Введение
Среднее расстояние между Землей и Солнцем
Астрономическая единица (символ: au, или AU) — это единица длины, определённая как точно равная 149 597 870 700 метрам. Исторически астрономическая единица понималась как среднее расстояние от Земли до Солнца (среднее значение между афелием и перигелием Земли), до её современного переопределения в 2012 году. Астрономическая единица используется главным образом для измерения расстояний внутри Солнечной системы или вокруг других звёзд. Она также является фундаментальным компонентом в определении другой единицы астрономической длины — парсека. Один астрономический единица эквивалентен 499 световым секундам с точностью до 10 частей на миллион.
История использования символов
Для астрономической единицы использовались различные обозначения и сокращения. В резолюции 1976 года Международный астрономический союз (МАС) использовал символ А для обозначения длины, равной астрономической единице. В ненадежном приложении C к ISO 80000-3:2006 (впоследствии отозванном), символом астрономической единицы также было ua. В 2012 году МАС, отметив «что в настоящее время используются различные символы для астрономической единицы», рекомендовал использовать символ «au». В пересмотренном издании 2014 года и издании 2019 года брошюры SI, BIPM использовал обозначение единицы измерения «au». В ISO 80000-3:2019, заменяющем ISO 80000-3:2006, астрономическая единица не упоминается.
Развитие определения единицы
Орбита Земли вокруг Солнца — эллипс. Большая полуось этой эллиптической орбиты определяется как половина отрезка прямой линии, соединяющего перигелий и афелий. Центр Солнца лежит на этом отрезке прямой линии, но не в его середине. Поскольку эллипсы — хорошо изученные фигуры, измерение точек их крайних положений позволило математически точно определить форму орбиты и выполнить расчеты для всей орбиты, а также прогнозы, основанные на наблюдениях. Кроме того, это позволило точно определить наибольшее расстояние, которое Земля проходит в течение года, определив время и место для наблюдения наибольшего параллакса (видимого сдвига положения) в близлежащих звездах. Зная смещение Земли и смещение звезды, можно было рассчитать расстояние до звезды. Однако все измерения подвержены определенной степени погрешности или неопределенности, и неопределенность в длине астрономической единицы лишь увеличивала неопределенность в расстояниях до звезд. Повышение точности всегда было ключевым фактором в углублении астрономического понимания. На протяжении двадцатого века измерения становились все более точными и сложными, и все больше зависели от точного наблюдения эффектов, описанных теорией относительности Эйнштейна, и от математических инструментов, которые она использовала. Улучшенные измерения постоянно проверялись и перекрестно проверялись посредством углубленного понимания законов небесной механики, которые управляют движением объектов в космосе. Ожидаемые положения и расстояния объектов в заданный момент времени рассчитываются (в а.е.) на основе этих законов и собираются в набор данных, называемый эфемеридой. Система NASA Jet Propulsion Laboratory HORIZONS предоставляет один из нескольких сервисов вычисления эфемерид. В 1976 году, чтобы установить еще более точное значение астрономической единицы, МАС официально приняла новое определение. Хотя определение было основано на лучших доступных на тот момент наблюдательных измерениях, оно было переформулировано с точки зрения лучших математических выводов из небесной механики и планетарных эфемерид. В нем утверждалось, что «астрономическая единица длины — это длина (A), при которой гауссова гравитационная постоянная (k) принимает значение 0,01720209895, когда единицы измерения — астрономические единицы длины, массы и времени». Эквивалентно, согласно этому определению, одна а.е. — это «радиус непомещенной круговой ньютоновской орбиты вокруг Солнца частицы с бесконечно малой массой, движущейся с угловой частотой 0,01720209895»; или, альтернативно, длина, при которой гелиоцентрическая гравитационная постоянная (произведение G) равна (0,01720209895)2 а.е.3/дн2, когда длина используется для описания положений объектов в Солнечной системе. Последующие исследования Солнечной системы с помощью космических аппаратов позволили получить точные измерения относительных положений внутренних планет и других объектов с помощью радиолокации и телеметрии. Как и все радиолокационные измерения, они основаны на измерении времени, необходимого для отражения фотонов от объекта. Поскольку все фотоны движутся со скоростью света в вакууме, фундаментальной константой Вселенной, расстояние до объекта от аппарата рассчитывается как произведение скорости света и измеренного времени. Однако для достижения точности расчетам требуется корректировка с учетом движения аппарата и объекта во время прохождения фотонов. Кроме того, измерение самого времени должно быть переведено в стандартный масштаб, учитывающий релятивистское замедление времени. Сравнение положений эфемерид с измерениями времени, выраженными в барицентрическом динамическом времени (TDB), приводит к значению скорости света в астрономических единицах в день (равному 86400). К 2009 году МАС обновила свои стандартные измерения, чтобы отразить улучшения, и рассчитала скорость света как 173,1446326847 (TDB). В 1983 году CIPM изменила Международную систему единиц (СИ), определив метр как расстояние, пройденное в вакууме светом за 1/299792458 секунды. Это заменило предыдущее определение, действовавшее в период с 1960 по 1983 год, согласно которому метр равнялся определенному числу длин волн определенной линии излучения криптона-86. (Причиной изменения стал улучшенный метод измерения скорости света.) Скорость света можно было тогда выразить точно как c0 = 299792458, стандарт, также принятый IERS. Исходя из этого определения и стандарта МАС 2009 года, время, необходимое свету для прохождения астрономической единицы, составляет τA = 499,0047838061, что немного больше 8 минут 19 секунд. Умножением получается наилучшая оценка МАС 2009 года: A = c0τA = 149597870700, основанная на сравнении эфемерид Jet Propulsion Laboratory и IAA–RAS. В 2006 году BIPM сообщила о значении астрономической единицы как 1,49597870691. Новое определение признает, как следствие, что астрономическая единица имеет уменьшенное значение, ограниченное использованием в качестве удобства в некоторых приложениях. Таким образом, расстояние в пределах Солнечной системы без указания системы отсчета для измерения является проблематичным. Определение астрономической единицы 1976 года было неполным, поскольку оно не указывало систему отсчета, в которой следует применять измерение, но оказалось практичным для вычисления эфемерид: было предложено более полное определение, согласующееся с общей теорией относительности, и последовали «ожесточенные дебаты», пока в августе 2012 года МАС не приняла текущее определение: 1 астрономическая единица = 149597870700 метров. Астрономическая единица обычно используется для расстояний в масштабе звездных систем, таких как размер протопланетного диска или гелиоцентрическое расстояние астероида, в то время как для других расстояний в астрономии используются другие единицы. Астрономическая единица слишком мала, чтобы быть удобной для межзвездных расстояний, где широко используются парсек и световой год. Парсек (параллакс-секунда) определяется через астрономическую единицу, будучи расстоянием до объекта с параллаксом в 1 секунду. Световой год часто используется в популярных работах, но не является утвержденной внесистемной единицей и редко используется профессиональными астрономами. При моделировании численной модели Солнечной системы астрономическая единица обеспечивает подходящий масштаб, который минимизирует ошибки (переполнения, потерю значимости и усечения) в вычислениях с плавающей точкой.
