How does stellar parallax shift relate to the distance of a star from Earth?

The concept of stellar parallax is fundamental in measuring the distances of stars from Earth based on their apparent shift in position relative to distant background stars as observed from two different points in Earth's orbit around the Sun.

When a nearby star is observed six months apart, it appears to move slightly against the background of more distant stars. This apparent shift is known as parallax. The key to understanding how distance relates to parallax is that the closer a star is to Earth, the larger the parallax shift will be. This is because the effect is more pronounced over shorter distances—the nearer the star, the greater the angle of parallax it exhibits.

In essence, a larger parallax angle indicates a shorter distance to the star, allowing astronomers to accurately measure how far away it is. Therefore, the statement that the closer the star is to Earth corresponds directly to a larger parallax angle and is the correct relationship to grasp in the context of measuring stellar distances.