Does the sun rise from the West in Middle Earth?

Question

In Lord of the Rings: The Return of the King (2003), there is a scene (starting around 02:17:52 in the Extended edition) showing the Rohan coalition leaving camp to head towards Minas Tirith. Then, the movie cuts to

• Minas Tirith where the battle rages and the Steward is proceeding through the funeral of the alive Faramir
• Cirith Ungol where Sam and Frodo are struggling against Shelob

In the scenes, I noticed

• It's already morning at the Rohan's camp, but still dark at Minas Tirith, and also dark at Cirith Ungol
• Edoras is west of Minas Tirith itself west of Cirith Ungol. Therefore, I'm guessing that Rohan's camp is somewhere between Edoras and Minas Tirith and so the camp itself must also be west of Minas Tirith. Indeed, the camp location appears to be Dunharrow which in fact is very much west of Minas Tirith. See map.
• The arrival of the Rohan's forces coincided with the sunrise in Minas Tirith

So my questions are:

1. Are there enough distances between these three places to show such time differences? The darkness of Cirith Ungol may be due to the evil cloud of Sauron but there is definitely some time difference between the Rohan's camp location and Minas Tirith?
2. Does the sun in Middle Earth rise on the West? For if it rose from the East like in the real world, Minas Tirith should get its morning first.

Answer 1

This might have been taken from the books without the explanation from the books included in the movie. In the books, Orodruin/Mount Doom is spewing out ash and smoke as Sauron starts the War of the Ring, since he commands the fires of the mountain. The smoke forms a canopy that extends outwards from Mordor and blocks out the sun from the lands around it. The in-universe reason for this is to cause despair among enemies and to enable trolls (normal mountain trolls turn to stone in sunlight - Sauron's trolls are resistant to that, but they still hate the sun) and orcs to fight with comfort.

At the time of the weapontake at Edoras and the setting forth of the Rohirrim, the smoke has blocked the sun from Cirith Ungol (of course, being actually part of Mordor) and has extended to block the sun from Minas Tirith, which is much closer to Mordor than Edoras or Meduseld, but the smokes have not reached Rohan.

So the sun is out in Rohan, but it is perpetual dusk/night in Gondor and Mordor.

When the Rohirrim ride into the Pelennor Fields, it is both sunrise of that day and there is a break in the smokes of Mordor. I don't recall a stated reason for a break in the smokes in the books, but it coincides both with the ride of the Rohirrim and the arrival of Aragorn leading the Army of the Dead, as well as the defeat of the Witch-King of Angmar.

Answer 2

No, Middle Earth is Analgmous to real Earth. Sun rises in the East and Sets in the west. Before the Battle of Helms Deep, Gandalf leaves instructions behind to Aragorn. Look to my coming on the first light of the fifth day, at dawn look to the east.