История
В книге «О размерах и расстояниях Солнца и Луны», приписываемой Аристарху, говорится, что расстояние до Солнца в 18–20 раз больше расстояния до Луны, тогда как истинное соотношение составляет около 389 174. Последняя оценка основана на угле между полумесяцем и Солнцем, который он оценил в 87 (истинное значение близко к 89,853). В зависимости от расстояния, которое, по предположению ван Хельдена, использовал Аристарх для расстояния до Луны, его расчетная дистанция до Солнца составит от 380 до 1520 земных радиусов. Согласно Евсевию в Praeparatio evangelica (Книга XV, Глава 53), Эратосфен нашел расстояние до Солнца равным "σταδιων μυριαδας τετρακοσιας και οκτωκισμυριας" (буквально «мириады стадий 400 и 80000»), но с дополнительной пометкой, что в греческом тексте грамматическое согласование происходит между мириадами (не стадиями) с одной стороны и числами 400 и 80000 с другой: все три – именительный падеж множественного числа, в то время как σταδιων – родительный падеж множественного числа («стадий»). Все три слова (или все четыре, включая стадии) имеют падежные окончания. Это было переведено как 4080000 стадий (перевод Эдвина Гамильтона Гиффорда 1903 года) или как 804000000 стадий (издание 1974–1991 годов). Используя греческий стадий, равный 185–190 метрам, первый перевод дает 754800–775200, что слишком мало, а второй – 148,7–152,8 миллиарда метров (с точностью в пределах 2%). Гиппарх также привел оценку расстояния Земли от Солнца, которую Папп цитирует как равную 490 земным радиусам. Согласно гипотетическим реконструкциям Ноэля Свердлоу и Г. Дж. Тумера, это было получено из его предположения о «наименее заметном» солнечном параллаксе, равном 7. Китайский математический трактат «Чжоуби Суаньцзин» (ок. I века до н.э.) показывает, как расстояние до Солнца можно вычислить геометрически, используя различные длины полуденных теней, наблюдаемые в трех местах, расположенных на расстоянии 1000 ли, и предположение о том, что Земля плоская.
In the 2nd century CE, Ptolemy estimated the mean distance of the Sun as 1210 times Earth's radius. To determine this value, Ptolemy started by measuring the Moon's parallax, finding what amounted to a horizontal lunar parallax of 1° 26′, which was much too large. He then derived a maximum lunar distance of Earth radii. Because of cancelling errors in his parallax figure, his theory of the Moon's orbit, and other factors, this figure was approximately correct. He then measured the apparent sizes of the Sun and the Moon and concluded that the apparent diameter of the Sun was equal to the apparent diameter of the Moon at the Moon's greatest distance, and from records of lunar eclipses, he estimated this apparent diameter, as well as the apparent diameter of the shadow cone of Earth traversed by the Moon during a lunar eclipse. Given these data, the distance of the Sun from Earth can be trigonometrically computed to be 1210 Earth radii. This gives a ratio of solar to lunar distance of approximately 19, matching Aristarchus's figure. Although Ptolemy's procedure is theoretically workable, it is very sensitive to small changes in the data, so much so that changing a measurement by a few per cent can make the solar distance infinite. Later in Europe, Copernicus and Tycho Brahe also used comparable figures (1142 and 1150 Earth radii), and so Ptolemy's approximate Earth–Sun distance survived through the 16th century. Johannes Kepler was the first to realize that Ptolemy's estimate must be significantly too low (according to Kepler, at least by a factor of three) in his Rudolphine Tables (1627). Kepler's laws of planetary motion allowed astronomers to calculate the relative distances of the planets from the Sun, and rekindled interest in measuring the absolute value for Earth (which could then be applied to the other planets). The invention of the telescope allowed far more accurate measurements of angles than is possible with the naked eye. Flemish astronomer Godefroy Wendelin repeated Aristarchus’ measurements in 1635, and found that Ptolemy's value was too low by a factor of at least eleven. A somewhat more accurate estimate can be obtained by observing the transit of Venus. By measuring the transit in two different locations, one can accurately calculate the parallax of Venus and from the relative distance of Earth and Venus from the Sun, the solar parallax α (which cannot be measured directly due to the brightness of the Sun). Jeremiah Horrocks had attempted to produce an estimate based on his observation of the 1639 transit (published in 1662), giving a solar parallax of 15, similar to Wendelin's figure. The solar parallax is related to the Earth–Sun distance as measured in Earth radii by
The smaller the solar parallax, the greater the distance between the Sun and Earth: a solar parallax of 15 is equivalent to an Earth–Sun distance of 13750 Earth radii. Christiaan Huygens believed that the distance was even greater: by comparing the apparent sizes of Venus and Mars, he estimated a value of about 24000 Earth radii, Another colleague, Ole Rømer, discovered the finite speed of light in 1676: the speed was so great that it was usually quoted as the time required for light to travel from the Sun to the Earth, or "light time per unit distance", a convention that is still followed by astronomers today. A better method for observing Venus transits was devised by James Gregory and published in his Optica Promata (1663). It was strongly advocated by Edmond Halley and was applied to the transits of Venus observed in 1761 and 1769, and then again in 1874 and 1882. Transits of Venus occur in pairs, but less than one pair every century, and observing the transits in 1761 and 1769 was an unprecedented international scientific operation including observations by James Cook and Charles Green from Tahiti. Despite the Seven Years' War, dozens of astronomers were dispatched to observing points around the world at great expense and personal danger: several of them died in the endeavour. The various results were collated by Jérôme Lalande to give a figure for the solar parallax of 8.6. Karl Rudolph Powalky had made an estimate of 8.83 in 1864. Date Method A/Gm Uncertainty 1895 aberration 149.25 0.12 1941 parallax 149.674 0.016 1964 radar 149.5981 0.001 1976 telemetry 149.597870 0.000001 2009 telemetry 149.597870700 0.000000003
Another method involved determining the constant of aberration. Simon Newcomb gave great weight to this method when deriving his widely accepted value of 8.80 for the solar parallax (close to the modern value of 8.794143), although Newcomb also used data from the transits of Venus. Newcomb also collaborated with A. A. Michelson to measure the speed of light with Earth based equipment; combined with the constant of aberration (which is related to the light time per unit distance), this gave the first direct measurement of the Earth–Sun distance in metres. Newcomb's value for the solar parallax (and for the constant of aberration and the Gaussian gravitational constant) were incorporated into the first international system of astronomical constants in 1896, which remained in place for the calculation of ephemerides until 1964. The name "astronomical unit" appears first to have been used in 1903. The discovery of the near Earth asteroid 433 Eros and its passage near Earth in 1900–1901 allowed a considerable improvement in parallax measurement. Another international project to measure the parallax of 433 Eros was undertaken in 1930–1931. Direct radar measurements of the distances to Venus and Mars became available in the early 1960s. Along with improved measurements of the speed of light, these showed that Newcomb's values for the solar parallax and the constant of aberration were inconsistent with one another.
