What phenomenon describes the apparent shift in position of an object due to the movement of the observer?

The phenomenon that describes the apparent shift in position of an object due to the movement of the observer is parallax. Parallax occurs when an observer moves and perceives an object from different angles, causing it to appear to shift position against a background. This effect is commonly used in astronomy to measure distances to nearby stars; as the Earth orbits the Sun, the apparent position of a star relative to more distant stars changes.

The other options represent different concepts: orbit refers to the gravitational path one object takes around another, an eclipse involves the obscuring of one celestial body by another, and rotation refers to the spinning motion of an object around its own axis. These concepts do not pertain to the observer's perception of an object's position in relation to their movement.