The sun doesn't move at all it's the earth that moves. The earth is slightly tilted on it's axis so the whole hemisphere gets the sun not only the center. The earth takes 23 hours 56 minutes and 4 seconds to rotate on it's axis that's how we see the sun moving through the sky. It travels from east to west throughout the day. At noon it is at the highest point. It is true that people living on the east see the sun rise before the people living more west side.
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The Sun appears to travel from east to west across the sky each day due to the rotation of the Earth on its axis.
east 2 west
The sun rises in the East and sets in the West.
Stars appear to move across the Earth's sky each night due to the rotation of the Earth on its axis. As the Earth rotates from west to east, different stars become visible in the sky. This apparent motion is known as the diurnal motion of stars.
Constellations appear to move across the sky each night due to the Earth's rotation on its axis. This rotation causes the stars to appear as though they are moving, when in fact it is the Earth that is moving. This phenomenon is known as the diurnal motion of the stars.
The sun and the moon appear to move across the sky each day due to Earth's rotation on its axis. The sun appears to rise in the east and set in the west because of the Earth's eastward rotation. The moon also follows a similar path across the sky, as it orbits around the Earth.