Системы небесных координат

16

СИСТЕМЫ НЕБЕСНЫХ КООРДИНАТ.

Географическая система координат. Географическая система координат
предназначена для определения места положения какой-либо точки на
поверхности Земли. Для этого земной шар мысленно окутывают координатной
сеткой (рис. 1.), которая очерчивает на поверхности планеты круги. Круг
наибольшего диаметра, перпендикулярный оси NS вращения Земли, называют
экватором, а малые круги, параллельные экватору – параллелями. Круги,
перпендикулярные экватору и проходящие через северный и южный
географические полюса планеты, называют меридианами. Начальной
параллелью принято считать экватор, а начальным меридианом – тот
меридиан, который проходит через Гринвичскую обсерваторию (Англия).
Географическая система координат позволяет однозначно определить
положение любой точки на поверхности планеты при помощи двух координат –
широты
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Рис. 1

Географической
долготойpicscalex1000100090000038500000002001000000000000500000009020000
00000400000002010100050000000102ffffff00040000002e0118000500000031020100
0000050000000b0200000000050000000c02c00160010e00000026060f001200ffffffff
000008000000c0ffccff20018c010b00000026060f000c004d6174685479706500003000
10000000fb0280fe0000000000009001010000020002001053796d626f6c000004000000
2d01000009000000320a60013700010000006c00d3000a00000026060f000a00ffffffff
01000000000010000000fb021000080000000000bc02000000000102022253797374656d
0006040000002d01010004000000f0010000030000000000 называется двугранный
угол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 между плоскостью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 нулевого меридиана и плоскостью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 меридиана (рис. 2), проходящего через данную точку М земной
поверхности. В астрономии принято отсчитывать долготы к востоку от
начального меридиана (т. е. в сторону суточного вращения Земли) в
пределах от 0 до 360 или от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 до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.
Однако, допускается отсчёт долготы от 0 до +180 (или от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 до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) к
востоку (восточная долгота) и от 0 до -180 к западу (западная долгота)
от нулевого меридиана.

Астрономической (или географической) широтой
picscalex100010009000003850000000200100000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02a00160010e00000026060f001200ffffffff00000800
0000c0ff2c002001cc010b00000026060f000c004d617468547970650000500010000000
fb0280fe0000000000009001010000020002001053796d626f6c0000040000002d010000
09000000320a00012000010000006a00e6000a00000026060f000a00ffffffff01000000
000010000000fb021000080000000000bc02000000000102022253797374656d00060400
00002d01010004000000f0010000030000000000 называется угол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 между плоскостью экватора и отвесной линией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 в
данной точки поверхности Земли. Отсчитывают широты от 0 до 90 в северном
полушарии и 0 до -90 в южном полушарии.

Поскольку земной шар представляет собой эллипсоид вращения и масса по
объёму земного шара распределена не равномерно, то отвесная линия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може
т не совпадать с нормалью к касательной плоскости в данной точке
поверхности планеты. Поэтому иногда, помимо астрономической широты,
приходится различать ещё геодезическую и геоцентрическую широты.

Геодезической широтой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 называется угол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 между плоскостью земного
экватора и отвесной линией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 в данной точки поверхности Земли
(рис.3).

Геоцентрической широтой (обозначения не имеет) называется угол
picscalex100010009000003dc0000000200160000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02000280050e00000026060f001200ffffffff00000800
0000c0ffacff4005ac010b00000026060f000c004d617468547970650000400016000000
fb0280fe0000000000009001010000ee0002001054696d6573204e657720526f6d616e20
43450009040000002d0100000a000000320a80016400020000004d4f3c01160109000000
320a80016603010000004d003c0115000000fb0220ff0000000000009001000000000002
001054696d6573204e657720526f6d616e00cc51040000002d01010004000000f0010000
09000000320ab901ac02010000003200700010000000fb0280fe00000000000090010000
00020002001053796d626f6c0000040000002d01000004000000f001010009000000320a
8401e80401000000a20060000a00000026060f000a00ffffffff01000000000010000000
fb021000080000000000bc02000000000102022253797374656d0006040000002d010100
04000000f0010000030000000000 между плоскостью экватора и отвесной линией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 в данной точки поверхности Земли.

Разность между геоцентрической и астрономической широтами на полюсах и
на экваторе равна нулю, а в других точках планеты не превышает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.

Геоцентрическую широту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 можно вычислить по следующей формуле:
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, (1)

где
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.

В этой формуле
picscalex100010009000003850000000200100000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02a00160010e00000026060f001200ffffffff00000800
0000c0ff2c002001cc010b00000026060f000c004d617468547970650000500010000000
fb0280fe0000000000009001010000020002001053796d626f6c0036040000002d010000
09000000320a00012000010000006a00e6000a00000026060f000a00ffffffff01000000
000010000000fb021000080000000000bc02000000000102022253797374656d00060400
00002d01010004000000f0010000030000000000 – астрономическая широта, а
picscalex100010009000003850000000200100000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02600180010e00000026060f001200ffffffff00000800
0000c0ff2c0040018c010b00000026060f000c004d617468547970650000300010000000
fb0280fe0000000000009001010000020002001053796d626f6c0065040000002d010000
09000000320a00012100010000006100f0000a00000026060f000a00ffffffff01000000
000010000000fb021000080000000000bc02000000000102022253797374656d00060400
00002d01010004000000f0010000030000000000 – сплюснутость Земли.

Радиус-вектор R можно определить по формуле
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, (2)

где а – экваториальный радиус Земли.

В 1976 г. Международным астрономическим союзом (МАС) были приняты
следующие значения параметров земного эллипсоида:

а=6 378 140 м, b=6 356 755 м,
picscalex100010009000003850000000200100000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02600180010e00000026060f001200ffffffff00000800
0000c0ff2c0040018c010b00000026060f000c004d617468547970650000300010000000
fb0280fe0000000000009001010000020002001053796d626f6c0065040000002d010000
09000000320a00012100010000006100f0000a00000026060f000a00ffffffff01000000
000010000000fb021000080000000000bc02000000000102022253797374656d00060400
00002d01010004000000f0010000030000000000=1 : 298,257.

С учётом этих данных формулы (1) и (2) принимают вид:
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, (3)
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. (4)

СИСТЕМЫ НЕБЕСНЫХ КООРДИНАТ.

Элементы небесной сферы. Небесной сферой называется некоторая сфера
произвольного и достаточно большого радиуса, проведённая из точки
наблюдения. Существует несколько способов графического представления
небесной сферы, отличающихся друг от друга лишь набором параметров,
необходимых для решения тех или иных задач.

Небесным меридианом называется большой круг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 небесной сферы, проходящий через отвесную линию и ось мира. Из
соображений удобства принято небесный меридиан изображать в плоскости
листа бумаги.

Отвесной (или вертикальной) линией называется линия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, параллельная или совпадающая с направлением нити
отвеса и проходящая через глаз наблюдателя О (центр небесной сферы).
Точки пересечения отвесной линии с небесной сферой называются зенитом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(точно
над головой наблюдателя) и надиром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 (точка,
диаметрально противоположная точке зенита).
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Рис. 1

Математическим (или истинным) горизонтом называется большой круг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 небесной сферы, перпендикулярный отвесной линии.

Осью мира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 называется ось, вокруг которой происходит кажущееся
вращение небесной сферы.

Небесным экватором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 называется
большой круг небесной сферы, перпендикулярный оси мира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.

Плоскостью эклиптики называется плоскость орбиты Земли, то есть
плоскость, перпендикулярная оси вращения планеты. Плоскость эклиптики
составляет с плоскостью небесного экватора угол 2326’, который
вследствие прецессии земной оси вращения периодически изменяется в
незначительных пределах.

Горизонтальная система координат. Основными параметрами горизонтальной
системы координат (рис. 5) являются круг высоты, отвесная линия и
плоскость истинного горизонта.

