Why are parallax measurements of stars limited to the closest stars?

Question

Why are parallax measurements of stars limited to the closest stars?

Answer 1

In astronomy, parallax (sometimes called “annual parallax”) means—specifically—the apparent angular displacement of a star against the background of much more distant stars, as seen by an observer on Earth moving in orbit around the Sun. The trigonometric parallax is defined as half the annual parallax. Parallax of a star is measured in arc seconds (1 arc second = 1” =1/3600 degree).

Error in the calculation of distance from parallax increases with diminishing parallax, and different authors accept different limits on distances over which parallax is useful in calculating distance with accuracy.

The resolution of current ground-based telescopes limits determinations of trigonometric parallax to around 0.01”. Atmospheric distortion of images makes measurement of smaller angles too unreliable to be useful. This limits distance measurement by parallax to approximately 100 pc. From the ground, the distances to only about 100 stars can be calculated within 5% accuracy.

The resolution of space-based telescopes, which do not have to contend with atmospheric distortion, is determined predominantly by the quality of the optics and size of the telescope objective. Specially designed space telescopes such as the Hipparcos have enabled accurate parallax measurement down to 1 milli-arc second (0.001”), giving distance measurements for nearly 120 000 stars out to about 1000 pc. The distances to over 7000 stars can now be calculated within 5% accuracy.

"Dark objects" lurking in the outskirts of the Milky Way are running out of places to hide. Astronomers have successfully measured the distance to one such object—probably a pair of orbiting black holes—for the first time, by triangulating observations made on Earth and in space.

The new method pinpoints the distance to the candidate MACHO by comparing the views out of each of two "eyes", one on Earth, the other in space. A 1.3-metre telescope in Chile called OGLE discovered the telltale brightening of a background star in 2005. Astronomers then commanded the Spitzer Space Telescope, then 30 million kilometres from Earth, to turn its eye towards the event.

Future space telescopes, including the planned SIM, GAIA and FAME, should be able to resolve parallax angles down to between 10–500 micro-arc seconds, depending on the brightness of stars (higher resolution for brighter stars). SIM's technical goal is to achieve a parallax precision of ~4 micro-arc seconds, which would yield 10% distances out to 25,000 parsecs (81,500 ly).

Answer 2

It's all about "distance", dear.

Precise parallax measurements of distance usually have an associated error. Thus a parallax may be described as some angle ± some angle-error. However this "± angle-error" will not translate directly into a ± error for the range, except for relatively small errors. The reason for this is that an error toward a smaller angle results in a greater error in distance than an error toward a larger angle.

So, with smaller angles happening with greater distances measured by this method, the error becomes significant

Answer 3

Because they're they only ones whose apparent positions vary enough to measure accurately.

In effect, parallax shows close stars "moving" relative to the background. Distant stars are that background.

Answer 4

as distance increases, parallax decreases.