More than 1,000 years ago, two medieval scholars separated by approximately 1,500 kilometres used a lunar eclipse to calculate the difference in longitude between Baghdad and Khwarezm. By turning an astronomical event into a shared time signal, they produced a result surprisingly close to the figure obtained from modern coordinates.
A recent preprint paper by Rizoi Bakhromzod on arXiv examines the experiment conducted by Abu Rayhan al-Biruni and Abu al-Wafa al-Buzjani in 997. The two scholars observed the same lunar eclipse from different cities, recorded when it occurred according to their respective local times and later compared their results.
Their observations suggested that the cities were separated by approximately 15 degrees of longitude. The actual difference, based on modern coordinates, is about 16.35 degrees, meaning their calculation was off by only about 8 per cent.
The medieval challenge of measuring longitude
To establish the location of a city, medieval geographers needed to determine two coordinates: latitude and longitude. Latitude was the easier of the two to calculate. Astronomers could estimate it by measuring the height of the Sun at noon or the position of the Pole Star above the horizon.
Longitude presented a more difficult problem because it required comparing the local time in two different places.
Earth completes a rotation of 360 degrees in 24 hours, meaning that it turns 15 degrees every hour. If astronomers discovered that the local times in two cities differed by one hour, they could conclude that the cities were separated by 15 degrees of longitude.
The calculation itself was straightforward. The challenge was finding an accurate way to compare time across a considerable distance.
Medieval astronomers had neither reliable portable clocks nor a way of communicating instantly. A clock could not simply be set in one city and carried to another without losing accuracy, while messages travelling between Baghdad and Khwarezm could take weeks to arrive.
Al-Biruni and Abu al-Wafa found their shared clock in the night sky.
Two scholars in two cities
Al-Biruni by Iraqi polymath Muntadher Saleh – Wikimedia Commons
Born in 973 in Khwarezm, al-Biruni became one of the most accomplished scholars of the medieval Islamic world. His interests included astronomy, mathematics, geography, geodesy, history and philology. Much of his work was devoted to measuring the Earth and determining the coordinates of different places.
Abu al-Wafa was born in 940 in Buzjan, in what is now Iran. He later moved to Baghdad, where he became a leading mathematician and astronomer. His work made important contributions to trigonometry and astronomical calculation, while his observations helped improve contemporary astronomical tables.
Despite living far apart, the two scholars corresponded with one another. They agreed in advance to observe the same lunar eclipse: al-Biruni from Kath, the capital of Khwarezm, and Abu al-Wafa from Baghdad.
The eclipse occurred during the night of 24–25 May 997. Modern astronomical calculations identify it as a partial lunar eclipse during which approximately 55 per cent of the Moon’s diameter entered the darkest part of Earth’s shadow.
A lunar eclipse was particularly useful because it could be seen at essentially the same moment from widely separated locations across the nighttime hemisphere. Provided that the Moon was visible from both cities, the eclipse supplied the observers with a common astronomical signal.
“Al-Biruni and Abu al-Wafa al-Buzjani approached these challenges with particular care,” Bakhromzod writes. “They used correspondence to coordinate their actions. By computing in advance, from astronomical tables, the date and approximate time of an upcoming lunar eclipse, they agreed to conduct simultaneous observations and subsequently exchange their results. In this way, the astronomical phenomenon itself served as the synchronizing “signal,” while written correspondence functioned as the carrier of information about the time difference after the experiment.”
Turning time into distance
Lunar eclipses – Walters Ms. W.659 fol. 10a
Each scholar recorded the local time at which an agreed stage of the eclipse occurred. The surviving evidence does not make it clear whether they timed the beginning of the partial eclipse, its maximum point or another easily identifiable phase.
After the eclipse, they exchanged and compared their observations. Although their reports might have taken weeks to travel between the two cities, the eclipse had allowed them to record the same event at the same moment.
Their observations revealed a difference of approximately one hour between the local times in Baghdad and Kath. Since one hour corresponds to 15 degrees of Earth’s rotation, the scholars calculated that Kath was about 15 degrees east of Baghdad.
Modern coordinates place Baghdad at approximately 44.4 degrees east and historical Kath, near the modern city of Biruni in Uzbekistan, at about 60.75 degrees east. The actual difference between them is therefore approximately 16.35 degrees. Expressed as local time, that difference is about one hour, five minutes and 24 seconds. The medieval estimate was short by approximately five minutes and 24 seconds, equivalent to about 1.35 degrees of longitude.
At the latitude of the two cities, this discrepancy represents an east–west distance of approximately 120 kilometres. While that would be considerable by modern surveying standards, the result is impressive for an experiment carried out without mechanical clocks, electronic communication or modern observational instruments.
What remains uncertain
Not every detail of the experiment is known. The scholars’ complete observational records have not survived, and the precise numerical values they originally calculated are unavailable.
