The author of the Quran clearly seems unaware of the fact that Sun doesn't actually orbit the Earth, and the apparent orbit is an illusion caused by Earth's rotation.
36:37 to 36:40 - A token unto them is night. We strip it of the day, and lo! they are in darkness. And the sun runneth on unto a resting-place for him. That is the measuring of the Mighty, the Wise. And for the moon We have appointed mansions till she return like an old shrivelled palm-leaf. It is not for the sun to overtake the moon, nor doth the night outstrip the day. They float each in an orbit.
As you can see, Quran mentions the orbit or course of the Sun in context with the onset of night. It never mentions the fact that Earth rotates - which is the actual cause of night. This leaves us with only one logical explanation: The Sun orbits the Earth according to Quran. We can also note the weird motion of the sun which involves a resting place during night time. Muslims defend these verses arguing that Sun’s rotation about its own axis or its revolution around galaxy is being talked about here. However this is logically absurd as there is no need to mention the day and the night in context with Sun’s rotation or its revolution around galaxy. The statement: "It is not allowed for sun to overtake the moon" would be meaningful only if the orbits are in a similar path and is a clear proof for the scientific error.
But if that's not enough evidence for you, check out this Sahih Hadith for Muhammad's statement which again clearly proves that the motion of the Sun mentioned here is neither about Sun's rotation nor its revolution around galaxy - but about sunset and sunrise - which are related to the apparent orbit of sun around earth. The silly story about sun taking rest at night is seemingly supported here as well.
Sahih al-Bukhari 3199 - Narrated Abu Dharr: The Prophet asked me at sunset, "Do you know where the sun goes (at the time of sunset)?" I replied, "Allah and His Apostle know better." He said, "It goes (i.e. travels) till it prostrates Itself underneath the Throne and takes the permission to rise again, and it is permitted and then (a time will come when) it will be about to prostrate itself but its prostration will not be accepted, and it will ask permission to go on its course but it will not be permitted, but it will be ordered to return whence it has come and so it will rise in the west. And that is the interpretation of the Statement of Allah (36.38): And the sun runneth on unto a resting-place for him. That is the measuring of the Mighty, the Wise.)