As we know, ʿĀshūra is the tenth day of Muharram; the first month of the Islamic lunar year. The start of lunar months, besides Ramaḍān and Dhul-Hijjah for those performing Ḥajj, is decided based on one of two criteria: a) sighting the new moon and b) the completion of the previous month. This view is found to be agreed on by all scholars based on the prophetic tradition, ‘Fast when you see it (the moon) and cease fasting when you see it, and if it is hidden or cloudy, complete the counting of Shʿabān as thirty days.’
The second principle applies only in the absence of the first, which is to complete thirty days for the month of Shaʿbān. The basis for this is also mentioned in the ḥadīth as well as by means of many other (similar) statements. It has been stated by a number of jurists that the overwhelming majority of scholars have agreed not to consider astronomy or calculations as a tool to confirm the beginning of hijri months.
If the month of Muharram were not to be confirmed according to the criteria set out in the ḥadīth, then the best choice a person has is to fast either 2 or 3 days in which the ʿĀshūra fasting should logically be achieved. So the individual should calculate when ʿĀshūra would take place if Dhul-Hijjah were either 29 or 30 days, and then fast these two consecutive days. Thus the fasting individual should be certain that he has fasted ʿĀshūra and would have fasted either the ninth and tenth, or the tenth and eleventh, both of which are good. For example, this year (1439 A.H.) Muharram began on the 21st of September according to most calendars. Last month (which was the year 1438 A.H.), Dhul-Hijjah was 29 days based on the sighting of the moon.
The 10th day of Muharram (ʿĀshūra) will be on Saturday 30th September 2017. However, if Dhul-Hijjah had been 30 days then ʿĀshūra would have been on Sunday 1st October.
Imām Aḥmad b. Hanbal stated that a person should fast three days if he doubts the beginning of the month to be sure that he has fasted the correct day. In fact al-Nawawi indicated that a possible reason as to why the Prophet (sall Allāhu ʿalayhi wa sallam) fasted the 9th of Muharram (as well as the 10th) was to ensure that he fasted on ʿĀshūra (and did not miss it).
ʿAbdullāh b. ʿAbbās (raḍiy Allāhu ʿanhumā) said, “When the Messenger of Allāh (sall Allāhu ʿalayhi wa sallam) fasted on ʿĀshūra and commanded the Muslims to fast as well, they said, ‘O Messenger of Allāh, it is a day that is venerated by the Jews and Christians.’ The Messenger of Allāh (sall Allāhu ʿalayhi wa sallam) said, ‘If I live to see the next year, inshāAllāh, we will fast on the ninth day too.’ But it so happened that the Messenger of Allāh (sall Allāhu ʿalayhi wa sallam) passed away before the next year came.”
If an individual also wants to be sure of fasting on the 9th of Muharram 1439, then he should fast the two days we have spoken about and the day immediately before them as well. Then he would have fasted Friday 29/9/2017, Saturday 30/9/2017 and Sunday 1/10/2017 and so he definitely would have fasted the 9th and 10th of Muharram 1439.
If someone finds it extremely difficult to fast three consecutive days, then he should opt to fast the two days. If it is difficult to fast two days for whatever reason, despite the fact that days are very short in Europe this ʿĀshūra, he should calculate ʿĀshūra according to the aforementioned criteria. In other words, if he knows and has accepted that the moon of Muharram was sighted, then he should calculate the day of ʿĀshūra accordingly, otherwise he should calculate it based on the second criterion that completes Dhul-Hijjah as thirty days. It would be incorrect to calculate the day of ʿĀshūra according to the calendar.
And Allāh knows best
Notes: Al-Bukhārī and Muslim, narrated by Abū Hurairah.  Muslim