Расстояние до Солнца, оцениваемое по: | Оценка | В а.е. | Процент погрешности | Солнечный параллакс | Земля радиус |
|---|---|---|---|---|
| Аристарх | 13 | 24–7 | 12 | 256,5–477,8 | 0,011–0,020 | 98,9%–98% |
| Архимед | 21 | 10000 | 0,426 | 57,4% |
| Гиппарх | 7 | 490 | 0,021 | 97,9% |
| Посидоний | 21 | 10000 | 0,426 | 57,4% |
| Птолемей | 2′ 50″ | 1210 | 0,052 | 94,8% |
| Годфрой Венделин | 15 | 14000 | 0,597 | 40,3% |
| Иеремия Хоррокс | 15 | 14000 | 0,597 | 40,3% |
| Кристиан Гюйгенс | 8,2 | 25086 | 1,068 | 6,8% |
| Кассини и Ричер | 9,5 | 21700 | 0,925 | 7,5% |
| Флеймстед | 9,5 | 21700 | 0,925 | 7,5% |
| Жером Лаланд | 8,6 | 24000 | 1,023 | 2,3% |
| Саймон Ньюкомб | 8,80 | 23440 | 0,9994 | 0,06% |
| Артур Хинкс | 8,807 | 23420 | 0,9985 | 0,15% |
| Г. Спенсер Джонс | 8,790 | 23466 | 1,0005 | 0,05% |
| Современная астрономия | 8,794143 | 23455 | 1,0000 |
In the 2nd century CE, Ptolemy estimated the mean distance of the Sun as 1210 times Earth's radius. To determine this value, Ptolemy started by measuring the Moon's parallax, finding what amounted to a horizontal lunar parallax of 1° 26′, which was much too large. He then derived a maximum lunar distance of Earth radii. Because of cancelling errors in his parallax figure, his theory of the Moon's orbit, and other factors, this figure was approximately correct. He then measured the apparent sizes of the Sun and the Moon and concluded that the apparent diameter of the Sun was equal to the apparent diameter of the Moon at the Moon's greatest distance, and from records of lunar eclipses, he estimated this apparent diameter, as well as the apparent diameter of the shadow cone of Earth traversed by the Moon during a lunar eclipse. Given these data, the distance of the Sun from Earth can be trigonometrically computed to be 1210 Earth radii. This gives a ratio of solar to lunar distance of approximately 19, matching Aristarchus's figure. Although Ptolemy's procedure is theoretically workable, it is very sensitive to small changes in the data, so much so that changing a measurement by a few per cent can make the solar distance infinite. Later in Europe, Copernicus and Tycho Brahe also used comparable figures (1142 and 1150 Earth radii), and so Ptolemy's approximate Earth–Sun distance survived through the 16th century. Johannes Kepler was the first to realize that Ptolemy's estimate must be significantly too low (according to Kepler, at least by a factor of three) in his Rudolphine Tables (1627). Kepler's laws of planetary motion allowed astronomers to calculate the relative distances of the planets from the Sun, and rekindled interest in measuring the absolute value for Earth (which could then be applied to the other planets). The invention of the telescope allowed far more accurate measurements of angles than is possible with the naked eye. Flemish astronomer Godefroy Wendelin repeated Aristarchus’ measurements in 1635, and found that Ptolemy's value was too low by a factor of at least eleven. A somewhat more accurate estimate can be obtained by observing the transit of Venus. By measuring the transit in two different locations, one can accurately calculate the parallax of Venus and from the relative distance of Earth and Venus from the Sun, the solar parallax α (which cannot be measured directly due to the brightness of the Sun). Jeremiah Horrocks had attempted to produce an estimate based on his observation of the 1639 transit (published in 1662), giving a solar parallax of 15, similar to Wendelin's figure. The solar parallax is related to the Earth–Sun distance as measured in Earth radii by
The smaller the solar parallax, the greater the distance between the Sun and Earth: a solar parallax of 15 is equivalent to an Earth–Sun distance of 13750 Earth radii. Christiaan Huygens believed that the distance was even greater: by comparing the apparent sizes of Venus and Mars, he estimated a value of about 24000 Earth radii, Another colleague, Ole Rømer, discovered the finite speed of light in 1676: the speed was so great that it was usually quoted as the time required for light to travel from the Sun to the Earth, or "light time per unit distance", a convention that is still followed by astronomers today. A better method for observing Venus transits was devised by James Gregory and published in his Optica Promata (1663). It was strongly advocated by Edmond Halley and was applied to the transits of Venus observed in 1761 and 1769, and then again in 1874 and 1882. Transits of Venus occur in pairs, but less than one pair every century, and observing the transits in 1761 and 1769 was an unprecedented international scientific operation including observations by James Cook and Charles Green from Tahiti. Despite the Seven Years' War, dozens of astronomers were dispatched to observing points around the world at great expense and personal danger: several of them died in the endeavour. The various results were collated by Jérôme Lalande to give a figure for the solar parallax of 8.6. Karl Rudolph Powalky had made an estimate of 8.83 in 1864. Date Method A/Gm Uncertainty 1895 aberration 149.25 0.12 1941 parallax 149.674 0.016 1964 radar 149.5981 0.001 1976 telemetry 149.597870 0.000001 2009 telemetry 149.597870700 0.000000003
Another method involved determining the constant of aberration. Simon Newcomb gave great weight to this method when deriving his widely accepted value of 8.80 for the solar parallax (close to the modern value of 8.794143), although Newcomb also used data from the transits of Venus. Newcomb also collaborated with A. A. Michelson to measure the speed of light with Earth based equipment; combined with the constant of aberration (which is related to the light time per unit distance), this gave the first direct measurement of the Earth–Sun distance in metres. Newcomb's value for the solar parallax (and for the constant of aberration and the Gaussian gravitational constant) were incorporated into the first international system of astronomical constants in 1896, which remained in place for the calculation of ephemerides until 1964. The name "astronomical unit" appears first to have been used in 1903. The discovery of the near Earth asteroid 433 Eros and its passage near Earth in 1900–1901 allowed a considerable improvement in parallax measurement. Another international project to measure the parallax of 433 Eros was undertaken in 1930–1931. Direct radar measurements of the distances to Venus and Mars became available in the early 1960s. Along with improved measurements of the speed of light, these showed that Newcomb's values for the solar parallax and the constant of aberration were inconsistent with one another.
