Астрономические инструменты. Угломерные инструменты (работа 1)

Астрономические инструменты. Угломерные инструменты.

Иван Арбатов

Интересно, что у почти у всех начинающих любителей астрономии бессознательно сложилось мнение, что первый прибор по астрономии, который они должны иметь – это хотя бы небольшой телескоп, или нечто подобное, бинокль или монокуляр. Но астрономы знали и менее "примитивных" помощников в своем труде, чем бинокли и телескопы, и эти помощники и ныне могут сыграть свою полезную роль при любительских наблюдениях, пусть и своебразную и небольшую (да и сейчас профессионалы-астрономы все еще пользуются механизмами этих приборов, оснащают ими телескопы для точности, и используют все для того же – определения углов на небесной сфере). До 1611 года, до знаменательного года изобретения телескопа всем достославным Галилео Галилеем (или кем-то еще раннее, но все равно он был первым, использавшим телескоп для серъезных астрономических наблюдений), астрономы пользовались всякими расчерченными на градусы в прямом смысле деревянными палочками и перекладинами, квадратиками и кружочками больших и малых размеров. Это были всякие там астрономические посохи, высотомеры, секстанты, квадранты и трикветры. Ими пользовались древнегреческие астрономы (а они почти все эти инструменты впервые и создали), и Аристарх, и Гиппарх, и Птолемей, и в средние века арабские астрономы довели их до совершенства. Использовались эти приборы для решения задач самого раннего зародившегося раздела астрономии – астрометрии, занимающейся вопросами над небесными светилами "Где, когда, и что" – для расчета положений светил на небесной сфере, расстояний между звездами, определению по небу времени, и поэтому они и называются угломерными инструментами. Как и все приборы они требовали большей точности, и их и делали для этого как можно большими, а у арабских астрономов они стали настоящими громадинами, так квадранты достигали радиуса 60 м, а Николай Коперник с помощью таких приборов определяющий координаты планет и рассчитывающий по ним уже свою гелиоцентрическую систему, пользовался приборами, намного превышающими его рост. Но не обязательно было всегда делать такие громадины, для многих задач подходили и маленькие приборы. И конечно же, такие приборы (пусть и станут они у вас самыми первыми – или новыми помощниками, если уже у вас есть бинокль или телескоп, делать их намного проще самого простого телескопа), по силу сделать их любому любителю астрономии, человеку. Основные материалы для этого найдутся у всех: дерево, пила, и транспортир… И благо, с ними можно и делать много полезного, они хорошие помощники в тех же визуальных наблюдениях метеоров, они помогают точнее, лучше и удобнее определить координаты метеора, положения серебристых облаков (которые также наблюдаются в основном визуально), совсем новичкам в наблюдениях звездного неба помогут легче понять смысл эфемерид и найти самим на небе планеты, понять структуру и определения начальных теорий небесной сферы. К тому же и просто приятно обнаружить себя в душе каким-то древним астрономом, ощутить на себе эхо далекого прошлого, посмотреть на небо глазами древнего грека, араба с жарких пустынь, Улугбека, Коперника или Тихо Браге! А ниже – пусть и некоторые угломерные инструменты, и как их делать, что я насобирал из всякой астролитературы, которой уже и не помню. Многое соорудил сам, видя лишь где-то картинку какого-то исторического угломерного инструмента.

Астролябия

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Естественно же более упрощенная, чем древний предок, решает намного меньше задач. Так, в трактате арабского астронома Х в. ас-Суфи перечислялось 1000 способов использования астролябии! Эта астролябия же поможет измерять горизонтальные углы азимутов светил. Для ее изготовления необходимо иметь:

Диск из многослойной фанеры, текстолита или оргстекла. Диаметр диска такой, чтобы на нем разместилась круговая шкала (лимб) из транспортира и за ней оставалось бы свободное поле 2-3 см.

Транспортир, лучше из тех, что есть, побольше.

Визирная планка. Изготовляется из плоскости латуни или дюралюминия шириной 2-3 см, и длиной, превышающей поперечник диска на 5-6 см. Выступающие за край диска концы полоски изогните под прямым углом вверх и пропилите в них продолговатые или круговые отверстия. На горизонтальной планке симметрично центру проделайте две большие широкие прорези, чтобы чрез них была виден градуируемый лимб транспортира. Середину визирной планки прикрепите к центру диска, с помощью болта, шайб и гаек, чтоб она вращалась в горизонтальной плоскости. На визирную планку к центру прикрепите и компас.

При наблюдениях направляйте визирную планку на светило так, чтобы оно было видно сквозь боковые прорези планки. Отношение градусной меры транспортира к планке (видную через поперечную прорез планки, через ту, что "ближе" к светилу) к стрелке севера компаса и будет азимутом светила.

