RIYADH — When is a moon not a moon? That is the question vexing Muslim astronomers after accusations that Saudi Arabia jumped the gun in declaring the festival of Eid ul-Fitr because they mistook Saturn for the Moon.

The festival is the most joyous moment in the Islamic calendar and celebrates the end of the fasting month of Ramadan. But every now and then celebrations are marred by bickering between competing Islamic authorities over when Eid starts. This year's row is over whether the festival should have begun last Monday or Tuesday.

According to the instructions laid down by the Prophet Muhammad, Muslims can only break their fast when the crescent of a new moon is spotted above the horizon.

Where once Muslim communities relied on local committees of star-gazers to locate the new moon – known in Arabic as the hilal – a growing number of mosques around the world now look to the Saudi authorities to decide when Eid celebrations can begin. Last week Saudi scholars declared that the end of Ramadan began on Monday evening and gave the signal that Eid celebrations could commence. But others were not so sure. In Indonesia, which often disagrees with the Saudis over the hilal, the official religious authorities insisted that celebrations could only begin on Tuesday evening. The Royal Observatory last week said the crescent moon could only be seen in Britain on Wednesday, but that didn't stop hundreds of UK mosques from following the Saudi lead and starting celebrations on Monday.

Some astronomers in the Gulf suggested that the object the Saudis claim they saw in the sky on Monday night was in fact Saturn. The accusation has infuriated the Kingdom's notoriously authoritarian scholars who have begun preaching against those who claim they made a mistake.

According to the Arab News website, Saudi Arabia's Grand Mufti Abdul Aziz bin Abdullah al-Asheikh condemned the lunar naysayers at Friday prayers, accusing them of being "motivated and deviated people with foul mouths that cast doubt on our religion and should be silenced."

The dispute has been seized upon in Shi'a Iran, which is hostile towards Saudi Arabia because the country's intolerant strand of Wahabi Islam views the Shi'a as heretics. The semi-official Fars news agency carried a report suggesting that the Saudis would have to pay kaffarah – an Islamic fine which is sometimes used by Muslims as recompense for missing a day's fasting or breaking an oath. At the time of writing there was no such admission from the Saudi authorities.