Bakhromzod therefore reconstructs some aspects of the procedure. For example, he suggests that the observers may have employed water clocks or observations of known stars to determine local time. He also proposes that the two sets of results were subsequently exchanged through correspondence carried by a courier or caravan.
These are plausible explanations of how the experiment operated, but they are not all firmly established by the surviving historical evidence.
It is similarly uncertain which stage of the eclipse the two scholars recorded. The moment when the Moon entered Earth’s darker shadow would have provided a recognisable reference point. If they recorded both the entry and exit, they could also have calculated the eclipse’s midpoint by averaging the two times.
Modern calculations nevertheless confirm that the eclipse was suitable for the experiment. Its partial phase lasted approximately 157 minutes and was visible from both Mesopotamia and Central Asia, providing the scholars with ample opportunity to observe and record it.
Using the sky as a clock
Arabic Illustration of different phases of the moon, from manuscript of the Kitab al-Tafhim by Al-Biruni (973–1048)
Accurate coordinates served several purposes in medieval Islamic science. They helped scholars construct maps, compare astronomical observations made in different locations and calculate the direction of Mecca from cities throughout the Islamic world.
The experiment also illustrates how scientific correspondence could connect scholars working across great distances. Al-Biruni and Abu al-Wafa could not communicate during the eclipse, but careful planning allowed them to conduct what amounted to a coordinated observation from two cities separated by around 1,500 kilometres.
As Bakhromzod concludes:
The experiment conducted by Abu Rayhan al-Biruni and Abu al-Wafa al-Buzjani to determine the longitude difference between Khwarezm and Baghdad through observation of a lunar eclipse is rightly regarded as an outstanding achievement of medieval science. It represents a remarkable synthesis of theoretical insight and practical implementation, astronomical knowledge and geographical purpose. The scholars succeeded in overcoming the principal limitation of their era–the absence of means for time synchronization–by using the sky itself as a set of “precise clocks.”
Unable to synchronize clocks across an enormous distance, the two scholars instead used the Moon’s passage through Earth’s shadow. Their experiment shows how medieval astronomers transformed a celestial event into a practical tool for measuring the world.
The preprint paper, “Determination of the longitude difference between Baghdad and Khwarezm using a lunar eclipse (the method of Abu Rayhan al-Biruni and Abu al-Wafa al-Buzjani),” by Rizoi Bakhromzod has been published on arXiv, a free online repository where researchers share academic papers, often before they have undergone formal peer review or appeared in a scholarly journal. Click here to read it.
Rizoi Bakhromzod is a member of the Tajik Academy of Sciences, where he researches astrophysics during the Middle Ages.
More than 1,000 years ago, two medieval scholars separated by approximately 1,500 kilometres used a lunar eclipse to calculate the difference in longitude between Baghdad and Khwarezm. By turning an astronomical event into a shared time signal, they produced a result surprisingly close to the figure obtained from modern coordinates.
A recent preprint paper by Rizoi Bakhromzod on arXiv examines the experiment conducted by Abu Rayhan al-Biruni and Abu al-Wafa al-Buzjani in 997. The two scholars observed the same lunar eclipse from different cities, recorded when it occurred according to their respective local times and later compared their results.
Their observations suggested that the cities were separated by approximately 15 degrees of longitude. The actual difference, based on modern coordinates, is about 16.35 degrees, meaning their calculation was off by only about 8 per cent.
The medieval challenge of measuring longitude
To establish the location of a city, medieval geographers needed to determine two coordinates: latitude and longitude. Latitude was the easier of the two to calculate. Astronomers could estimate it by measuring the height of the Sun at noon or the position of the Pole Star above the horizon.
Longitude presented a more difficult problem because it required comparing the local time in two different places.
Earth completes a rotation of 360 degrees in 24 hours, meaning that it turns 15 degrees every hour. If astronomers discovered that the local times in two cities differed by one hour, they could conclude that the cities were separated by 15 degrees of longitude.
The calculation itself was straightforward. The challenge was finding an accurate way to compare time across a considerable distance.
Medieval astronomers had neither reliable portable clocks nor a way of communicating instantly. A clock could not simply be set in one city and carried to another without losing accuracy, while messages travelling between Baghdad and Khwarezm could take weeks to arrive.
Al-Biruni and Abu al-Wafa found their shared clock in the night sky.
Two scholars in two cities
Born in 973 in Khwarezm, al-Biruni became one of the most accomplished scholars of the medieval Islamic world. His interests included astronomy, mathematics, geography, geodesy, history and philology. Much of his work was devoted to measuring the Earth and determining the coordinates of different places.
Abu al-Wafa was born in 940 in Buzjan, in what is now Iran. He later moved to Baghdad, where he became a leading mathematician and astronomer. His work made important contributions to trigonometry and astronomical calculation, while his observations helped improve contemporary astronomical tables.