Как найти самому азимут, высоту и зенитное расстояние

Да вообще, не трудно догадаться, что измерять самому высоту и азимут светила можно и при помощи транспортира. Но как его положить, чтобы он "видел" круги небесной сферы? Один из простейших инструментов для этого – высотомер, с которым мы и познакомимся сейчас. Высотомер состоит из как можно большего (ну, и не метрового конечно – трудно будет делать!) транспортира, содержащего 1800. Из центра окружности А транспортира и перпендикулярно его радиусу (разделяющего наш транспортир на две равные части) устанавливается линейка (или рейка) такой длины, чтобы она в 3-4 раза превосходила радиус транспортира. А в центр транспортира привинчивают шарнир, а к нему веревку с грузом, так, чтобы веревка была тонка, а груз ее не порвал. Если веревка в точке скрепления проходит вдоль линейки, то значит она прикреплена верно. К транспортиру, выше линии 0-1800 его шкалы и параллельно ей устанавливают еще визиры, из трехизогнутой (как у астролябии) планки, средняя сторона которой равна диаметру транспортира, другие (боковые) равны друг другу, и в точке пересечения диагоналей этих квадратов или прямоугольников проделайте дырки-окружности диаметром 3-5 мм. Противоположный конец линейки перпендикулярно к центру прикрепите к не очень толстой дощечке так, чтобы она без колебаний держала линейку к своему креплению, и чтоб линейка вращалась вокруг своего центра, а этот центр вставляется в центр окружности еще одного транспортира, на этот раз на полную окружность (3600). Внизу к линейке прикрепите какую-нибудь стрелку, чтобы та исходила из этого центра транспортира и "доставала" до его внешнего края. Так же к дощечке желательно прикрепить компас, для указания юга, от которого отсчитываются астрономические азимуты. Прибор перед началом наблюдений устанавливают так, чтобы дощечка находилась неподвижно и по горизонтали, а нижний транспортир на 00 шкалы по компасу направлен на юг, часть от 0 до 1800 направлена к востоку, другая к западу. При измерении азимута и высоты светила (измеряются одновременно!) мы направляем на него визиры так, чтобы сквозь них оно было видно, и конечно, центр вращения А (для отсчитывания высоты) направляется сверху вниз, а в месте крепления к доске вправо-влево. Таким образом, получив изображение искомого светила в визире мы увидем, что верхний транспортир наклонен под определенным углом, отмеченным на шкале веревкой, это и есть высота h светила, а стрелка к нижнему транспортиру покажет значение азимута. Зенитное расстояние z же можно легко узнать по формуле z+h = 900.

Углы между светилами

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Т.н. астрономические грабли – простейший вариант угломерного прибора, состоит из двух деревянных линеек (например, по 60 см длиной), скрепленных в форме буквы Т. На конце линейки, противоположно перекладине, укрепляется визир. На перекладине по дуге окружности 57,3 см (построить можно с помощью шнура) с интервалом в 1 см (либо в 0,5 см) вбиваются гвоздики. Центром окружности является визир. При интервале разбития гвоздиков в 1 см соответствует угол в 1 градус на небесной сфере, при 0,5 см угол в полградуса. С помощью этого нехитрого инструмента можно проводить регулярные (скажем, каждый вечер в одно и то же время) измерения угловых расстояний планет и Луны относительно некоторых "опорных" звезд и тем самым устанавливать особенности движения упомянутых светил на небесной сфере.

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Другой прибор так и называется угломерным инструментом. Состоит он из прямоугольного куска дерева 35*20 см. С одной из его сторон неподвижно прикреплена рейка (или линейка) длиной 60 см. В противоположном конце рейки прикрепляется другая такая же так, чтоб она вращалась вокруг центра крепления. По обеим концам реек параллельно прикрепляются визиры. На доске, аналогично астрономическим граблям, очерчена дуга радиусом 57,3 см, на ней нанесена шкала градусов. При наблюдениях обычно визиры одной рейки направляют на звезду, неподвижной – на планету. Полученное на шкале расстояние концов реек и есть их угловое расстояние. С помощью этих приборов можно находить и горизонтальные координаты светила. Так, найдя юг (отметив его по компосу) мы от него отмерим расстояние до светила, и по градуируемой шкале получим его азимут. Отложив от светила прямое и точное направление на горизонт, получим его высоту, а от зенита – его зенитное расстояние. Подумайте, как тогда надо распложить приборы относительно горизонта и вертикали.

Заключение

Наконец, теперь замечу, если кто захочет или кому понадобится найденные с инструментами горизонтальные координаты перевести в "общие" для всех экваториальные, то сделать это можно просто по формулам:

Sin δ = sin φ cos z - cos φ sin z cos A

Cos δ sin t = sin z sin A

Cos δ cos t = cos φ cos z + sin φ sin z cos A

где δ - склонение, t – часовой угол светила (с помощью его можно легко найти прямое восхождение α по формуле α = s – t, где s – звездное время момента наблюдений), z – зенитное расстояние, h – высота светила, А – его азимут, φ - широта места наблюдения. Не забудьте и об значении рефракции, влияющей на координаты светила (хотя, в основном, если координаты светила измерять, когда оно близ зенита, эта малая величина). И наверное, описанных нами угломерных инструментов, пока достаточно, чтобы понять основной механизм их постройки, и делать все остальное полностью самому – лишь увидев какой-то угломерный инструмент на рисунке.

Список литературы

1.Энциклопедический словарь юного астронома

2.Ф.Ю. Зигель "Астрономы наблюдают"

Для подготовки данной применялись материалы сети Интернет из общего доступа