The apparent motion of celestial objects across the sky is influenced by several factors, including the rotation of the Earth and the orbit of the Moon around the Earth. The Sun and the Moon appear to move at different speeds due to their respective distances from the Earth and the Earth's rotation.
The Moon is much closer to Earth compared to the Sun. It orbits around the Earth at an average distance of about 384,400 kilometers (238,900 miles), whereas the average distance between the Earth and the Sun, known as an astronomical unit (AU), is about 149.6 million kilometers (93 million miles). Because of the Moon's proximity, it appears to move relatively quickly across the sky.
On the other hand, the Sun's greater distance makes its apparent motion across the sky slower. The Sun is so far away that its movement is primarily influenced by the Earth's rotation on its axis. The Earth completes one full rotation approximately every 24 hours, causing the Sun to rise in the east, reach its highest point in the sky at noon, and set in the west. This apparent motion of the Sun takes place at a relatively constant rate, resulting in a slower apparent movement compared to the Moon.
It's important to note that the actual motion of the celestial objects themselves is consistent and governed by their orbits, but the observed motion from Earth is influenced by our vantage point and the rotation of the Earth.