Кругом высоты (или вертикальным кругом или вертикалом) называется
большой круг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 небесной сферы, проходящий через зенит, надир и
данное светило М. Координатами светила в горизонтальной системе
координат являются высота и азимут.
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Рис. 2

Высота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 светила
над горизонтом определяется величиной центрального угла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 между плоскостью истинного горизонта и направлением
на светило М. Измеряется высота от 0 до 90 в северном полушарии и 0 до
-90 в южном полушарии. Высота светила над горизонтом может быть выражена
зенитным расстоянием этого светила, т. е. величиной центрального угла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 между отвесной линией и направлением на светило М. Зенитное
расстояние отсчитывается от точки зенита вдоль вертикала, проходящего
через данное светило М от 0 до 180 (или от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 до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).
Понятно, что высота светила и его зенитное расстояние связаны между
собой простым соотношением:
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. (5)

Малый круг небесной сферы, параллельный истинному горизонту и проходящий
через данное светило М, называется альмукантаратом. Все светила одного и
того же альмукантарата имеют одну и ту же высоту над горизонтом. Для
того, чтобы окончательно определить положение данного светила,
используется вторая координата – азимут.

Астрономическим азимутом А светила называется угловое расстояние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, отсчитываемое вдоль плоскости истинного горизонта
от точки юга S до вертикала, проходящего через данное светило M. Обычно
азимут отсчитывают в сторону запада (в сторону суточного вращения
небесной сферы) от 0 до 360 (или от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 до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). Это
– астрономический азимут. Однако, в геодезии принято пользоваться
геодезическим азимутом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, отсчитываемым от
точки севера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 в
пределах от 0 до 180 (или от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 до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) к
западу (западный азимут) и от 0 до -180 (или от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 до
-12picscalex1000100090000038b0000000200160000000000050000000902000000000
400000002010100050000000102ffffff00040000002e011800050000003102010000000
50000000b0200000000050000000c02400200010e00000026060f001200ffffffff00000
8000000f0ffb4fff000f4010b00000026060f000c004d617468547970650000200016000
000fb02e0fe0000000000009001010000ee0002001054696d6573204e657720526f6d616
e2043450009040000002d01000009000000320a2d01370001000000680090000a0000002
6060f000a00ffffffff01000000000010000000fb021000080000000000bc02000000000
102022253797374656d0006040000002d01010004000000f0010000030000000000) к
востоку (восточный азимут). Между астрономическим и геодезическим
азимутами имеет место очевидное соотношение:
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. (6)

Экваториальные системы координат. Различают две экваториальные системы
координат, которые отличаются друг от друга лишь одной из координат.
Каждая из экваториальных систем может быть получена путём поворота
горизонтальной системы координат вокруг её центра на угол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(picscalex10001000900000385000000020010000000000005000000090200000000040
0000002010100050000000102ffffff00040000002e01180005000000310201000000050
000000b0200000000050000000c02a00160010e00000026060f001200ffffffff0000080
00000c0ff2c002001cc010b00000026060f000c004d61746854797065000050001000000
0fb0280fe0000000000009001010000020002001053796d626f6c0076040000002d01000
009000000320a00012000010000006a00e6000a00000026060f000a00ffffffff0100000
0000010000000fb021000080000000000bc02000000000102022253797374656d0006040
000002d01010004000000f0010000030000000000 – астрономическая широта
пункта наблюдения). При этом все элементы горизонтальной системы
отобразятся в совершенно аналогичные элементы экваториальных систем
координат: отвесная линия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 перейдёт в ось мира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, плоскость истинного горизонта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 – в плоскость небесного экватора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, а круг высоты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 заменится кругом склонений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 (рис. 6).
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Рис. 3

Первой координатой светила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на небесной сфере в обеих экваториальных системах координат является
склонение или полярное расстояние. Второй координатой является часовой
угол (в первой экваториальной системе координат) или прямое восхождением
(во второй экваториальной системе координат).

Склонением
picscalex100010009000003850000000200100000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02c00140010e00000026060f001200ffffffff00000800
0000c0ffccff00018c010b00000026060f000c004d617468547970650000300010000000
fb0280fe0000000000009001010000020002001053796d626f6c0000040000002d010000
09000000320a60012300010000006400c0000a00000026060f000a00ffffffff01000000
000010000000fb021000080000000000bc02000000000102022253797374656d00060400
00002d01010004000000f0010000030000000000 называется центральный угол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, отсчитываемый вдоль круга склонений от плоскости
небесного экватора до направления на светило М. Склонение отсчитывается
от 0 до 90 в северном полушарии и от 0 до -90 в южном. Склонение может
быть заменено полярным расстоянием р, т. е. центральным углом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, отсчитываемым вдоль круга склонений от северного полюса мира до
направления на светило. Полярное расстояние измеряется от северного
полюса мира к южному в пределах от 0 до 180 (или от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 до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).
Между склонением и полярным расстоянием очевидна простая связь:
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. (7)

Малый круг небесной сферы, параллельный небесному экватору, называется
суточной (или небесной) параллелью. Понятно, что все светила, имеющие
одно и то же склонение, лежат на одной суточной параллели.

Часовым углом t называется угловое расстояние, отсчитываемое вдоль
небесного экватора от верхней его точки до круга склонений, проходящего
через данное светило. Часовой угол отсчитывается в сторону запада (т. е.
в сторону суточного вращения небесной сферы) от 0 до 360 (или от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 до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).

Прямым восхождением
picscalex100010009000003850000000200100000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02600180010e00000026060f001200ffffffff00000800
0000c0ff2c0040018c010b00000026060f000c004d617468547970650000300010000000
fb0280fe0000000000009001010000020002001053796d626f6c007f040000002d010000
09000000320a00012100010000006100f0000a00000026060f000a00ffffffff01000000
000010000000fb021000080000000000bc02000000000102022253797374656d00060400
00002d01010004000000f0010000030000000000 светила называется угловое
расстояние, отсчитываемое вдоль небесного экватора от точки весеннего
равноденствия до круга склонений, проходящего через данное светило.
Прямое восхождение отсчитывается в сторону востока от 0 до 360 (или от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 до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).

ГОРИЗОНТАЛЬНАЯ СИСТЕМА КООРДИНАТЭКВАТОРИАЛЬНЫЕ СИСТЕМЫ КООРДИНАТНебесный
меридиан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Небесный меридиан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Точки зенита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 и
надира
picscalex100010009000003ac0000000200160000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02a00100020e00000026060f001200ffffffff00000800
0000c0ffccffc0016c010b00000026060f000c004d617468547970650000200010000000
fb0280fe0000000000009001000000020002001053796d626f6c0076040000002d010000
09000000320a64014a0101000000a200600016000000fb0280fe00000000000090010100
00ee0002001054696d6573204e657720526f6d616e2043450009040000002d0101000400
0000f001000009000000320a60014000010000005a00d3000a00000026060f000a00ffff
ffff01000000000010000000fb021000080000000000bc02000000000102022253797374
656d0006040000002d01000004000000f0010100030000000000Точки северного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 и
южного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 полюсов
мираОтвесная линия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Ось мира
picscalex100010009000003b50000000200160000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02a001e0020e00000026060f001200ffffffff00000800
0000c0ffccffa0026c010b00000026060f000c004d617468547970650000200016000000
fb0280fe0000000000009001010000ee0002001054696d6573204e657720526f6d616e20
43450009040000002d01000009000000320a60015800010000005000dc0009000000320a
60013401010000005000dc0010000000fb0280fe00000000000090010000000200020010
53796d626f6c0000040000002d01010004000000f001000009000000320a64013e020100
0000a20060000a00000026060f000a00ffffffff01000000000010000000fb0210000800
00000000bc02000000000102022253797374656d0006040000002d01000004000000f001
0100030000000000Точки севера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 и юга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Нижняя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 и верхняя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 точки
небесного экватораПлоскость истинного горизонта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Плоскость небесного экватора Вертикал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Круг склонений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Высота светила над горизонтом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Склонени
е
picscalex100010009000003850000000200100000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02c00140010e00000026060f001200ffffffff00000800
0000c0ffccff00018c010b00000026060f000c004d617468547970650000300010000000
fb0280fe0000000000009001010000020002001053796d626f6c0077040000002d010000
09000000320a60012300010000006400c0000a00000026060f000a00ffffffff01000000
000010000000fb021000080000000000bc02000000000102022253797374656d00060400
00002d01010004000000f0010000030000000000Зенитное расстояние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Полярное
расстояние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Астроном
ический азимут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Часовой
угол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ГОРИЗОНТАЛЬНАЯ СИСТЕМА КООРДИНАТПЕРВАЯ ЭКВАТОРИАЛЬНАЯ СИСТЕМА
КООРДИНАТВТОРАЯ ЭКВАТОРИАЛЬНАЯ СИСТЕМА КООРДИНАТ