Во II веке н.э. Птолемей оценил среднее расстояние до Солнца в 1210 земных радиусов. Чтобы определить это значение, Птолемей начал с измерения параллакса Луны, получив горизонтальный параллакс Луны, равный 1° 26′, что было слишком большим значением. Затем он вывел максимальное расстояние до Луны, выраженное в земных радиусах. Из-за компенсирующих ошибок в его значении параллакса, его теории орбиты Луны и других факторов, это значение оказалось приблизительно верным. Затем он измерил видимые размеры Солнца и Луны и пришел к выводу, что видимый диаметр Солнца равен видимому диаметру Луны в самой дальней точке ее орбиты. На основании записей лунных затмений он оценил этот видимый диаметр, а также видимый диаметр конуса тени Земли, пересекаемого Луной во время лунного затмения. Имея эти данные, расстояние от Солнца до Земли можно тригонометрически вычислить как 1210 земных радиусов. Это дает соотношение расстояния от Солнца до Луны, приблизительно равное 19, что соответствует значению, полученному Аристархом. Хотя процедура Птолемея теоретически работоспособна, она очень чувствительна к небольшим изменениям данных, настолько, что изменение измерения всего на несколько процентов может привести к бесконечному расстоянию до Солнца. Позже в Европе Коперник и Тихо Браге также использовали сопоставимые значения (1142 и 1150 земных радиусов), поэтому приблизительное расстояние Земля-Солнце, оцененное Птолемеем, сохранилось в течение XVI века. Иоганн Кеплер первым понял, что оценка Птолемея должна быть значительно занижена (по словам Кеплера, как минимум в три раза) в своих «Рудольфинских таблицах» (1627). Законы Кеплера о движении планет позволили астрономам рассчитать относительные расстояния планет от Солнца и возродили интерес к измерению абсолютного значения для Земли (которое затем можно было применить к другим планетам). Изобретение телескопа позволило измерять углы с гораздо большей точностью, чем это возможно невооруженным глазом. Фламандский астроном Годфрой Венделин повторил измерения Аристарха в 1635 году и обнаружил, что значение Птолемея занижено как минимум в одиннадцать раз.
In the 2nd century CE, Ptolemy estimated the mean distance of the Sun as 1210 times Earth's radius. To determine this value, Ptolemy started by measuring the Moon's parallax, finding what amounted to a horizontal lunar parallax of 1° 26′, which was much too large. He then derived a maximum lunar distance of Earth radii. Because of cancelling errors in his parallax figure, his theory of the Moon's orbit, and other factors, this figure was approximately correct. He then measured the apparent sizes of the Sun and the Moon and concluded that the apparent diameter of the Sun was equal to the apparent diameter of the Moon at the Moon's greatest distance, and from records of lunar eclipses, he estimated this apparent diameter, as well as the apparent diameter of the shadow cone of Earth traversed by the Moon during a lunar eclipse. Given these data, the distance of the Sun from Earth can be trigonometrically computed to be 1210 Earth radii. This gives a ratio of solar to lunar distance of approximately 19, matching Aristarchus's figure. Although Ptolemy's procedure is theoretically workable, it is very sensitive to small changes in the data, so much so that changing a measurement by a few per cent can make the solar distance infinite. Later in Europe, Copernicus and Tycho Brahe also used comparable figures (1142 and 1150 Earth radii), and so Ptolemy's approximate Earth–Sun distance survived through the 16th century. Johannes Kepler was the first to realize that Ptolemy's estimate must be significantly too low (according to Kepler, at least by a factor of three) in his Rudolphine Tables (1627). Kepler's laws of planetary motion allowed astronomers to calculate the relative distances of the planets from the Sun, and rekindled interest in measuring the absolute value for Earth (which could then be applied to the other planets). The invention of the telescope allowed far more accurate measurements of angles than is possible with the naked eye. Flemish astronomer Godefroy Wendelin repeated Aristarchus’ measurements in 1635, and found that Ptolemy's value was too low by a factor of at least eleven. A somewhat more accurate estimate can be obtained by observing the transit of Venus. By measuring the transit in two different locations, one can accurately calculate the parallax of Venus and from the relative distance of Earth and Venus from the Sun, the solar parallax α (which cannot be measured directly due to the brightness of the Sun). Jeremiah Horrocks had attempted to produce an estimate based on his observation of the 1639 transit (published in 1662), giving a solar parallax of 15, similar to Wendelin's figure. The solar parallax is related to the Earth–Sun distance as measured in Earth radii by
The smaller the solar parallax, the greater the distance between the Sun and Earth: a solar parallax of 15 is equivalent to an Earth–Sun distance of 13750 Earth radii. Christiaan Huygens believed that the distance was even greater: by comparing the apparent sizes of Venus and Mars, he estimated a value of about 24000 Earth radii, Another colleague, Ole Rømer, discovered the finite speed of light in 1676: the speed was so great that it was usually quoted as the time required for light to travel from the Sun to the Earth, or "light time per unit distance", a convention that is still followed by astronomers today. A better method for observing Venus transits was devised by James Gregory and published in his Optica Promata (1663). It was strongly advocated by Edmond Halley and was applied to the transits of Venus observed in 1761 and 1769, and then again in 1874 and 1882. Transits of Venus occur in pairs, but less than one pair every century, and observing the transits in 1761 and 1769 was an unprecedented international scientific operation including observations by James Cook and Charles Green from Tahiti. Despite the Seven Years' War, dozens of astronomers were dispatched to observing points around the world at great expense and personal danger: several of them died in the endeavour. The various results were collated by Jérôme Lalande to give a figure for the solar parallax of 8.6. Karl Rudolph Powalky had made an estimate of 8.83 in 1864. Date Method A/Gm Uncertainty 1895 aberration 149.25 0.12 1941 parallax 149.674 0.016 1964 radar 149.5981 0.001 1976 telemetry 149.597870 0.000001 2009 telemetry 149.597870700 0.000000003
Another method involved determining the constant of aberration. Simon Newcomb gave great weight to this method when deriving his widely accepted value of 8.80 for the solar parallax (close to the modern value of 8.794143), although Newcomb also used data from the transits of Venus. Newcomb also collaborated with A. A. Michelson to measure the speed of light with Earth based equipment; combined with the constant of aberration (which is related to the light time per unit distance), this gave the first direct measurement of the Earth–Sun distance in metres. Newcomb's value for the solar parallax (and for the constant of aberration and the Gaussian gravitational constant) were incorporated into the first international system of astronomical constants in 1896, which remained in place for the calculation of ephemerides until 1964. The name "astronomical unit" appears first to have been used in 1903. The discovery of the near Earth asteroid 433 Eros and its passage near Earth in 1900–1901 allowed a considerable improvement in parallax measurement. Another international project to measure the parallax of 433 Eros was undertaken in 1930–1931. Direct radar measurements of the distances to Venus and Mars became available in the early 1960s. Along with improved measurements of the speed of light, these showed that Newcomb's values for the solar parallax and the constant of aberration were inconsistent with one another.
