
…
One must not forget that the biggest drawback to the initial use of the chronometer at sea at this period was the scarcity and prohibitive cost of the watches, and if lunars were ever to be widely used, then an easily-manufactured, modestly priced, and wholly reliable hand-held astronomical instrument for making the necessary sightings had to be quickly developed. The hand division of ten-inch scales to the astronomical standard of accuracy required for lunars was not commercially viable in 1760. Although John Bird could probably have done it over the weeks which it supposedly took him to engrave a homogeneous scale, the finished sextants could have been as scarce and expensive as Larcum Kendall’s replica of the Harrison IV chronometer.’ The superb 20-inch sextant which Bird engraved for Captain Campbell in 1757 indicates what rarities such instruments were likely to be. It was in Jesse Ramsden’s development of the dividing engine that the problem found a solution, to bring out the industrial revolution parallels, for Ramsden was transforming an existing technology to meet new demands, greatly improving quality, and making it possible for a labourer to do in thirty minutes what an established craftsman could not do in a fortnight. But Ramsden’s first dividing engine of 1766 was soon found to fall short of its inventor’s expectations, and while it was found to be good for the manufacture of conventional mathematical instruments, it was not good enough for sextant scales.! In consequence, Ramsden set about the construction of an improved model with a 45-inch plate which became operational in 1774. It was this machine that so impressed the Admiralty that they purchased it for £315, while permitting Ramsden to retain it for his own use. The Government also paid him a further £300 to write and publish a detailed description of the engine for the public benefit.’! And though Ramsden did this, he strategically avoided describing the critical process whereby he laid off the 2160 circumference teeth on the dividing wheel, the accuracy of which made the machine so significant. Over the next quarter of a century, Ramsden’s firm divided annually about forty sextants! on this machine—more than enough to supply each capital ship in the Royal Navy and part of the Merchant Fleet as well. The ease of manufacture of engine- divided sextants, reading down to 20 or 30 arc seconds, made possible precision instrumentation on a truly industrial scale, and one can understand why the cost-conscious Admiralty tended to favour the lunar’s method of finding the longitude against that of the chronometer. It seemed cheaper, after all, to teach officers how to use a £15 sextant, solve equations, and compute from Maskelyne’s tables, than it was to provide every ship with a chronometer.’//

Похоже, реальность не интересует именно вас. Впрочем, для человека, скорей всего не державшего в руках реальных инструментов (разве какой нибудь модный дремель или подобные игрушки), это вполне закономерно.

//Как улучшить инструмент было понятно любому здравомыслящему человеку — берешь лупу, шлифуешь поверхность, точишь лезвие и пьешь поменьше, как и сделал Bird. //
неодходимость определенного уровня точности приборов для метода лунных дистанций была очевидна в начале XVIII в., достичь ее смогли полвека спустя не только одним воздержанием от алкоголя. К лупе для разметки шкалы еще добавьте линзы для зрительной трубы, желательно ахроматической, для самого секстанта.

Попробуйте, в конце концов, недельку не пить и после этого разметить металлическую полоску на равные деления вручную, циркулеи измерителем, а потом оценить точность положения рисок.

Вообще, мне надоела эта дискуссия, и я ее заканчиваю. Я указал вам на важный элемент, необходимый для использования лунных дистанций, и множество указаний из различных источников, указывающих на важность этого элемента. Любой адекватный человек бы просто добавил бы информацию о том, какая точность нужна была от навигационных инструментов и как такую точность можно было бы достичь, от вас же удалось получить лишь постоянный перевод темы на точность стационарных приборов вместо портативных, высосанные из пальца утверждения о феноменальной точности первых октантов и секстантов (с попытками искажения информации из цитируемых вами же источников), бредовые идеи вроде использования бэкстаффа, и вдобавок ко всему манеру общения на грани хамства, что, похоже, для вас характерно в ситуации с отсутствием других аргументов.