Первая

координатаВысота:
h=picscalex96010009000003e9000000020015000000000005000000090200000000040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h=picscalex96010009000003e9000000020015000000000005000000090200000000040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Склонение:

=picscalex96010009000003e90000000200150000000000050000000902000000000400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=picscalex96010009000003e90000000200150000000000050000000902000000000400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Склонение:

=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=picscalex96010009000003e90000000200150000000000050000000902000000000400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Зенитное расстояние:
Z=picscalex100010009000003e200000002001500000000000500000009020000000004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Полярное
расстояние:

p=picscalex100010009000003e200000002001500000000000500000009020000000004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Полярное
расстояние:

p=picscalex100010009000003e200000002001500000000000500000009020000000004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Вторая

координатаАстрономический азимут:
А=picscalex96010009000003e2000000020015000000000005000000090200000000040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(к западу) Часовой угол:

t=picscalex96010009000003e2000000020015000000000005000000090200000000040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t=picscalex100010009000003e400000002001500000000000500000009020000000004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(к западу) Геодезический азимут:
А’=picscalex96010009000003e200000002001500000000000500000009020000000004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(к востоку)Прямое восхождение:

=picscalex96010009000003e20000000200150000000000050000000902000000000400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=picscalex100010009000003e4000000020015000000000005000000090200000000040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(к востоку)

Эклиптическая система координат. Эклиптическая система координат (рис.
7) может быть получена из экваториальной системы путём мысленного его
поворота вокруг центра небесной сферы на угол 2326’ (угол наклона оси
вращения Земли к плоскости эклиптики (плоскости земной орбиты)). При
этом аналогом оси мира становится ось эклиптики, а аналогом плоскости
небесного экватора – плоскость эклиптики. Точки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и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, в которых ось
эклиптики пересекает небесный меридиан, называются северным и южным
полюсами эклиптики соответственно. Точки пересечения эклиптики с
плоскостью небесного экватора называются точками весеннего равноденствия
(точка, в которой Солнце переходит из южного полушария в северное) и
осеннего равноденствия (точка, в которой Солнце переходит из северного
полушария в южное). Точки, отстоящие от равноденственных на 90
называются точками летнего
(picscalex1000100090000038d000000020015000000000005000000090200000000040
0000002010100050000000102ffffff00040000002e01180005000000310201000000050
000000b0200000000050000000c02a00180011200000026060f001a00ffffffff0000100
00000c0ffffffc6ffffff40010000660100000b00000026060f000c004d6174685479706
50000200015000000fb0280fe0000000000009001010000000402001054696d6573204e6
57720526f6d616e00009c040000002d01000008000000320a600146000100000045000a0
0000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000
000cc0102022253797374656d00cc040000002d01010004000000f001000003000000000
0) и зимнего
(picscalex100010009000003ad000000020015000000000005000000090200000000040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)
солнцестояния. Большой круг небесной сферы, проходящий через полюсы
эклиптики и светило, называется кругом астрономической широты.
Координаты светила в эклиптической системе координат определяются
астрономической широтой и астрономической долготой.
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00000000000000002200040000002d010f000800000025030200a8014601b70145010400
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000000000000000000002200040000002d01100010000000250306004c02a5004902a300
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2d01040004000000f001100009000000fa02000000000000000000002200040000002d01
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000000002200040000002d0110000800000025030200a901d8009c01df00040000002d01
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0a000000250303008b01ea008401ee007e01f200040000002d01040004000000f0011000
09000000fa02000000000000000000002200040000002d01100008000000250302006d01
fc0061010501040000002d01040004000000f001100009000000fa020000000000000000
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04000000f001100009000000fa02000000000000000000002200040000002d0110000800
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000000000000000000002200040000002d0110000a000000250303001801390110013f01
0b014301040000002d01040004000000f001100009000000fa0200000000000000000000
2200040000002d0110000a00000025030300fc004f01fb005001f0005901040000002d01
040004000000f001100009000000fa02000000000000000000002200040000002d011000
0800000025030200e1006601d6007001040000002d01040004000000f001100009000000
fa02000000000000000000002200040000002d0110000a00000025030300c7007d01c200
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04000000f001100009000000fa02000000000000000000002200040000002d0110000800
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000000000000000000002200040000002d0110000a000000250303008200cc017c00d501
7a00d901040000002d01040004000000f001100009000000fa0200000000000000000000
2200040000002d0110000e000000250305007500ec017500ef017600f3017800f5017800
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0000000000002200040000002d0110001e00000025030d004f02aa005002ae004f02b400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Рис. 4

Астрономической широтой называется угловое расстояние от плоскости
эклиптики до светила, отсчитываемое вдоль круга широты. Астрономическая
широта отсчитывается от 0 до 90 в северном полушарии и от 0 до -90 – в
южном.

Астрономической долготой называется угловое расстояние от точки
весеннего равноденствия до круга широты данного светила. Отсчитывается
астрономическая долгота вдоль плоскости эклиптики в сторону видимого
годичного движения Солнца от 0 до 360.

Светила, расположенные на одном круге широты, имеют одинаковые
астрономические долготы.

Галактическая система координат.

Галактическим экватором называется большой круг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 небесной
сферы (рис. 8), наиболее близкий к средней линии Млечного Пути.
Положение галактического экватора задаётся экваториальными координатами
его северного полюса Г, то есть точки, отстоящей на 90 от всех точек
галактического экватора и находящейся в северном полушарии небесной
сферы. Диаметрально противоположная точка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 называются южным галактическим полюсом.

Кругом галактической широты светила называется большой круг небесной
сферы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, проходящий через
галактические полюсы и через светило М.

Восходящим узлом b галактического экватора на небесном экваторе
называется точка пересечения небесного экватора с галактическим
экватором, где Млечный Путь переходит из южного полушария в северное,
если при этом идти против часовой стрелки и смотреть со стороны
северного галактического полюса.

Галактической широтой светила называется угловое расстояние по кругу
галактической широты СМ от галактического экватора до светила.
Галактические широты обозначаются буквой b и отсчитываются от 0 до +90 к
северному галактическому полюсу и от 0 до -90 к южному галактическому
полюсу.

Галактической долготой светила называется угловое расстояние по
галактическому экватору bС от восходящего узла галактического экватора
на небесном экваторе до круга галактической широты, проходящего через
светило. Галактические долготы обозначаются буквой l и отсчитываются от
0 до 360 в каждую сторону, противоположную движению часовой стрелки,
если смотреть на плоскость галактического экватора со стороны его
северного полюса.

С 1971 года принята новая система галактических координат, в которой
долгота l отсчитывается не от восходящего узла b, а от точки
галактического экватора, соответствующей направлению на центр Галактики.
Эта точка отстоит на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 = 33, 0 к западу от восходящего узла. Следовательно, галактическая
долгота l в новой системе и долгота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 в старой
системе связаны соотношением:
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.

Если при этом окажется l > 360, то из полученного значения l следует
вычесть 360.

СИСТЕМЫ СЧЁТА ВРЕМЕНИ

Основной единицей меры времени являются сутки. Сутками называется
промежуток времени, в течении которого Земля совершает один полный
оборот вокруг своей оси вращения относительно какой-либо точки на
небесной сфере. В зависимости от специфики решаемой задачи принято
выбирать одну из трёх точек на небесной сфере:

1) истинное Солнце (или просто Солнце),

2) среднее экваториальное солнце,

3) точка весеннего равноденствия.