Более точную оценку можно получить, наблюдая прохождение Венеры по диску Солнца. Измеряя прохождение в двух разных местах, можно точно вычислить параллакс Венеры и, исходя из относительного расстояния Земли и Венеры от Солнца, солнечный параллакс α (который нельзя измерить напрямую из-за яркости Солнца). Иеремия Хоррокс попытался получить оценку на основе своего наблюдения прохождения Венеры в 1639 году (опубликованного в 1662 году), получив солнечный параллакс, равный 15, что похоже на значение Венделина. Солнечный параллакс связан с расстоянием между Землей и Солнцем, выраженным в земных радиусах, следующим образом:
In the 2nd century CE, Ptolemy estimated the mean distance of the Sun as 1210 times Earth's radius. To determine this value, Ptolemy started by measuring the Moon's parallax, finding what amounted to a horizontal lunar parallax of 1° 26′, which was much too large. He then derived a maximum lunar distance of Earth radii. Because of cancelling errors in his parallax figure, his theory of the Moon's orbit, and other factors, this figure was approximately correct. He then measured the apparent sizes of the Sun and the Moon and concluded that the apparent diameter of the Sun was equal to the apparent diameter of the Moon at the Moon's greatest distance, and from records of lunar eclipses, he estimated this apparent diameter, as well as the apparent diameter of the shadow cone of Earth traversed by the Moon during a lunar eclipse. Given these data, the distance of the Sun from Earth can be trigonometrically computed to be 1210 Earth radii. This gives a ratio of solar to lunar distance of approximately 19, matching Aristarchus's figure. Although Ptolemy's procedure is theoretically workable, it is very sensitive to small changes in the data, so much so that changing a measurement by a few per cent can make the solar distance infinite. Later in Europe, Copernicus and Tycho Brahe also used comparable figures (1142 and 1150 Earth radii), and so Ptolemy's approximate Earth–Sun distance survived through the 16th century. Johannes Kepler was the first to realize that Ptolemy's estimate must be significantly too low (according to Kepler, at least by a factor of three) in his Rudolphine Tables (1627). Kepler's laws of planetary motion allowed astronomers to calculate the relative distances of the planets from the Sun, and rekindled interest in measuring the absolute value for Earth (which could then be applied to the other planets). The invention of the telescope allowed far more accurate measurements of angles than is possible with the naked eye. Flemish astronomer Godefroy Wendelin repeated Aristarchus’ measurements in 1635, and found that Ptolemy's value was too low by a factor of at least eleven. A somewhat more accurate estimate can be obtained by observing the transit of Venus. By measuring the transit in two different locations, one can accurately calculate the parallax of Venus and from the relative distance of Earth and Venus from the Sun, the solar parallax α (which cannot be measured directly due to the brightness of the Sun). Jeremiah Horrocks had attempted to produce an estimate based on his observation of the 1639 transit (published in 1662), giving a solar parallax of 15, similar to Wendelin's figure. The solar parallax is related to the Earth–Sun distance as measured in Earth radii by
The smaller the solar parallax, the greater the distance between the Sun and Earth: a solar parallax of 15 is equivalent to an Earth–Sun distance of 13750 Earth radii. Christiaan Huygens believed that the distance was even greater: by comparing the apparent sizes of Venus and Mars, he estimated a value of about 24000 Earth radii, Another colleague, Ole Rømer, discovered the finite speed of light in 1676: the speed was so great that it was usually quoted as the time required for light to travel from the Sun to the Earth, or "light time per unit distance", a convention that is still followed by astronomers today. A better method for observing Venus transits was devised by James Gregory and published in his Optica Promata (1663). It was strongly advocated by Edmond Halley and was applied to the transits of Venus observed in 1761 and 1769, and then again in 1874 and 1882. Transits of Venus occur in pairs, but less than one pair every century, and observing the transits in 1761 and 1769 was an unprecedented international scientific operation including observations by James Cook and Charles Green from Tahiti. Despite the Seven Years' War, dozens of astronomers were dispatched to observing points around the world at great expense and personal danger: several of them died in the endeavour. The various results were collated by Jérôme Lalande to give a figure for the solar parallax of 8.6. Karl Rudolph Powalky had made an estimate of 8.83 in 1864. Date Method A/Gm Uncertainty 1895 aberration 149.25 0.12 1941 parallax 149.674 0.016 1964 radar 149.5981 0.001 1976 telemetry 149.597870 0.000001 2009 telemetry 149.597870700 0.000000003
Another method involved determining the constant of aberration. Simon Newcomb gave great weight to this method when deriving his widely accepted value of 8.80 for the solar parallax (close to the modern value of 8.794143), although Newcomb also used data from the transits of Venus. Newcomb also collaborated with A. A. Michelson to measure the speed of light with Earth based equipment; combined with the constant of aberration (which is related to the light time per unit distance), this gave the first direct measurement of the Earth–Sun distance in metres. Newcomb's value for the solar parallax (and for the constant of aberration and the Gaussian gravitational constant) were incorporated into the first international system of astronomical constants in 1896, which remained in place for the calculation of ephemerides until 1964. The name "astronomical unit" appears first to have been used in 1903. The discovery of the near Earth asteroid 433 Eros and its passage near Earth in 1900–1901 allowed a considerable improvement in parallax measurement. Another international project to measure the parallax of 433 Eros was undertaken in 1930–1931. Direct radar measurements of the distances to Venus and Mars became available in the early 1960s. Along with improved measurements of the speed of light, these showed that Newcomb's values for the solar parallax and the constant of aberration were inconsistent with one another.
