Final answer:
The Sun's apparent displacement is due to Earth's orbit, making the Sun seem to move 1° eastward each day against the stars. The path of this apparent movement is called the ecliptic, influenced by Earth's axial tilt. Ancient Greek thinkers like Aristarchus of Samos proposed the idea of Earth orbiting the Sun, but this was not widely accepted until later.
Step-by-step explanation:
The displacement of the Sun with respect to Earth is an apparent movement caused by Earth's orbit around the Sun. On the celestial sphere, the Sun appears to move each day about 1° to the east relative to the stars. This motion is due to Earth completing its rotation on its axis and having to rotate a little more for the Sun to be seen in the same position in the sky, leading to the Sun rising approximately 4 minutes later each day when compared to the stars.
The path that the Sun seems to take through the sky over the course of the year is called the ecliptic, which is tilted by about 23.5° because of the tilt of Earth's axis. This tilt causes the Sun's position to change in our sky throughout the year, influencing seasons and the length of daylights. Ancient Greek scholars like Aristotle thought that the Sun was moving around Earth, but it is now understood that it is Earth's orbit around the Sun that results in these observations.
Moreover, the ancient Greek thinker Aristarchus of Samos correctly hypothesized that Earth orbits the Sun, but his ideas were not widely accepted until much later. Without realizing it, ancient observers were witnessing the effects of parallax, where the position of objects changes based on the observer's position, similar to how trees may appear to move against a distant hill when viewed from a moving train.