Why is parallax method not useful for measuring the distances of stars more than 100 light years away?

The parallax method is based on the principle of measuring the apparent shift of a star against the background of more distant stars as the Earth orbits around the Sun. This shift is called parallax.

The reason why the parallax method is not useful for measuring distances of stars further than 100 light years away is due to the limitations of human observation. The amount of parallax shift diminishes as the distance to the star increases. It becomes very challenging to measure the minute angular changes accurately for distant stars.

The angular shift is inversely proportional to the distance of the star. As the distance increases, the parallax angle becomes smaller, making it difficult to measure with precision. Beyond 100 light years, the parallax angles are extremely small, often measured in milliarcseconds (mas), which is equivalent to the angle subtended by an object 1 meter in size at a distance of 3.09 kilometers.

The accuracy required to measure such tiny angles is beyond our current observational capabilities. Even with the most advanced telescopes, the accuracy of measuring distances using the parallax method decreases significantly for stars beyond this range.

To measure the distances of stars beyond 100 light years, astronomers rely on alternative methods such as using standard candles (objects with known intrinsic brightness) like supernovae or Cepheid variable stars, or using the properties of the stars themselves, such as their spectral type, luminosity, and temperature, to estimate their distances via various distance indicators.