Чем меньше солнечный параллакс, тем больше расстояние между Солнцем и Землей: солнечный параллакс, равный 15, эквивалентен расстоянию Земля-Солнце в 13750 земных радиусов. Кристиан Гюйгенс считал, что расстояние еще больше: сравнивая видимые размеры Венеры и Марса, он оценил его примерно в 24000 земных радиусов. Другой коллега, Оле Рёмер, открыл конечность скорости света в 1676 году: скорость была настолько велика, что обычно указывалось время, необходимое свету для прохождения от Солнца до Земли, или «время света на единицу расстояния», что до сих пор практикуется астрономами. Более совершенный метод наблюдения прохождений Венеры был разработан Джеймсом Грегори и опубликован в его «Optica Promata» (1663). Эдмонд Галлей настоятельно рекомендовал его, и он был применен к прохождениям Венеры, наблюдаемым в 1761 и 1769 годах, а затем снова в 1874 и 1882 годах. Прохождения Венеры происходят парами, но менее одного раза в столетие, и наблюдение за прохождениями в 1761 и 1769 годах было беспрецедентной международной научной операцией, включавшей наблюдения Джеймса Кука и Чарльза Грина с Таити. Несмотря на Семилетнюю войну, десятки астрономов были отправлены в наблюдательные пункты по всему миру с большими затратами и личной опасностью: несколько из них погибли в ходе этой работы. Различные результаты были сведены вместе Жеромом Лаландом, чтобы получить значение солнечного параллакса, равное 8,6. Карл Рудольф Повальки сделал оценку в 8,83 в 1864 году.
In the 2nd century CE, Ptolemy estimated the mean distance of the Sun as 1210 times Earth's radius. To determine this value, Ptolemy started by measuring the Moon's parallax, finding what amounted to a horizontal lunar parallax of 1° 26′, which was much too large. He then derived a maximum lunar distance of Earth radii. Because of cancelling errors in his parallax figure, his theory of the Moon's orbit, and other factors, this figure was approximately correct. He then measured the apparent sizes of the Sun and the Moon and concluded that the apparent diameter of the Sun was equal to the apparent diameter of the Moon at the Moon's greatest distance, and from records of lunar eclipses, he estimated this apparent diameter, as well as the apparent diameter of the shadow cone of Earth traversed by the Moon during a lunar eclipse. Given these data, the distance of the Sun from Earth can be trigonometrically computed to be 1210 Earth radii. This gives a ratio of solar to lunar distance of approximately 19, matching Aristarchus's figure. Although Ptolemy's procedure is theoretically workable, it is very sensitive to small changes in the data, so much so that changing a measurement by a few per cent can make the solar distance infinite. Later in Europe, Copernicus and Tycho Brahe also used comparable figures (1142 and 1150 Earth radii), and so Ptolemy's approximate Earth–Sun distance survived through the 16th century. Johannes Kepler was the first to realize that Ptolemy's estimate must be significantly too low (according to Kepler, at least by a factor of three) in his Rudolphine Tables (1627). Kepler's laws of planetary motion allowed astronomers to calculate the relative distances of the planets from the Sun, and rekindled interest in measuring the absolute value for Earth (which could then be applied to the other planets). The invention of the telescope allowed far more accurate measurements of angles than is possible with the naked eye. Flemish astronomer Godefroy Wendelin repeated Aristarchus’ measurements in 1635, and found that Ptolemy's value was too low by a factor of at least eleven. A somewhat more accurate estimate can be obtained by observing the transit of Venus. By measuring the transit in two different locations, one can accurately calculate the parallax of Venus and from the relative distance of Earth and Venus from the Sun, the solar parallax α (which cannot be measured directly due to the brightness of the Sun). Jeremiah Horrocks had attempted to produce an estimate based on his observation of the 1639 transit (published in 1662), giving a solar parallax of 15, similar to Wendelin's figure. The solar parallax is related to the Earth–Sun distance as measured in Earth radii by
The smaller the solar parallax, the greater the distance between the Sun and Earth: a solar parallax of 15 is equivalent to an Earth–Sun distance of 13750 Earth radii. Christiaan Huygens believed that the distance was even greater: by comparing the apparent sizes of Venus and Mars, he estimated a value of about 24000 Earth radii, Another colleague, Ole Rømer, discovered the finite speed of light in 1676: the speed was so great that it was usually quoted as the time required for light to travel from the Sun to the Earth, or "light time per unit distance", a convention that is still followed by astronomers today. A better method for observing Venus transits was devised by James Gregory and published in his Optica Promata (1663). It was strongly advocated by Edmond Halley and was applied to the transits of Venus observed in 1761 and 1769, and then again in 1874 and 1882. Transits of Venus occur in pairs, but less than one pair every century, and observing the transits in 1761 and 1769 was an unprecedented international scientific operation including observations by James Cook and Charles Green from Tahiti. Despite the Seven Years' War, dozens of astronomers were dispatched to observing points around the world at great expense and personal danger: several of them died in the endeavour. The various results were collated by Jérôme Lalande to give a figure for the solar parallax of 8.6. Karl Rudolph Powalky had made an estimate of 8.83 in 1864. Date Method A/Gm Uncertainty 1895 aberration 149.25 0.12 1941 parallax 149.674 0.016 1964 radar 149.5981 0.001 1976 telemetry 149.597870 0.000001 2009 telemetry 149.597870700 0.000000003
Another method involved determining the constant of aberration. Simon Newcomb gave great weight to this method when deriving his widely accepted value of 8.80 for the solar parallax (close to the modern value of 8.794143), although Newcomb also used data from the transits of Venus. Newcomb also collaborated with A. A. Michelson to measure the speed of light with Earth based equipment; combined with the constant of aberration (which is related to the light time per unit distance), this gave the first direct measurement of the Earth–Sun distance in metres. Newcomb's value for the solar parallax (and for the constant of aberration and the Gaussian gravitational constant) were incorporated into the first international system of astronomical constants in 1896, which remained in place for the calculation of ephemerides until 1964. The name "astronomical unit" appears first to have been used in 1903. The discovery of the near Earth asteroid 433 Eros and its passage near Earth in 1900–1901 allowed a considerable improvement in parallax measurement. Another international project to measure the parallax of 433 Eros was undertaken in 1930–1931. Direct radar measurements of the distances to Venus and Mars became available in the early 1960s. Along with improved measurements of the speed of light, these showed that Newcomb's values for the solar parallax and the constant of aberration were inconsistent with one another.
