The distance of an observer from Earth does not directly affect the movement of stars. The apparent movement of stars as observed from Earth is primarily caused by the rotation of the Earth on its axis and its revolution around the Sun. These motions create an effect known as diurnal motion and annual motion, respectively.
Diurnal motion refers to the daily rotation of the Earth on its axis, causing the stars to appear to move across the sky from east to west. This apparent motion is responsible for the rising and setting of celestial objects. The speed of this apparent motion is determined by the Earth's rotation period, which is approximately 24 hours.
Annual motion is the result of the Earth's orbit around the Sun. As the Earth completes its orbit, the position of the Sun appears to shift relative to the background stars. This creates the illusion that the stars are moving slowly eastward throughout the year. The speed of this apparent motion is determined by the Earth's orbital period, which is about 365.25 days.
The observer's distance from Earth, in most cases, does not significantly affect these apparent motions. Regardless of the observer's location on Earth, they will perceive the same diurnal and annual motions. However, the observer's latitude can influence which stars are visible and how they appear to move. For example, observers closer to the Earth's poles will experience more pronounced circular paths of stars around the celestial poles due to the Earth's axis of rotation.
It's important to note that while stars appear to move due to the Earth's rotation and orbit, they are actually distant objects fixed in space. The vast majority of stars are so far away that their positions appear unchanged over human timescales, even when observed from different locations on Earth.