Question

How can we explain the lack of observable parallax in the stars, which should be noticeable if the Earth is moving in an orbit around the Sun?

Answer 1

The lack of observable parallax in most stars is not due to a failure of the Earth's motion around the Sun but rather because of the vast distances involved.

Parallax is the apparent shift in the position of an object when observed from different perspectives. It occurs when the observer's position changes, such as when viewing an object from two different points separated by a distance. In the case of stars, astronomers observe their positions from opposite ends of the Earth's orbit around the Sun, with a six-month interval between observations.

However, the stars are incredibly far away, and their distances are measured in light-years, which is the distance that light travels in one year. Due to this enormous distance, even though the Earth orbits the Sun, the change in perspective is extremely small.

The angle of parallax is related to the distance to the object and the baseline—the separation between the two observing positions. For stars, the baseline is the diameter of Earth's orbit around the Sun, which is about 300 million kilometers (186 million miles). Despite this seemingly large distance, it is still minuscule compared to the vast cosmic distances to the stars.

The closest star to us, Proxima Centauri, is about 4.24 light-years away. Its parallax angle is approximately 0.77 arcseconds, which is the angle subtended by an object of about 1 meter seen at a distance of approximately 3.1 kilometers (1.9 miles). This angle is incredibly small, making it difficult to detect with the naked eye.

To measure stellar parallax accurately, astronomers use precise instruments such as telescopes equipped with detectors capable of detecting tiny shifts in star positions. Through these observations, astronomers can determine the distances to nearby stars and create three-dimensional maps of our galaxy.

In conclusion, the lack of observable parallax in most stars is due to their enormous distances. While the Earth does orbit the Sun, the vast cosmic scales make the parallax angles too small to be detected without specialized instruments.