I came across this Hadith in Bukhari. The Prophet (sws) explains to Abu Dharr:

Do you know where the sun sets...? Indeed it travels till it prostates itself underneath the throne. (No: 4428)

This Hadith clearly seems to contradict the fact that sunset is brought about by the rotation of the earth. How should this Hadith be interpreted, and how do we counter criticisms by non-Muslims who might make use of this Hadith to assert that some of the Prophetic sayings contradict scientific facts?

The apparent meaning of the Hadith seems to go against what today is an established scientific fact. However, a careful analysis of this Hadith would show that this is not true: This subject has been discussed in the Qur’an also. Consider the following verse:

أَلَمْ تَرَ أَنَّ اللَّهَ يَسْجُدُ لَهُ مَن فِي السَّمَاوَاتِ وَمَن فِي الْأَرْضِ وَالشَّمْسُ وَالْقَمَرُ وَالنُّجُومُ وَالْجِبَالُ وَالشَّجَرُ وَالدَّوَابُّ وَكَثِيرٌ مِّنَ النَّاسِ (١٨:٢٢)

Do you not see that all those in the heavens and the earth, the sun and the moon and the stars, the mountains and the trees, the beasts, and countless men bow before God alone? (22:18)

Imam Amin Ahsan Islahi  explains this verse as follows:

This refers to the argument for the oneness of God practically witnessed by everything in the universe. We have explained at various places in this book that every thing in the universe is of Abrahamic nature regarding its attitude towards God. The sun, the moon, the stars, the mountains and beasts all submit before God’s will. None of them dare to deviate from the rules they are subjected to. The sun, which has been the most favourite deity of the naive, evidences that it stands, bows and prostrates before God everyday. At sunrise, it lifts its head from prostration and keeps standing till noon. In the afternoon, it bows down and again prostrates before the Lord at sunset. It continues in this position till the next morning.1

After elaborating upon this point to a great length, he cites the following verse:

وَلِلّهِ يَسْجُدُ مَن فِي السَّمَاوَاتِ وَالأَرْضِ طَوْعًا وَكَرْهًا وَظِلالُهُم بِالْغُدُوِّ وَالآصَالِ (١٥:١٣)

All who dwell in the heavens and on the earth prostrate themselves before God alone: willingly or perforce and their very shadows too prostrate before Him morning and evening. (13:15)

He says that this and other similar verses allude to the very fact under discussion. The Almighty says that nothing disobeys him and nothing deviates from the rules set for them. It is clear that the Hadith you have quoted also explains this theme.