An observer's distance from Earth does not directly affect the movement they notice in stars. The apparent movement of stars in the night sky is primarily influenced by the rotation of the Earth on its axis and the revolution of the Earth around the Sun. These movements cause the stars to appear to move across the celestial sphere over the course of a night or a year.
However, an observer's distance from Earth can indirectly affect their perception of stellar movement due to parallax. Parallax is the apparent shift in the position of an object when viewed from different vantage points. When observing nearby stars, their positions can appear to shift slightly against the more distant background stars as the observer's position changes.
The amount of parallax observed depends on the baseline distance between the observer's positions. The baseline is the distance between two observation points, such as the Earth's position at different times of the year. The larger the baseline, the greater the parallax shift. Parallax can be used to determine the distances to nearby stars by measuring the angular shift in their positions over a six-month period.
So, in summary, an observer's distance from Earth doesn't directly affect the movement they notice in stars, but it can affect the amount of parallax observed, which can provide valuable information about the distances to nearby stars.