| Дата | Метод | A/Gm | Неопределенность |
|---|---|---|---|
| 1895 | Аберрация | 149,25 | 0,12 |
| 1941 | Параллакс | 149,674 | 0,016 |
| 1964 | Радар | 149,5981 | 0,001 |
| 1976 | Телеметрия | 149,597870 | 0,000001 |
| 2009 | Телеметрия | 149,597870700 | 0,000000003 |
In the 2nd century CE, Ptolemy estimated the mean distance of the Sun as 1210 times Earth's radius. To determine this value, Ptolemy started by measuring the Moon's parallax, finding what amounted to a horizontal lunar parallax of 1° 26′, which was much too large. He then derived a maximum lunar distance of Earth radii. Because of cancelling errors in his parallax figure, his theory of the Moon's orbit, and other factors, this figure was approximately correct. He then measured the apparent sizes of the Sun and the Moon and concluded that the apparent diameter of the Sun was equal to the apparent diameter of the Moon at the Moon's greatest distance, and from records of lunar eclipses, he estimated this apparent diameter, as well as the apparent diameter of the shadow cone of Earth traversed by the Moon during a lunar eclipse. Given these data, the distance of the Sun from Earth can be trigonometrically computed to be 1210 Earth radii. This gives a ratio of solar to lunar distance of approximately 19, matching Aristarchus's figure. Although Ptolemy's procedure is theoretically workable, it is very sensitive to small changes in the data, so much so that changing a measurement by a few per cent can make the solar distance infinite. Later in Europe, Copernicus and Tycho Brahe also used comparable figures (1142 and 1150 Earth radii), and so Ptolemy's approximate Earth–Sun distance survived through the 16th century. Johannes Kepler was the first to realize that Ptolemy's estimate must be significantly too low (according to Kepler, at least by a factor of three) in his Rudolphine Tables (1627). Kepler's laws of planetary motion allowed astronomers to calculate the relative distances of the planets from the Sun, and rekindled interest in measuring the absolute value for Earth (which could then be applied to the other planets). The invention of the telescope allowed far more accurate measurements of angles than is possible with the naked eye. Flemish astronomer Godefroy Wendelin repeated Aristarchus’ measurements in 1635, and found that Ptolemy's value was too low by a factor of at least eleven. A somewhat more accurate estimate can be obtained by observing the transit of Venus. By measuring the transit in two different locations, one can accurately calculate the parallax of Venus and from the relative distance of Earth and Venus from the Sun, the solar parallax α (which cannot be measured directly due to the brightness of the Sun). Jeremiah Horrocks had attempted to produce an estimate based on his observation of the 1639 transit (published in 1662), giving a solar parallax of 15, similar to Wendelin's figure. The solar parallax is related to the Earth–Sun distance as measured in Earth radii by
The smaller the solar parallax, the greater the distance between the Sun and Earth: a solar parallax of 15 is equivalent to an Earth–Sun distance of 13750 Earth radii. Christiaan Huygens believed that the distance was even greater: by comparing the apparent sizes of Venus and Mars, he estimated a value of about 24000 Earth radii, Another colleague, Ole Rømer, discovered the finite speed of light in 1676: the speed was so great that it was usually quoted as the time required for light to travel from the Sun to the Earth, or "light time per unit distance", a convention that is still followed by astronomers today. A better method for observing Venus transits was devised by James Gregory and published in his Optica Promata (1663). It was strongly advocated by Edmond Halley and was applied to the transits of Venus observed in 1761 and 1769, and then again in 1874 and 1882. Transits of Venus occur in pairs, but less than one pair every century, and observing the transits in 1761 and 1769 was an unprecedented international scientific operation including observations by James Cook and Charles Green from Tahiti. Despite the Seven Years' War, dozens of astronomers were dispatched to observing points around the world at great expense and personal danger: several of them died in the endeavour. The various results were collated by Jérôme Lalande to give a figure for the solar parallax of 8.6. Karl Rudolph Powalky had made an estimate of 8.83 in 1864. Date Method A/Gm Uncertainty 1895 aberration 149.25 0.12 1941 parallax 149.674 0.016 1964 radar 149.5981 0.001 1976 telemetry 149.597870 0.000001 2009 telemetry 149.597870700 0.000000003
Another method involved determining the constant of aberration. Simon Newcomb gave great weight to this method when deriving his widely accepted value of 8.80 for the solar parallax (close to the modern value of 8.794143), although Newcomb also used data from the transits of Venus. Newcomb also collaborated with A. A. Michelson to measure the speed of light with Earth based equipment; combined with the constant of aberration (which is related to the light time per unit distance), this gave the first direct measurement of the Earth–Sun distance in metres. Newcomb's value for the solar parallax (and for the constant of aberration and the Gaussian gravitational constant) were incorporated into the first international system of astronomical constants in 1896, which remained in place for the calculation of ephemerides until 1964. The name "astronomical unit" appears first to have been used in 1903. The discovery of the near Earth asteroid 433 Eros and its passage near Earth in 1900–1901 allowed a considerable improvement in parallax measurement. Another international project to measure the parallax of 433 Eros was undertaken in 1930–1931. Direct radar measurements of the distances to Venus and Mars became available in the early 1960s. Along with improved measurements of the speed of light, these showed that Newcomb's values for the solar parallax and the constant of aberration were inconsistent with one another.
Другой метод включал определение постоянной аберрации. Саймон Ньюкомб придал большое значение этому методу при получении широко принятого значения солнечного параллакса, равного 8,80 (близкого к современному значению 8,794143), хотя Ньюкомб также использовал данные о прохождениях Венеры. Ньюкомб также сотрудничал с А. А. Микельсоном для измерения скорости света с использованием земного оборудования; в сочетании с постоянной аберрации (которая связана со временем света на единицу расстояния), это дало первое прямое измерение расстояния Земля-Солнце в метрах. Значение солнечного параллакса (и постоянной аберрации и гравитационной постоянной Гаусса), полученное Ньюкомбом, было включено в первую международную систему астрономических постоянных в 1896 году, которая оставалась в силе для вычисления эфемерид до 1964 года.
