Astrometry (Astronomical Distance Determinations)

The branch of astronomy that concentrates on the precision measurement of positions and distances of celestial bodies is called astrometry, a conceptually difficult but very important science.
Knowing the exact distance of an object is important to understand its real characetristics, such but: For example, if we don't know their distance, a nearby, relatively small and faint object (such as a candle) and a distant, huge and very bright object (such as a star) can both look the same to us!
The difficulty of measuring distances is illustrated by how long it took astronomers to find the distance to a star. Greek astronomers developed the method to make the determination more than 2000 years ago, but it was not until the 1830s that the first distance was measured. The quest for distances continues today and there are several large projects now being developed for this purpose.

There are many and many methods to measure celestial distances. Let's first see the classical, historical methods:

Triangulation

The basic method of measuring distances in astronomy uses the geometry of triangles.
To begin, we measure a distance that serves as the base of the triangle (being located where we are, this distance can be measured directly). The tip of the triangle is located at the object whose distance we want to find. We can measure the angles defined by the base and sides connecting the base to the tip of the triangle and using a fundamental theorem of geometry, knowing these quantities is sufficient to determine everything else about the triangle.
In practice, astronomical triangles are extremely long and skinny, making it almost impossible to measure the two angles at the end of the base (they both seem to be almost 90°).

Parallax
From the above procedure, we can also imagine of measuring the angle at the tip of the triangle (which is the 180° minus the two angles at the base). But how can you measure an angle at such a great distance? The trick is to observe the object whose distance we want to know from the ends of the baseline at different istants: if the object is not too far, it appears to shift compared to the more distant background objects. This apparent shift is called parallax and measuring it is more accurate than estimating the two nearly 90° angles at the base.
Parallax can also be esaily explained with the familiar example of looking at a finger first with one eye and then with the other. The finger appears to shift back and forth relative to the background because the two eyes are separated by a certain distance.
The reality of parallax applied to stars distances measures is more complicated. Two measurements are the minimum, but it is normal to make many measurements over several years to map fully the star's parallax shift.

Several modern facilities are being developed to determine distances. Very briefly, here are some of the ways that we are using to improve and extend our direct determinations of distances.
The abilities of these modern facilities are truly revolutionary: the best observer before the invention of the telescope, Tycho Brahe around 1600, could locate stars with an accuracy of about 1´ = 60´´. The best ground-based telescope, the Canada-France-Hawaii Telescope, is able to determine star positions to about 0.1´´ in 1999.
In the 400 years since Tycho, this is an improvement of a factor 600. Satellites and ground-based optical interferometers are now, in 1999, achieving positions to 0.002´´ to 0.0002´´. This is better than the CFHT by factors of from 50 to 500 in just a few years.

This approach is to measure and remove the blurring effects of Earth's atmosphere. The goal is to reduced the size of the blurred image from 1´´ to the diffraction limit of the telescope. For example, the diffraction limit of a 5-m telescope is about 0.025´´. If we can determine the centre of this much smaller image to 1%, we could locate the star to ± 0.00025´´. If the minimum parallactic angle were twice this, the corresponding distance would be 2000 pc.

Optical Interferometry
This method uses tiny telescopes, typically only 20 cm in diameter. This small size is about the same size as a single blurring region in Earth's atmosphere. By using a telescope of this size, the star is viewed through one blurring element at a time.
The light of several small telescopes is brought together. The angular resolution is then set by the separation of the telescopes, not the diameter of the individual telescopes. Working interferometers now have separations of up to 37 m, much larger than any existing or planned telescope. In the near future, the separations will be increased to more than 400 m. These interferometers are able to locate the centres of stellar images more precisely than any single telescope, and so they can find even smaller parallax shifts.

Satellite Observatories
There has been one special-purpose satellite designed specifically to measure star positions and parallax shifts, called HIPPARCOS. Even though its mirror diameter is quite small, it has produced distance measurements out to 500 pc, a 10× increase over the traditional methods.
Several more specialized satellites are now in the planning stage. When these missions are launched, they will extend our ability to locate stars down to the micro-arc second range, or even smaller, with a corresponding increase in the distances that can be measured directly.