The perception that the Sun doesn't appear to move quickly across the sky despite the Earth's fast rotation is due to a combination of factors, including the vast distances involved and our frame of reference.
Firstly, it's important to understand that the Earth rotates on its axis, completing one full rotation in approximately 24 hours. This rotation gives us the perception of day and night. As the Earth spins, different parts of the planet come into and go out of view of the Sun, causing the cycle of sunrise and sunset.
However, the apparent motion of the Sun across the sky is not solely due to the Earth's rotation. It is also influenced by the Earth's orbit around the Sun. The Earth takes about 365.25 days to complete one orbit around the Sun. This means that as the Earth rotates on its axis, it is also moving along its orbit around the Sun.
The combination of Earth's rotation and its orbital motion causes the Sun to appear to move across the sky at an average rate of 15 degrees per hour. This motion corresponds to the Earth's rotation speed, but it is not as noticeable because we are moving along with the Earth. It's similar to how if you are traveling in a car at a constant speed, the objects outside the car appear to move slower compared to when you are standing still and observing them.
Additionally, the vast distance between the Earth and the Sun plays a role in our perception of the Sun's motion. The average distance from the Earth to the Sun is about 93 million miles (150 million kilometers). This enormous distance means that even though the Earth is spinning relatively quickly, the apparent motion of the Sun across the sky appears gradual and smooth.
So, while the Earth is indeed spinning rapidly on its axis, the combination of its rotational motion and orbital motion around the Sun, along with the vast distances involved, gives us the perception of the Sun's relatively slow apparent motion across the sky.