Сутки, связанные с выбором одной из этих точек на небесной сфере,
называются соответственно истинными солнечными, средними солнечными и
звёздными сутками.

Истинное солнечное время. Истинным солнцем называется центр видимого на
небе солнечного диска. Истинными солнечными сутками называется
промежуток времени между двумя ближайшими одноимёнными кульминациями
истинного Солнца на одном и том же географическом меридиане. За начало
истинных солнечных суток принимается момент нижней кульминации истинного
солнца, называемый истинной полночью. Промежуток времени от начала
истинных солнечных суток до любого другого момента времени называется
истинным солнечным временем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на данном географическом
меридиане.

Истинное солнечное время
picscalex100010009000003ab0000000200150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02000200020e00000026060f001200ffffffff00000800
0000c0ffacffc001ac010b00000026060f000c004d617468547970650000400015000000
fb0280fe0000000000009001010000000002001054696d6573204e657720526f6d616e00
0700040000002d01000009000000320a80013400010000005400d30010000000fb02e0fe
0000000000009001000000020002001053796d626f6c0000040000002d01010004000000
f001000009000000320ab901e80001000000c400df000a00000026060f000a00ffffffff
01000000000010000000fb021000080000000000bc02000000000102022253797374656d
0006040000002d01000004000000f0010100030000000000на данном меридиане
числено равно часовому углу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 истинного солнца,
выраженному в часовой мере, пляс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:
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. (1)

Пользоваться в повседневной жизни истинными солнечными сутками крайне
неудобно по двум причинам. Во-первых, линейная скорость Земли по орбите
не постоянна (это связано с эллиптичностью земной орбиты). Летом она
меньше чем зимой. Это приводит к непостоянству скорости суточного
движения истинного солнца по небесной сфере. Поэтому продолжительность
истинных солнечных суток оказывается разной в разное время года: летом
истинные солнечные сутки короче, а зимой – длиннее. Во – вторых,
истинное Солнце движется, как известно, не по небесному экватору, а в
плоскости эклиптики, наклонённой к плоскости небесного экватора на угол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. В результате центр
солнечного диска каждый раз в моменты восхода и захода появляется над
горизонтом в различных точках. Избавиться от этих двух неприятных
обстоятельств можно, если ввести две фиктивные (ничем на небе не
отмеченные) точки, называемые средним эклиптическим и средним
экваториальным солнцем. Это позволяет ввести понятие средних солнечных
суток, лишённых упомянутых выше недостатков, связанных с непостоянством
продолжительности истинных солнечных суток и с наклоном эклиптики к
плоскости экватора.

Среднее солнечное время и уравнение времени. Средним эклиптическим
солнцем называется некоторая фиктивная точка (никак на небе не
отмеченная), движущаяся по той же траектории что и истинное Солнце, т.
е. по эклиптике, с постоянной скоростью, равной средней скорости
истинного Солнца. Введение среднего эклиптического солнца, таким
образом, устраняет неприятность, связанную с зависимостью
продолжительности солнечных суток от времени года, но не снимает
проблемы, связанной с наклоном эклиптики к экватору. Для устранения
второго обстоятельства вводят ещё одну фиктивную точку, называемую
средним экваториальным солнцем.

Средним экваториальным солнцем называется некоторая фиктивная точка,
движущаяся по небесному экватору с постоянной скоростью, равной
скорости среднего эклиптического солнца. Таким образом среднее
экваториальное солнце, поскольку оно движется по небесному экватору и с
постоянной скоростью, позволяет строить такую систему счёта времени, в
которой продолжительность суток в течении года остаётся неизменной. В
этой системе счёта времени средними солнечными сутками называется
промежуток между двумя ближайшими одноимёнными кульминациями среднего
экваториального солнца на одном и том же географическом меридиане. За
начало средних солнечных суток принимается момент нижней кульминации
среднего экваториального солнца, называемый средней полночью. Промежуток
времени от начала средних солнечных суток до любого другого момента
времени называется средним солнечным временем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 на данном
географическом меридиане.

Среднее солнечное время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на данном меридиане числено равно часовому углу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 среднего экваториального солнца, выраженному в часовой мере, плюс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:
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. (2)

По причине непостоянства скорости истинного Солнца моменты времени в
обеих системах совпадают далеко не всегда. Среднее экваториальное солнце
то отстаёт от истинного, то опережает его. Соответствующая разность
моментов времени обеих систем называется уравнением времени:
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. (3)

Уравнение времени позволяет получить связь между истинным и средним
солнечными временами. Для этого достаточно в уравнения (1) и (2)
подставить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 и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, выраженные из уравнения времени (3):
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 (4)

Звёздное время. Звёздными сутками называется промежуток между двумя
ближайшими одноимёнными кульминациями точки весеннего равноденствия на
одном и том же географическом меридиане. За начало звёздных суток
принимается момент верхней кульминации точки весеннего равноденствия,
называемый звёздным полднем. Промежуток времени от начала звёздных суток
до любого другого момента времени называется звёздным временем s на
данном географическом меридиане.

Звёздное время s на данном географическом меридиане числено равно
часовому углу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 точки весеннего
равноденствия, выраженному в часовой мере:
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. (5)

Звёздное время s на данном географическом меридиане также может быть
определено суммой часового угла t любого светила и прямого
восхожденияpicscalex1000100090000038500000002001000000000000500000009020
00000000400000002010100050000000102ffffff00040000002e0118000500000031020
1000000050000000b0200000000050000000c02600180010e00000026060f001200fffff
fff000008000000c0ff2c0040018c010b00000026060f000c004d6174685479706500003
00010000000fb0280fe0000000000009001010000020002001053796d626f6c006104000
0002d01000009000000320a00012100010000006100f0000a00000026060f000a00fffff
fff01000000000010000000fb021000080000000000bc020000000001020222537973746
56d0006040000002d01010004000000f0010000030000000000 того же светила:
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. (6)

Иногда приходится осуществлять переход от звёздного времени к солнечному
или наоборот. Для этого необходимо сначала найти звёздное время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 на начало солнечных суток (положение точки весеннего равноденствия
на небесной сфере на начало солнечных суток), а затем по таблицам
отыскать звёздное время
picscalex1000100090000038d0000000200150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02600120011200000026060f001a00ffffffff00001000
0000c0ffffff26000000e0000000860100000b00000026060f000c004d61746854797065
0000300015000000fb0280fe0000000000009001010000000402001054696d6573204e65
7720526f6d616e0000f2040000002d01000008000000320a000140000100000073000a00
000026060f000a00ffffffff01000000000010000000fb021000070000000000bc020000
00cc0102022253797374656d00cc040000002d01010004000000f0010000030000000000
на данный момент истинного солнечного времени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. Приближённо это можно сделать по формуле:
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.

Величина
picscalex100010009000003b20000000200150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c024002c0011200000026060f001a00ffffffff00001000
0000c0ffffffa6ffffff80010000e60100000b00000026060f000c004d61746854797065
0000600015000000fb0220ff0000000000009001000000000402001054696d6573204e65
7720526f6d616e000081040000002d01000008000000320ae0011a010100000030001500
0000fb0280fe0000000000009001010000000402001054696d6573204e657720526f6d61
6e000081040000002d01010004000000f001000008000000320a80014000010000005300
0a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02
000000cc0102022253797374656d00cc040000002d01000004000000f001010003000000
0000 приводится в астрономических календарях, а приближённо её можно
рассчитать по формуле:
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,

Такое несовпадение моментов солнечного и звёздного времени объясняется
тем, что Солнце движется в направлении, противоположном суточному
вращению Земли (с запада на восток). За сутки это перемещение составляет
почти 1, в результате чего солнечные сутки оказываются длиннее звёздных
на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. За год это
составляет ровно одни сутки: звёздный год на одни сутки длиннее
солнечного. Начала истинных солнечных и звёздных суток совпадают 23
сентября каждого года.

