Final answer:
The Sun, the Moon, and stars appear to move across the sky from east to west because Earth rotates from west to east on its axis. Celestial patterns like equinoxes and retrograde motion help in understanding these movements.
Step-by-step explanation:
The Sun, the Moon, and the stars appear to move from east to west across the sky because the Earth rotates from west to east. This eastward rotation of Earth is also why most celestial objects, including planets, normally move eastward in the sky over time. However, due to the motion of Earth in its orbit, there can be perceived exceptions like the retrograde motion of planets.
During an equinox, the Sun rises exactly in the east and sets exactly in the west, a behavior that is due to Earth’s rotation around its axis and its orbit around the Sun.
Observing the sky from Earth, it is convenient to think of a celestial sphere that appears to rotate, but in reality, it is the rotation of Earth on its axis that causes these daily movements. The axis through Earth's North and South Poles defines the direction of this rotation.