Despite living far apart, the two scholars corresponded with one another. They agreed in advance to observe the same lunar eclipse: al-Biruni from Kath, the capital of Khwarezm, and Abu al-Wafa from Baghdad.
The eclipse occurred during the night of 24–25 May 997. Modern astronomical calculations identify it as a partial lunar eclipse during which approximately 55 per cent of the Moon’s diameter entered the darkest part of Earth’s shadow.
A lunar eclipse was particularly useful because it could be seen at essentially the same moment from widely separated locations across the nighttime hemisphere. Provided that the Moon was visible from both cities, the eclipse supplied the observers with a common astronomical signal.
“Al-Biruni and Abu al-Wafa al-Buzjani approached these challenges with particular care,” Bakhromzod writes. “They used correspondence to coordinate their actions. By computing in advance, from astronomical tables, the date and approximate time of an upcoming lunar eclipse, they agreed to conduct simultaneous observations and subsequently exchange their results. In this way, the astronomical phenomenon itself served as the synchronizing “signal,” while written correspondence functioned as the carrier of information about the time difference after the experiment.”
Turning time into distance
Each scholar recorded the local time at which an agreed stage of the eclipse occurred. The surviving evidence does not make it clear whether they timed the beginning of the partial eclipse, its maximum point or another easily identifiable phase.
After the eclipse, they exchanged and compared their observations. Although their reports might have taken weeks to travel between the two cities, the eclipse had allowed them to record the same event at the same moment.
Their observations revealed a difference of approximately one hour between the local times in Baghdad and Kath. Since one hour corresponds to 15 degrees of Earth’s rotation, the scholars calculated that Kath was about 15 degrees east of Baghdad.
Modern coordinates place Baghdad at approximately 44.4 degrees east and historical Kath, near the modern city of Biruni in Uzbekistan, at about 60.75 degrees east. The actual difference between them is therefore approximately 16.35 degrees. Expressed as local time, that difference is about one hour, five minutes and 24 seconds. The medieval estimate was short by approximately five minutes and 24 seconds, equivalent to about 1.35 degrees of longitude.
At the latitude of the two cities, this discrepancy represents an east–west distance of approximately 120 kilometres. While that would be considerable by modern surveying standards, the result is impressive for an experiment carried out without mechanical clocks, electronic communication or modern observational instruments.
What remains uncertain
Not every detail of the experiment is known. The scholars’ complete observational records have not survived, and the precise numerical values they originally calculated are unavailable.
Bakhromzod therefore reconstructs some aspects of the procedure. For example, he suggests that the observers may have employed water clocks or observations of known stars to determine local time. He also proposes that the two sets of results were subsequently exchanged through correspondence carried by a courier or caravan.
These are plausible explanations of how the experiment operated, but they are not all firmly established by the surviving historical evidence.
It is similarly uncertain which stage of the eclipse the two scholars recorded. The moment when the Moon entered Earth’s darker shadow would have provided a recognisable reference point. If they recorded both the entry and exit, they could also have calculated the eclipse’s midpoint by averaging the two times.
Modern calculations nevertheless confirm that the eclipse was suitable for the experiment. Its partial phase lasted approximately 157 minutes and was visible from both Mesopotamia and Central Asia, providing the scholars with ample opportunity to observe and record it.
Using the sky as a clock
Accurate coordinates served several purposes in medieval Islamic science. They helped scholars construct maps, compare astronomical observations made in different locations and calculate the direction of Mecca from cities throughout the Islamic world.
The experiment also illustrates how scientific correspondence could connect scholars working across great distances. Al-Biruni and Abu al-Wafa could not communicate during the eclipse, but careful planning allowed them to conduct what amounted to a coordinated observation from two cities separated by around 1,500 kilometres.
As Bakhromzod concludes:
The experiment conducted by Abu Rayhan al-Biruni and Abu al-Wafa al-Buzjani to determine the longitude difference between Khwarezm and Baghdad through observation of a lunar eclipse is rightly regarded as an outstanding achievement of medieval science. It represents a remarkable synthesis of theoretical insight and practical implementation, astronomical knowledge and geographical purpose. The scholars succeeded in overcoming the principal limitation of their era–the absence of means for time synchronization–by using the sky itself as a set of “precise clocks.”
Unable to synchronize clocks across an enormous distance, the two scholars instead used the Moon’s passage through Earth’s shadow. Their experiment shows how medieval astronomers transformed a celestial event into a practical tool for measuring the world.
The preprint paper, “Determination of the longitude difference between Baghdad and Khwarezm using a lunar eclipse (the method of Abu Rayhan al-Biruni and Abu al-Wafa al-Buzjani),” by Rizoi Bakhromzod has been published on arXiv, a free online repository where researchers share academic papers, often before they have undergone formal peer review or appeared in a scholarly journal. Click here to read it.
Rizoi Bakhromzod is a member of the Tajik Academy of Sciences, where he researches astrophysics during the Middle Ages.
See also: How medieval people described solar eclipses
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