Местное, всемирное и поясное время. Истинное, среднее и звёздное время
на том или ином географическом меридиане называют также местным
истинным, местным средним или местным солнечным временем. Мы для
краткости все такие времена будем именовать просто местным временем.
Вполне понятно, что местное время в один и тот же момент на каждом
географическом меридиане будет различным. Разность местных времён двух
географических меридианов в один и тот же момент равен разности долгот
этих меридианов, выраженных в часовой мере:

picscalex100010009000003940200000200150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c028007800d1200000026060f001a00ffffffff00001000
0000c0ffffffaeffffff400d00002e0700000b00000026060f000c004d61746854797065
0000b00115000000fb0280fe0000000000009001000000000402001054696d6573204e65
7720526f6d616e000067040000002d01000008000000320a9c06ca0c010000002e000800
0000320a2004d60c010000002c0008000000320aa901d60c010000002c0015000000fb02
20ff0000000000009001000000000402001054696d6573204e657720526f6d616e000067
040000002d01010004000000f001000008000000320af0052a0c01000000680008000000
320afc06320c01000000320008000000320af0053b0901000000680008000000320afc06
2a0901000000310008000000320afc06270601000000320008000000320afc0625020100
0000310008000000320a74032a0c01000000680008000000320a8004320c010000003200
08000000320a74033b0901000000680008000000320a80042a0901000000310008000000
320a8104270601000000320008000000320a8104a70201000000310008000000320afd00
2a0c01000000680008000000320a0902320c01000000320008000000320afd003b090100
0000680008000000320a09022a0901000000310008000000320a09022706010000003200
08000000320a09027c0301000000310010000000fb0280fe000000000000900101000002
0002001053796d626f6c0002040000002d01000004000000f001010008000000320a9c06
4f0b010000006c0008000000320a9c066008010000006c0008000000320a20044f0b0100
00006c0008000000320a20046008010000006c0008000000320aa9014f0b010000006c00
08000000320aa9016008010000006c0010000000fb0280fe000000000000900100000002
0002001053796d626f6c0002040000002d01010004000000f001000008000000320a9c06
350a010000002d0008000000320a9c062e07010000003d0008000000320a9c0603030100
00002d0008000000320a2004350a010000002d0008000000320a20042e07010000003d00
08000000320a20048503010000002d0008000000320aa901350a010000002d0008000000
320aa9012e07010000003d0008000000320aa9015a04010000002d0010000000fb0200ff
0000000000009001000000020002001053796d626f6c0002040000002d01000004000000
f001010008000000320a81045a0501000000c40008000000320a8104f30101000000c400
15000000fb02e0fe0000000000009001000000cc04020030436f7572696572204e657720
43797200cc67040000002d01010004000000f001000008000000320afc06ca0402000000
f1f008000000320afc06e10002000000f1f015000000fb0280fe00000000000090010100
00000402001054696d6573204e657720526f6d616e000067040000002d01000004000000
f001010008000000320a9c060b0401000000540008000000320a9c062200010000005400
08000000320a20048d0401000000540008000000320a2004260101000000540008000000
320aa901800501000000730008000000320aa901ee020100000073000a00000026060f00
0a00ffffffff01000000000010000000fb021000070000000000bc02000000cc01020222
53797374656d00cc040000002d01010004000000f0010000030000000000 (7)

Естественно, что пользоваться местным временем в повседневной жизни не
удобно. Поэтому из всего множества меридианов выбрали 24 основных,
отстоящих друг от друга на 15. Один из них, проходящий через Гринвичскую
обсерваторию (Англия), стали называть нулевым или Гринвичским
меридианом, а местное время на нём всемирным временем или временем по
Гринвичу. Все остальные меридианы пронумеровали от 0 да 23 в сторону к
востоку от Гринвичского. Кроме того, с каждым из этих меридианов связали
полоску земной поверхности шириной в 15 (7,5 к востоку от
соответствующего меридиана и на 7,5 к западу от него). Такие полосы
земной поверхности стали называть часовыми поясами и считать время в
любой точке данного часового пояса одинаковым и равным местному времени
на центральном меридиане данного часового пояса. Такое время называется
поясным временем. Поясное время связано со всемирным временем очень
простым соотношением:
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, (8)

где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-
номер часового пояса, отсчитываемый от нулевого меридиана в сторону
востока.

Следует отметить, что в действительности границы между часовыми поясами
не совпадают в точности с меридианами, отстоящими от основного меридиана
на 7,5, а согласуются с государственными и административными границами
и, при необходимости, могут изменяться.

Разность поясных времён двух часовых поясов всегда является целым
числом, равным разности номеров этих часовых поясов:
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. (9)

Поясное время какого-либо пункта с восточной долготой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 может быть
определено по формулам:
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 (10)

Декретное время. Весной 1930 г. правительством Советского Союза было
принято постановление о переводе стрелок часов на 1 час вперёд
относительно поясного времени:
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. (4)

Такое время называется декретным. Местное время связано с декретным
следующим выражением:

picscalex100010009000003d50100000200150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c028003200f0e00000026060f001200ffffffff00000800
0000c0ffb3ffe00e33030b00000026060f000c004d617468547970650000b00010000000
fb02a8fcdb00000000009001000000020002001053796d626f6c0081040000002d010000
08000000320a8c02680601000000280010000000fb02a8fcdb0000000000900100000002
0002001053796d626f6c0081040000002d01010004000000f001000008000000320a8c02
f70b01000000290015000000fb0280fe0000000000009001010000000002001054696d65
73204e657720526f6d616e000800040000002d01000004000000f001010009000000320a
20023400010000005400d30009000000320a20027303010000005400d30009000000320a
20021107010000004e00030115000000fb02e0fe00000000000090010100000000020010
54696d6573204e657720526f6d616e000000040000002d01010004000000f00100000900
0000320a4d015808010000006800900009000000320a4d012d0b01000000680090001000
0000fb02e0fe0000000000009001010000020002001053796d626f6c0000040000002d01
000004000000f001010009000000320a5902ee00010000006c009e0010000000fb0280fe
0000000000009001010000020002001053796d626f6c0000040000002d01010004000000
f001000009000000320a2002e30d010000006c00d30010000000fb0280fe000000000000
9001000000020002001053796d626f6c0000040000002d01000004000000f00101000900
0000320a20023902010000003d00d30009000000320a20024f05010000002d00d3000900
0000320a20026c09010000002b00d30009000000320a2002be0c010000002b00d3001500
0000fb02e0fe0000000000009001000000cc00020030436f7572696572204e6577204379
72000000040000002d01010004000000f001000009000000320a59022a0401000000e400
ac0015000000fb0280fe0000000000009001000000000002001054696d6573204e657720
526f6d616e000800040000002d01000004000000f001010009000000320a2002760a0100
00003100c0000a00000026060f000a00ffffffff01000000000010000000fb0210000800
00000000bc02000000000102022253797374656d0006040000002d01010004000000f001
0000030000000000. (5)

Из соображений более рационального использования светлой части суток в
большинстве регионов страны используется, так называемое, летнее время:

picscalex100010009000003380100000200150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02a002e0070e00000026060f001200ffffffff00000800
0000c0ffb4ffa00754020b00000026060f000c004d617468547970650000500015000000
fb0280fe0000000000009001010000000002001054696d6573204e657720526f6d616e00
0100040000002d01000009000000320a00023400010000005400d30009000000320a0002
6003010000005400d30015000000fb02e0fe000000000000900101000000000200105469
6d6573204e657720526f6d616e008b01040000002d01010004000000f001000009000000
320a2d01fe06010000006800900015000000fb02e0fe0000000000009001000000cc0002
0030436f7572696572204e657720437972000100040000002d01000004000000f0010100
09000000320a3902eb0001000000eb00ac0009000000320a3902170401000000e400ac00
10000000fb0280fe0000000000009001000000020002001053796d626f6c000004000000
2d01010004000000f001000009000000320a00022602010000003d00d30009000000320a
00023d05010000002b00d30015000000fb0280fe00000000000090010000000000020010
54696d6573204e657720526f6d616e000100040000002d01000004000000f00101000900
0000320a00024706010000003100c0000a00000026060f000a00ffffffff010000000000
10000000fb021000080000000000bc02000000000102022253797374656d000604000000
2d01010004000000f0010000030000000000 (6)

Эфемеридное и атомное время. Вследствие непрерывного уменьшения скорости
вращения Земли все рассмотренные выше единицы счёта времени изменяются.
Так, например, в 1900 году секунда была несколько короче тем сейчас. Это
недопустимо сильно сказывается при расчётах движения тел в пределах
Солнечной системы. Поэтому в астрономии вводится понятие эфемеридного
(или ньютоновского) времени, единицей измерения которого является
отрезок времени, равный одной средней солнечной секунде 1900 года.

