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.

**
Adaptive Optics
**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.

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.