How to determine the beginning of Ramadan in non-Muslim countries?
Is it permissible to depend on astronomical accounts or to follow an Islamic country?
“Ramaḍān enters by one of two ways:”
Shaykh Ṣālih al-Fawzān, may Allāh protect him, explained:
The Messenger of Allāh, prayers and peace upon, said: “Begin fasting when you sight the moon, and end fasting when you sight the moon. And if you are unable to sight it, complete the month of Shabān thirty days." [al-Bukhārī and Muslim]
Shaykh Ṣāliḥ al-Fawzān, may Allāh protect him, explained:
“Those who seek to begin fasting the month of Ramaḍān by using astrological calculations have added and innovated into the religion that which Allāh and Messenger, prayers and peace upon him, did not command us with.”
Source: A Concise Study Guide to Fasting
You can prove it by seeing the new moon (the small sliver of it). Basically that is astronomy, or part of it, I would say you could rely on astronomy if it is trusted, and yes you could also just follow the most closest Islamic country of the same time.