Существует и более строгое определение секунды, как отрезка времени,
равного 9 192 631 770 периодам колебаний электромагнитной волны,
излучаемой атомом цезия. Система счёта времени, построенная на таком
определении секунды называется атомным временем. Переход на атомное
время был осуществлён в 1964 году, а в качестве эталона атомного времени
Международным комитетом мер и весов были приняты атомные цезиевые часы.
С 1 января 1972 года все страны мира перешли на счёт времени по этим
часам.

ПЕРЕХОД ОТ ОДНОЙ СИСТЕМЫ КООРДИНАТ К ДРУГОЙ

При решении многих задач практической астрономии приходится осуществлять
переход от одной системы координат к другой и обратно. Эта операция
выполняется при помощи сферической тригонометрии, для чего необходимо
уметь решать так называемые сферические треугольники. Поэтому прежде
рассмотрим основные понятия и начала математического аппарата
сферической тригонометрии, после чего применим эту информацию к решению
поставленной задачи.

ЭЛЕМЕНТЫ СФЕРИЧЕСКОЙ ТРИГОНОМЕТРИИ

Сферическим треугольником называется фигура на поверхности сферы,
образованная пересечением трёх дуг больших кругов этой сферы (рис. 9).
Вершины сферического треугольника принято обозначать большими буквами
латинского алфавита, а противолежащие этим сторонам угла –
соответственно малыми буквами.

Каждая сторона сферического треугольника меньше суммы двух других
сторон:
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.

Каждая сторона сферического треугольника больше разности двух других его
сторон:
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Полупериод сферического треугольника всегда больше каждой из его сторон:
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Сумма сторон сферического треугольника всегда меньше 360:
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.

Сумма углов сферического треугольника всегда меньше 540 и больше 180:
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.

Разность между суммой трёх углов сферического треугольника и 180
называется сферическим избытком Е:
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.

Площадь сферического треугольника s равна произведению сферического
избытка на величину
picscalex1000100090000032f0100000300150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02200460031200000026060f001a00ffffffff00001000
0000c0ffffffa9ffffff20030000c90300000b00000026060f000c004d61746854797065
0000c00009000000fa02000010000000000000002200040000002d010000050000001402
400240000500000013024002140310000000fb0280fe0000000000009001000000020002
001053796d626f6c0002040000002d01010008000000320acc03700201000000b0001500
0000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d61
6e000083040000002d01020004000000f001010009000000320acc033000030000003138
300015000000fb0220ff0000000000009001000000000402001054696d6573204e657720
526f6d616e000083040000002d01010004000000f001020008000000320a02013f020100
0000320015000000fb0280fe0000000000009001010000000402001054696d6573204e65
7720526f6d616e000083040000002d01020004000000f001010008000000320aae012e01
01000000520010000000fb0280fe0000000000009001010000020002001053796d626f6c
0002040000002d01010004000000f001020008000000320aae015c000100000070000a00
000026060f000a00ffffffff01000000000010000000fb021000070000000000bc020000
00cc0102022253797374656d00cc040000002d01020004000000f0010100030000000000
:
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, (8)

где R – радиус сферы, на поверхности которой образован треугольник.

Косинус одной стороны сферического треугольника равен сумме произведения
косинусов двух других его сторон и произведения синусов тех же сторон на
косину угла между ними:
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. (9)

Синусы сторон сферического треугольника пропорциональны синусам
противолежащих им углов:

picscalex100010009000003f70100000300150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02e003401a1200000026060f001a00ffffffff00001000
0000c0ffffffb8ffffff001a0000980300000b00000026060f000c004d61746854797065
0000c00009000000fa02000010000000000000002200040000002d010000050000001402
0002400005000000130200022c030500000014020002dc0405000000130200020a080500
00001402000266090500000013020002520c0500000014020002020e0500000013020002
241105000000140200023812050000001302000212150500000014020002c21605000000
13020002f01915000000fb0280fe0000000000009001010000000402001054696d657320
4e657720526f6d616e000089040000002d01010008000000320a8c03c818010000004300
08000000320a6e01e61801000000420008000000320a8c034a1401000000630008000000
320a6e013e1401000000620008000000320a8c03201001000000420008000000320a6e01
321001000000410008000000320a8c03750b01000000620008000000320a6e01780b0100
0000610008000000320a8c03e20601000000430008000000320a6e011207010000004100
08000000320a8c035b0201000000630008000000320a6e01520201000000610015000000
fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e00
0089040000002d01020004000000f001010009000000320a8c03d0160300000073696e00
09000000320a6e01d6160300000073696e0009000000320a8c034c120300000073696e00
09000000320a6e0146120300000073696e0008000000320a60025411010000003b000900
0000320a8c03100e0300000073696e0009000000320a6e01100e0300000073696e000900
0000320a8c037d090300000073696e0009000000320a6e0174090300000073696e000800
0000320a60023a08010000003b0009000000320a8c03ea040300000073696e0009000000
320a6e01f0040300000073696e0009000000320a8c035d000300000073696e0009000000
320a6e014e000300000073696e0010000000fb0280fe0000000000009001000000020002
001053796d626f6c0002040000002d01010004000000f001020008000000320a60028415
010000003d0008000000320a6002c40c010000003d0008000000320a60029e0301000000
3d000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000
bc02000000cc0102022253797374656d00cc040000002d01020004000000f00101000300
00000000. (10)

или
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. (11)

Синус стороны сферического треугольника, умноженный на косинус
прилежащего угла, равен произведению синуса другой стороны,
ограничивающей прилежащий угол, на косинус третьей стороны минус косинус
стороны, ограничивающей угол, умноженный на произведение синуса третьей
стороны на косинус угла, противолежащего первой стороне:
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. (12)

Полярным треугольником для данного сферического треугольника называется
такой сферический треугольник, по отношению сторон которого вершины
данного являются полюсами, то есть отстоят от сторон на 90 (рис. 10).

Сумма угла данного сферического треугольника и соответствующей стороны
полярного треугольника равна 180:
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 (13)

и наоборот:
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. (14)

’’’

’’’

На основе этих свойств полярного треугольника и исходя из (8) – (12),
можно получить другие зависимости между сторонами и углами сферического
треугольника. Так, например:
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.

Эти формулы, равно как и другие, которые могут быть получены на
основании выражений (13) и (14), справедливы не только для полярного
треугольника, но и вообще для всякого сферического треугольника.

Если в сферическом треугольнике один из углов равен 90, то треугольник
называется прямоугольным. Для решения прямоугольных сферических
треугольников наиболее употребительны следующие формулы:
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.

Для решения сферических треугольников со стороной a = 90 употребляются
следующие формулы:
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.

ПЕРЕХОД ОТ ЭКВАТОРИАЛЬНЫХ КООРДИНАТ К ГОРИЗОНТАЛЬНЫМ И ОБРАТНО

В основе преобразований экваториальных координат в горизонтальные лежит
сферический треугольник PZM (рис. 11), который называется
параллактическим. Вершинами его являются зенит Z, полюс мира P и светило
М. Сторона ZP представляет собой дугу небесного меридиана, сторона ZM –
дугу вертикального круга, а сторона PM – дугу часового круга. Угол q
треугольника называется параллактическим углом.

