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xt, Abü-l\'Wafa\' and al-Birüni worked together to a lunar eclipse in order to m

ID: 3197395 • Letter: X

Question

xt, Abü-l'Wafa' and al-Birüni worked together to a lunar eclipse in order to measure the difference in longitude their two cities. Since a lunar eclipse is an event that happens 4. According to the te between on the moon (so doesn't depend on where you are on the earth) and that is easy to see, if one records the time when the eclipse is seen, one can then compare it with another person's record and find the difference in local time between two locations. a. The observers found that there was about one hour's difference be- tween local time at their positions. What does this tell you abourt the longitudes? in Uzbekhistan. Find out the longitudes of both cities. Did they get the difference right? b. Abü-l'Wafa' was in Baghdad, in Iraq, while al-Birüni was in Khiva,

Explanation / Answer

a) the time difference is observed as 1 hour....
since 24 hours of time corresponds to 360 degrees of longitude...
1 hour corresponds to 360/24= 15 degrees.
b) longitude of baghdad(abu-l- wafa ) is 44.3615 degrees East
longitude of khiva (al-Biruni) is 60.3415 degrees East
their difference is 60.3415-44.3615=15.98 degrees which approximates to 15 degrees

YES, they got the difference right.


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