If astronomical calculations differ regarding the advent of the month of Shawwal, and one is convinced of the error in announcing the advent of the month in their country, must they fast an additional day in compensation for the last days of Ramadan?

The criterion for the beginning of the Hijri months is the sighting of the crescent moon, and it does not depend on astronomical calculations. This is based on the Prophet Muhammad (peace be upon him) saying: "Do not fast until you see it (the new moon), and do not break your fast until you see it. If it is obscured from you, then complete the number of days," and "Fast when you see it, and break your fast when you see it."

The wisdom behind this is to simplify matters for the responsible individuals, as the Prophet (peace be upon him) said: "We are an unlettered nation; we neither write nor calculate."

The Salaf (early Muslims) have unanimously agreed on abandoning astronomical calculations, and they considered anyone who said otherwise to be mistaken. Therefore, it is not permissible to rely on the statements of astronomers to confirm the beginning of the month. Rather, the criterion is the Shariah-compliant sighting. Whenever trustworthy individuals testify to having seen the crescent moon, fasting and breaking fast become obligatory. You are not required to make up the Eid day due to the statement of some astronomers, and your belief in the error of the Shariah-compliant sighting is not an argument against the Shariah.