What is the fundamental mechanism causing the Sun and Venus to appear to move from East to West across the heavens?
Answer
Earth rotates on its axis from west to east.
The perception that celestial objects rise in the east and set in the west is an illusion caused by the motion of the observer, not the motion of the observed objects themselves relative to the local horizon plane over a 24-hour cycle. Earth spins on its axis in a direction moving from west toward the east. This continuous rotation makes everything visible above the horizon appear to sweep across the sky in the opposite direction, resulting in the familiar apparent motion from east to west.

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