Переход от экваториальных координат к географическим.

Пусть даны географическая широта
picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02a00160011200000026060f001a00ffffffff00001000
0000c0ffffff2600000020010000c60100000b00000026060f000c004d61746854797065
0000500010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a00011c00010000006a000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000 точки наблюдения,
склонение светила
picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02c00160011200000026060f001a00ffffffff00001000
0000c0ffffffc6ffffff20010000860100000b00000026060f000c004d61746854797065
0000300010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a600122000100000064000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000 и его прямое
восхождение
picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02600160011200000026060f001a00ffffffff00001000
0000c0ffffff2600000020010000860100000b00000026060f000c004d61746854797065
0000300010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a000116000100000061000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000. Требуется найти
зенитное расстояние z и азимут А для некоторого момента Т среднего
солнечного времени (местного, поясного или декретного).

Прежде всего необходимо по моменту Т найти местное звёздное время s и
вычислить часовой угол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. Затем s и A вычисляются по формулам:
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.

Так же возможно использование других формул:
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.

Если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, то М нужно брать в первом или третьем квадранте;
если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, то во втором или третьем квадранте. Если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, то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; если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, то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. Кроме того, всегда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.

Для контроля вычислений служит формула:
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.

Переход от горизонтальных координат к экваториальным.

Пусть даны географическая широта
picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02a00160011200000026060f001a00ffffffff00001000
0000c0ffffff2600000020010000c60100000b00000026060f000c004d61746854797065
0000500010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a00011c00010000006a000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000 точки наблюдения,
зенитное расстояние z и азимут A. Требуется найти склонение светила
picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02c00160011200000026060f001a00ffffffff00001000
0000c0ffffffc6ffffff20010000860100000b00000026060f000c004d61746854797065
0000300010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a600122000100000064000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000, часовой угол t и
прямое восхождение
picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02600160011200000026060f001a00ffffffff00001000
0000c0ffffff2600000020010000860100000b00000026060f000c004d61746854797065
0000300010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a000116000100000061000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000, если известно
местное звёздное время s
(picscalex100010009000003dd000000020015000000000005000000090200000000040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).

Вычисления производятся по следующим формулам:
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.

Возможно применение и других формул:
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.

Квадранты M и t выбираются из тех же условий, что и в предыдущем случае.

Для контроля вычислений служит формула:
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.

ПЕРЕХОД ОТ ЭКВАТОРИАЛЬНЫХ КООРДИНАТ К ЭКЛИПТИЧЕСКИМ И ОБРАТНО

В основе преобразований лежит сферический треугольник РМП (рис. 12). Его
вершинами являются: полюс мира Р, полюс эклиптики П и светило М. Сторона
ПР равна углу наклона эклиптики к экватору
picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02600140011200000026060f001a00ffffffff00001000
0000c0ffffff2600000000010000860100000b00000026060f000c004d61746854797065
0000300010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a000128000100000065000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000, сторона ПМ равна
полярному расстоянию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, сторона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,
где
picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02000280011200000026060f001a00ffffffff00001000
0000c0ffffffc6ffffff40010000c60100000b00000026060f000c004d61746854797065
0000500010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a600146000100000062000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000 – астрономическая
широта светила. Угол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, где
picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02c00160011200000026060f001a00ffffffff00001000
0000c0ffffffc6ffffff20010000860100000b00000026060f000c004d61746854797065
0000300010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a60013400010000006c000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000 – астрономическая
долгота светила, а угол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.

Переход от экваториальных координат к эклиптическим.

Пусть даны прямое восхождение
picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02600160011200000026060f001a00ffffffff00001000
0000c0ffffff2600000020010000860100000b00000026060f000c004d61746854797065
0000300010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a000116000100000061000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000 светила, его
склонение
picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02c00160011200000026060f001a00ffffffff00001000
0000c0ffffffc6ffffff20010000860100000b00000026060f000c004d61746854797065
0000300010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a600122000100000064000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000 и угол наклона
эклиптики к экватору
picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02600140011200000026060f001a00ffffffff00001000
0000c0ffffff2600000000010000860100000b00000026060f000c004d61746854797065
0000300010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a000128000100000065000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000. Требуется найти
астрономическую долготу светила
picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02c00160011200000026060f001a00ffffffff00001000
0000c0ffffffc6ffffff20010000860100000b00000026060f000c004d61746854797065
0000300010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a60013400010000006c000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000 и его
астрономическую широту
picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02000280011200000026060f001a00ffffffff00001000
0000c0ffffffc6ffffff40010000c60100000b00000026060f000c004d61746854797065
0000500010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a600146000100000062000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000.

Вычисления производятся по следующим формулам:
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.

Возможно применение других формул:
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.

Квадрант для М выбирается по знаку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, а
picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02c00160011200000026060f001a00ffffffff00001000
0000c0ffffffc6ffffff20010000860100000b00000026060f000c004d61746854797065
0000300010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a60013400010000006c000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000 лежит в том же
квадранте, что и прямое восхождение
picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02600160011200000026060f001a00ffffffff00001000
0000c0ffffff2600000020010000860100000b00000026060f000c004d61746854797065
0000300010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a000116000100000061000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000.

Формула для контроля имеет вид:

picscalex100010009000003b10100000300150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02e003800f1200000026060f001a00ffffffff00001000
0000c0ffffffb8ffffff400f0000980300000b00000026060f000c004d61746854797065
0000c00009000000fa02000010000000000000002200040000002d010000050000001402
000240000500000013020002bc0610000000fb0205fee300000000009001000000020002
001053796d626f6c0002040000002d01010008000000320a6c01830a0100000028001000
0000fb0205fee300000000009001000000020002001053796d626f6c0002040000002d01
020004000000f001010008000000320a6c01bb0e01000000290005000000140200026c08
05000000130200022d0f15000000fb0280fe000000000000900101000000040200105469
6d6573204e657720526f6d616e000090040000002d01010004000000f001020008000000
320a8c032c0c010000004d0008000000320a6e01010b010000004d0015000000fb0280fe
0000000000009001000000000402001054696d6573204e657720526f6d616e0000900400
00002d01020004000000f001010009000000320a8c03f20903000000636f730009000000
320a6e01800803000000636f730009000000320a8c03a5030300000073696e0009000000
320a8c03630003000000636f730009000000320a6e01c0030300000073696e0009000000
320a6e01540003000000636f730010000000fb0280fe0000000000009001010000020002
001053796d626f6c0002040000002d01010004000000f001020008000000320a6e01d70d
01000000650008000000320a8c03850501000000610008000000320a8c037f0201000000
640008000000320a6e01be05010000006c0008000000320a6e0194020100000062001000
0000fb0280fe0000000000009001000000020002001053796d626f6c0002040000002d01
020004000000f001010008000000320a6e01c90c010000002d0008000000320a60022e07
010000003d000a00000026060f000a00ffffffff01000000000010000000fb0210000700
00000000bc02000000cc0102022253797374656d00cc040000002d01010004000000f001
0200030000000000.

Переход от эклиптических координат к экваториальным.

Пусть даны астрономическая долгота светила
picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02c00160011200000026060f001a00ffffffff00001000
0000c0ffffffc6ffffff20010000860100000b00000026060f000c004d61746854797065
0000300010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a60013400010000006c000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000, его
астрономическая широта
picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02000280011200000026060f001a00ffffffff00001000
0000c0ffffffc6ffffff40010000c60100000b00000026060f000c004d61746854797065
0000500010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a600146000100000062000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000 и угол наклона
эклиптики к экватору
picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02600140011200000026060f001a00ffffffff00001000
0000c0ffffff2600000000010000860100000b00000026060f000c004d61746854797065
0000300010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a000128000100000065000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000. Требуется найти
прямое восхождение
picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02600160011200000026060f001a00ffffffff00001000
0000c0ffffff2600000020010000860100000b00000026060f000c004d61746854797065
0000300010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a000116000100000061000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000 и склонение
picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02c00160011200000026060f001a00ffffffff00001000
0000c0ffffffc6ffffff20010000860100000b00000026060f000c004d61746854797065
0000300010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a600122000100000064000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000 светила.

