Is it permissible to rely on astronomical calculations to determine the beginning of Eid, and should one follow the sole mosque in the city that adopted this, or should one follow Saudi Arabia or their home country, and what are the implications of breaking the fast with them without the sighting being confirmed?

"The disagreement regarding reliance on astronomical calculations to determine the beginning and end of the month is an existing one. However, the fatwa we follow is that it is not permissible to rely on it. Instead, reliance is placed on sighting the crescent moon or completing the month's count. The crescent moon was sighted in most Muslim countries, and it was confirmed that Friday is the first day of Shawwal."