In the 2nd century CE, Ptolemy estimated the mean distance of the Sun as 1210 times Earth's radius. To determine this value, Ptolemy started by measuring the Moon's parallax, finding what amounted to a horizontal lunar parallax of 1° 26′, which was much too large. He then derived a maximum lunar distance of Earth radii. Because of cancelling errors in his parallax figure, his theory of the Moon's orbit, and other factors, this figure was approximately correct. He then measured the apparent sizes of the Sun and the Moon and concluded that the apparent diameter of the Sun was equal to the apparent diameter of the Moon at the Moon's greatest distance, and from records of lunar eclipses, he estimated this apparent diameter, as well as the apparent diameter of the shadow cone of Earth traversed by the Moon during a lunar eclipse. Given these data, the distance of the Sun from Earth can be trigonometrically computed to be 1210 Earth radii. This gives a ratio of solar to lunar distance of approximately 19, matching Aristarchus's figure. Although Ptolemy's procedure is theoretically workable, it is very sensitive to small changes in the data, so much so that changing a measurement by a few per cent can make the solar distance infinite. Later in Europe, Copernicus and Tycho Brahe also used comparable figures (1142 and 1150 Earth radii), and so Ptolemy's approximate Earth–Sun distance survived through the 16th century. Johannes Kepler was the first to realize that Ptolemy's estimate must be significantly too low (according to Kepler, at least by a factor of three) in his Rudolphine Tables (1627). Kepler's laws of planetary motion allowed astronomers to calculate the relative distances of the planets from the Sun, and rekindled interest in measuring the absolute value for Earth (which could then be applied to the other planets). The invention of the telescope allowed far more accurate measurements of angles than is possible with the naked eye. Flemish astronomer Godefroy Wendelin repeated Aristarchus’ measurements in 1635, and found that Ptolemy's value was too low by a factor of at least eleven. A somewhat more accurate estimate can be obtained by observing the transit of Venus. By measuring the transit in two different locations, one can accurately calculate the parallax of Venus and from the relative distance of Earth and Venus from the Sun, the solar parallax α (which cannot be measured directly due to the brightness of the Sun). Jeremiah Horrocks had attempted to produce an estimate based on his observation of the 1639 transit (published in 1662), giving a solar parallax of 15, similar to Wendelin's figure. The solar parallax is related to the Earth–Sun distance as measured in Earth radii by
The smaller the solar parallax, the greater the distance between the Sun and Earth: a solar parallax of 15 is equivalent to an Earth–Sun distance of 13750 Earth radii. Christiaan Huygens believed that the distance was even greater: by comparing the apparent sizes of Venus and Mars, he estimated a value of about 24000 Earth radii, Another colleague, Ole Rømer, discovered the finite speed of light in 1676: the speed was so great that it was usually quoted as the time required for light to travel from the Sun to the Earth, or "light time per unit distance", a convention that is still followed by astronomers today. A better method for observing Venus transits was devised by James Gregory and published in his Optica Promata (1663). It was strongly advocated by Edmond Halley and was applied to the transits of Venus observed in 1761 and 1769, and then again in 1874 and 1882. Transits of Venus occur in pairs, but less than one pair every century, and observing the transits in 1761 and 1769 was an unprecedented international scientific operation including observations by James Cook and Charles Green from Tahiti. Despite the Seven Years' War, dozens of astronomers were dispatched to observing points around the world at great expense and personal danger: several of them died in the endeavour. The various results were collated by Jérôme Lalande to give a figure for the solar parallax of 8.6. Karl Rudolph Powalky had made an estimate of 8.83 in 1864. Date Method A/Gm Uncertainty 1895 aberration 149.25 0.12 1941 parallax 149.674 0.016 1964 radar 149.5981 0.001 1976 telemetry 149.597870 0.000001 2009 telemetry 149.597870700 0.000000003
Another method involved determining the constant of aberration. Simon Newcomb gave great weight to this method when deriving his widely accepted value of 8.80 for the solar parallax (close to the modern value of 8.794143), although Newcomb also used data from the transits of Venus. Newcomb also collaborated with A. A. Michelson to measure the speed of light with Earth based equipment; combined with the constant of aberration (which is related to the light time per unit distance), this gave the first direct measurement of the Earth–Sun distance in metres. Newcomb's value for the solar parallax (and for the constant of aberration and the Gaussian gravitational constant) were incorporated into the first international system of astronomical constants in 1896, which remained in place for the calculation of ephemerides until 1964. The name "astronomical unit" appears first to have been used in 1903. The discovery of the near Earth asteroid 433 Eros and its passage near Earth in 1900–1901 allowed a considerable improvement in parallax measurement. Another international project to measure the parallax of 433 Eros was undertaken in 1930–1931. Direct radar measurements of the distances to Venus and Mars became available in the early 1960s. Along with improved measurements of the speed of light, these showed that Newcomb's values for the solar parallax and the constant of aberration were inconsistent with one another.
Примеры
В следующей таблице приведены некоторые расстояния, выраженные в астрономических единицах. В неё включены примеры расстояний, которые обычно не приводятся в астрономических единицах, поскольку они либо слишком малы, либо слишком велики. Расстояния обычно меняются со временем. Примеры перечислены в порядке возрастания расстояния. Объект или длина Длина или расстояние в а.е. Диапазон Комментарий и точка отсчета Источники Световая секунда 0.002 – Расстояние, которое свет проходит за одну секунду – Лунное расстояние 0.0026 – Среднее расстояние от Земли (миссиям "Аполлон" потребовалось около 3 дней, чтобы преодолеть его) – Солнечный радиус 0.005 – Радиус Солнца (695500, 432450, в сто раз больше радиуса Земли или в десять раз больше среднего радиуса Юпитера) – Световая минута 0.12 – Расстояние, которое свет проходит за одну минуту – Меркурий 0.39 – Среднее расстояние от Солнца – Венера 0.72 – Среднее расстояние от Солнца – Земля 1.00 – Среднее расстояние орбиты Земли от Солнца (солнечный свет достигает Земли за 8 минут и 19 секунд) – Марс 1.52 – Среднее расстояние от Солнца – Юпитер 5.2 – Среднее расстояние от Солнца – Световой час 7.2 – Расстояние, которое свет проходит за один час – Сатурн 9.5 – Среднее расстояние от Солнца – Уран 19.2 – Среднее расстояние от Солнца – Пояс Койпера 30 – Внутренняя граница начинается примерно на расстоянии 30 а.е. – Нептун 30.1 – Среднее расстояние от Солнца – Эрида 67.8 – Среднее расстояние от Солнца – Voyager 2 134 – Расстояние от Солнца в августе 2023 года – Voyager 1 161 – Расстояние от Солнца в августе 2023 года – Проксима Центавра 268000 ± 126 – Расстояние до ближайшей звезды к Солнечной системе – Центр Галактики Млечный Путь 1700000000 – Расстояние от Солнца до центра Млечного Пути – Примечание: Значения в этой таблице обычно являются округлёнными оценками, часто приблизительными, и могут значительно отличаться от других источников. В таблице также приведены другие единицы длины для сравнения.