Вычисления производятся по следующим формулам:
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или
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.

Квадранты для М и
picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02600160011200000026060f001a00ffffffff00001000
0000c0ffffff2600000020010000860100000b00000026060f000c004d61746854797065
0000300010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a000116000100000061000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000 выбираются из
условий, аналогичных предыдущему случаю.

Формула для контроля вычислений имеют вид:
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.

ПЕРЕХОД ОТ ЭКВАТОРИАЛЬНЫХ КООРДИНАТ К ГАЛАКТИЧЕСКИМ

В основе преобразований лежит сферический треугольник РГМ (рис. 13),
вершинами которого являются: северный полюс мира Р, северный
галактический полюс Г и светило М. Сторона РМ равна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, сторона ГМ равна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 (b – галактическая широта светила), сторона ГР
равна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 (D – склонение северного галактического полюса,
угол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 (l – галактическая
долгота светила), угол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(picscalex10001000900000388000000020012000000000005000000090200000000040
0000002010100050000000102ffffff00040000002e01180005000000310201000000050
000000b0200000000050000000c02600160011200000026060f001a00ffffffff0000100
00000c0ffffff2600000020010000860100000b00000026060f000c004d6174685479706
50000300010000000fb0280fe0000000000009001010000020002001053796d626f6c000
2040000002d01000008000000320a000116000100000061000a00000026060f000a00fff
fffff01000000000010000000fb021000070000000000bc02000000cc010202225379737
4656d00cc040000002d01010004000000f0010000030000000000прямое восхождение
светила, а А – прямое восхождение северного галактического полюса).

Пусть даны
picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02600160011200000026060f001a00ffffffff00001000
0000c0ffffff2600000020010000860100000b00000026060f000c004d61746854797065
0000300010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a000116000100000061000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000, склонение светила
picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02c00160011200000026060f001a00ffffffff00001000
0000c0ffffffc6ffffff20010000860100000b00000026060f000c004d61746854797065
0000300010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a600122000100000064000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000, D и А. Требуется
найти b и l. Вычисления производятся по следующим формулам:
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. (15)

Возможно применение других формул:
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.

Для контроля вычислений применяется формула:
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.

В этих формулах положение галактического экватора задано прямым
восхождением А и склонением D его северного полюса Г. Очень часто
положение галактического экватора задаётся прямым восхождением b его
восходящего узла и углом наклонения i галактического экватора к
небесному экватору. Эти четыре величины связаны между собой
соотношениями:
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,
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.

Следовательно, сторона
picscalex100010009000003020100000200150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02c001800a1200000026060f001a00ffffffff00001000
0000c0ffffffc6ffffff400a0000860100000b00000026060f000c004d61746854797065
0000300015000000fb0280fe0000000000009001010000000402001054696d6573204e65
7720526f6d616e000076040000002d01000008000000320a6001d6090100000069000800
0000320a60012a0701000000440008000000320a60011e0101000000500010000000fb02
80fe0000000000009001000000020002001053796d626f6c0002040000002d0101000400
0000f001000008000000320a6001aa08010000003d0008000000320a6001fe0501000000
2d0008000000320a6001200501000000b00008000000320a60017402010000003d000800
0000320a6001340001000000470015000000fb0280fe0000000000009001000000000402
001054696d6573204e657720526f6d616e000076040000002d01000004000000f0010100
08000000320a6001a0030200000039300a00000026060f000a00ffffffff010000000000
10000000fb021000070000000000bc02000000cc0102022253797374656d00cc04000000
2d01010004000000f0010000030000000000, а угол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 и формулы (15) приобретают вид:

picscalex1000100090000034d0300000200150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c020007a01b1200000026060f001a00ffffffff00001000
0000c0ffffffb2ffffff601b0000b20600000b00000026060f000c004d61746854797065
0000900110000000fb02f8fde300000000009001000000020002001053796d626f6c0002
040000002d01000008000000320a98013b1301000000280010000000fb02f8fde3000000
00009001000000020002001053796d626f6c0002040000002d01010004000000f0010000
08000000320a98015e1701000000290010000000fb02f8fde30000000000900100000002
0002001053796d626f6c0002040000002d01000004000000f001010008000000320ade03
171601000000280010000000fb02f8fde300000000009001000000020002001053796d62
6f6c0002040000002d01010004000000f001000008000000320ade033a1a010000002900
10000000fb02f8fde300000000009001000000020002001053796d626f6c000204000000
2d01000004000000f001010008000000320a2406d50c01000000280010000000fb02f8fd
e300000000009001000000020002001053796d626f6c0002040000002d01010004000000
f001000008000000320a2406f81001000000290010000000fb0280fe0000000000009001
000000020002001053796d626f6c0002040000002d01000004000000f001010008000000
320a9205a21a01000000ef0008000000320a9406a21a01000000fe0008000000320a0203
a21a01000000ef0008000000320a2204a21a01000000fd0008000000320ab001a21a0100
0000fc0008000000320a2606880e010000002d0008000000320a26065806010000003d00
08000000320ae003ca17010000002d0008000000320ae003180d010000002b0008000000
320ae0032206010000003d0008000000320a9a01ee14010000002d0008000000320a9a01
780a010000002d0008000000320a9a014c03010000003d0012000000fb0280fe00000000
00009001000000020402000057696e6764696e6773000200040000002d01010004000000
f001000008000000320a2606900f01000000620008000000320ae003d218010000006200
08000000320a9a01f61501000000620010000000fb0280fe000000000000900101000002
0002001053796d626f6c0002040000002d01000004000000f001010008000000320a2606
260d01000000610008000000320a2606a60901000000640008000000320ae00368160100
0000610008000000320ae003541001000000640008000000320ae0033a09010000006400
08000000320a9a018c1301000000610008000000320a9a01ae0d01000000640008000000
320a9a01640601000000640015000000fb0280fe00000000000090010000000004020010
54696d6573204e657720526f6d616e000083040000002d01010004000000f00100000900
0000320a2606d20a03000000636f730009000000320a26068a0703000000636f73000900
0000320a26060a0303000000636f730009000000320a2606340003000000636f73000900
0000320ae00344140300000073696e0009000000320ae003801103000000636f73000900
0000320ae003380e03000000636f730009000000320ae003600a0300000073696e000900
0000320ae0034e070300000073696e0009000000320ae003d40203000000636f73000900
0000320ae0032e000300000073696e0009000000320a9a0168110300000073696e000900
0000320a9a01d40e0300000073696e0009000000320a9a01920b03000000636f73000900
0000320a9a01900703000000636f730009000000320a9a0178040300000073696e000900
0000320a9a012e000300000073696e0015000000fb0280fe000000000000900101000000
0402001054696d6573204e657720526f6d616e000083040000002d01000004000000f001
010008000000320a2606320501000000620008000000320a26065c02010000006c000800
0000320ae003a81301000000690008000000320ae003580c01000000690008000000320a
e003fc0401000000620008000000320ae0032602010000006c0008000000320a9a01cc10
01000000690008000000320a9a01b80901000000690008000000320a9a01260201000000
62000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000
bc02000000cc0102022253797374656d00cc040000002d01010004000000f00100000300
00000000. (16)

Так как положение галактического экватора определяется с точностью в
лучшем случае до долей градуса, то l и b также вычисляются с точностью
до одной десятой градуса. При этом пользуются готовыми таблицами,
например, Ольсана «Lund Observatory Tables for the Conversion of
Equatorial into Galactic Coordinates».

В этих таблицах приняты координаты северного галактического полюса для
эпохи 1900,0, а именно: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, D = +28. Следовательно, i = 62, а прямое
восхождение узла b = 280.

В 1961 году Тургорд опубликовал аналогичные таблицы с координатами
северного галактического полюса для эпохи 1950б0. В этих таблицах
принято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, D = +27,4, i = 62,6 и b = 282,2.

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