Abu Dawud

Benefits and Issues:
The intent of Ibn Abbas (radi Allahu anhu) is that for the people of every region, their own sighting (of the moon) is to be considered valid.
Imam Shafi'i (rahimahullah) further states regarding this that if the horizon (matla‘) of different regions is the same, then the sighting of one is valid for the others as well; otherwise, it is not.
This is also the position of Imam Ibn Taymiyyah (rahimahullah).

(1) “This is what has been commanded”—that you should begin fasting upon sighting the crescent moon and celebrate Eid upon sighting the crescent moon. This does not mean that every individual must sight the moon themselves; rather, if even a single trustworthy person sights the moon, or if news of the moon being sighted in another place reaches, then all the people of that region will fast or celebrate Eid, and the new month will commence. However, it is necessary to ascertain that the distance between the two places is not so great that it could result in a difference of one or two days in moon sighting. In the area where the moon has been sighted, the sighting will be considered valid for all the surrounding regions where the moon could also be seen. In this matter, guidance should be sought from scholars of astronomy. Nowadays, every Islamic country is so small that if the moon is sighted anywhere within the country, it can be seen throughout the entire country; therefore, if the moon is sighted in any part of a country, fasting or Eid can be observed throughout the whole country. However, the moon may differ between different countries; for example, Saudi Arabia and Pakistan are quite distant from each other. In this matter, only scholars of astronomy and celestial observation can make the correct decision; therefore, their participation in the moon sighting committee is extremely necessary. There are a few established principles in this regard:
➊ When the moon is sighted in one city, it will also be present in all cities located on similar longitudes, even if the distance between them is thousands of miles.
➋ If the moon is sighted in a city, then in all areas to its west, the moon will certainly be visible, and there is no need to sight it separately, even if the distance is thousands of miles. However, the reverse is not necessary; that is, the moon sighted in the west is not valid for the east, and it must be sighted separately.
➌ If the moon is sighted in an elevated area, it is not necessary that it will be visible in the lower area; however, the reverse is necessary, meaning if the moon is sighted in a lower area, then it will certainly be present in the elevated area. These principles are self-evident and there can be no disagreement in them.

(2) Although there is a considerable distance between Madinah Munawwarah and Damascus, in terms of longitude there is only a difference of six degrees. That is, there is a difference of 24 minutes in sunrise and sunset, and such a difference does not affect the sighting of the moon. The moon should be the same in both places on the same day. However, in that era, due to the lack of rapid means of communication, it was impossible for news to reach over such a distance in a timely manner. Therefore, Ibn Abbas radi Allahu anhu did not consider the sighting of the moon in Shaam (i.e., Damascus, which was the capital at that time) as sufficient for Madinah Munawwarah.