//In 1763 Ramsden set up business on his own account in Haymarket and in 1775 he moved to Piccadilly, London, where he remained until his death in 1800. From the outset of his business life, his skill as an engraver and divider attracted the attention of leading London makers such as Nairne, Sisson, Adams and Dollond.
His design and construction of one machine revolutionized the dividing of the scales of sextants and other instruments. The Board of Longitude (set up by the Admiralty in 1714) awarded Ramsden £615 on the understanding that he would undertake to divide octant and sextant scales for other makers.
There is little doubt that it was directly due to the inventive genius and practical skills of Ramsden that the sextant was improved to the point that an accuracy of 10 or 20 seconds rather than 1 minute became the order of the day. In addition, the finely engraved scales made possible by the use of the dividing machine permitted sextants to be made smaller than previously without loss of accuracy.
Ramsden’s improvements to the sextant eased life for the sailor, for latitude could now be determined with an unprecedented degree of accuracy. Even longitude, which had seemed to present insurmountable problems, was in the process of being solved, the solution being the provision of a suitable timekeeper, an accurate sextant and a nautical almanac.//

//An important factor is the introduction of mechanical scale division. Chapman argues that the expense and slow production of hand-graduated instruments limited the full potential of the lunar method. He differentiates the work of instrument makers Jesse Ramsden and Edward Troughton, both operating with the new dividing engines in the period under consideration, from that of earlier followers of the classical tradition: George Graham, John Bird and Jeremiah Sisson. He notes that Ramsden and Troughton were part of the movement that introduced the industrial revolution. Producing sextants in considerable quantities was required for widespread use of the lunar distance method. ‘Machine graduation offered the prospect not only of cheaper, more plentiful instruments, but of easily attested accuracy that was free from personal errors’.» Ramsden’s second engine, specifically for nautical instruments, came into use in 1775.

McConnell relates Bird’s approval of Ramsden’s engine and his assessment that it was accurate to two thousandths of an inch. She relates that after the introduction of this second engine, hand dividing quickly gave way to engine division. Ramsden took in instruments from other makers, producing over 1200 by 1794, if the serial numbers are an accurate reflection. McConnell gives a figure of 1450 by 1800, and claims Troughton produced at a similar rate. The most detailed analysis of the number of sextants produced comes from Stimson’s 1975 survey.78 It is not necessary to go outside London, indeed outside Greenwich, for tangible evidence of the successful production of these exquisite instru- ments from the Ramsden and Troughton stables. After 1775, the slow production of sextants cannot stand up as an impediment to the adoption of the lunar distance method.//

//Where backstaffs and octants sufficed for measuring altitudes above the horizon, sextants enabled the measurement of lunar distance in two ways. First, their arcs measured one sixth of the circumference of a circle, permitting the measurement of wider angles. Since sextants reflected images from an index mirror onto a horizon mirror, the 60-degree arc could be used to read angles of 120 degrees. Second, their arcs had graduated scales precise enough to measure lunar distances down to a sixtieth of a degree. John Bird produced the first sextant accurate enough to measure lunar distances in 1759. But the process of engraving scales with a beam compass was arduous, requiring weeks of skilled labor.
For the celestial solution to the longitude problem to be practicable, it would be necessary to reduce the cost of production. And when Jesse Ramsden completed his dividing engine for cheaply manufacturing sextants in the 1770s, he did exactly this. The dividing engine’s wheel, cut precisely with 2160 gear teeth, enabled unskilled workers to engrave an accurate measuring scale onto a blank sextant frame within minutes. As Allan Chapman explains, ‘Ramsden turned the scientific instrument … into a cost-effective industrial artefact, … where high quality was made to cost less in real terms than ever before.’//

погрешности модели Ньютона 1702 года (после исправления знака одного из членов — возможно опечатка) (модель основана на эмпирических формулах, а не прямом моделировании)
https://www.dropbox.com/scl/fi/hzh1mm39kunemy7xcn0kr/newton_model_errors.png?rlkey=5uf82g5bh9one2zg7mvt43um9
это за 8 месяцев — хорошо видно что большие выбросы случаются за этот период несколько раз

Галлей сначала утверждал что точность его модели 1820х была 1-2 минуты, но в 1830 сам же обнаружил отклонения до 8 минут
проблем добавил тот факт что он не любил делиться данными и его результаты нормально опубликовали лишь в 1749

cудя по всему Галлей заметил что паттерн ошибок повторяется в цикле сароса и пытался улучшить модель Ньютона учетом этого паттерна
https://www.dropbox.com/scl/fi/ao68blbrtfd4icllgyi81/saros_cycle.png?rlkey=h56gq6nme0mqebevd0kt3uqot
прекрасно видно что точность данных наблюдений прекрасно позволяла разрешить этот паттерн
проблема в том что эффект бабочки делала этот метод бессмысленным

анализ данных Галлея — средняя ошибка в 10-14 секунд плюс стандартное отклонение в 20-30 секунд.