Astronomy Principles and Practice Fourth Edition.pdf

130 The reduction of positional observations: I
10.7.4 The parsec
We have seen that the distances of the stars are so great that any measured parallax is less than 1 second
of arc. There is, therefore, a need to introduce a unit of length for use in describing such distances that
will lead to convenient numerical values.
The parsec is the more usual unit used by astronomers: it is the distance of a celestial body whose
parallax is 1 second of arc. Now 1 second of arc is approximately 1/206 265 of a radian; therefore, a
distance of 206 265 astronomical units will be the distance at which one astronomical unit subtends 1
second of arc. Hence, we may write
1parsec= 206 265 AU
or, using the accepted value of the AU, namely 149·6 × 10 6 km,
1parsec= 30·86 × 10 12 km approximately.
A larger unit, the kiloparsec (= 10 3 parsec) is often used in expressing the distances of stars or
the size of galaxies.
In popular books on astronomy, the light-year is often employed as a unit of length. As its name
implies, it is the distance travelled by light in 1 year. The velocity of light is 299 792 km s −1 and there
are 31·56 × 10 6 s in 1 year. Hence,
1 light-year = 9·46 × 10 12 km, approximately
so that
1 parsec is equal to about 3·26 light-years.
The use of the light-year as the unit of length does emphasize one important aspect of astronomical
observations, namely that distant objects are seen not as they are now but as they were at a time when
the light entering the observer’s telescope left them. In the case of galaxies, this ‘timescope’ property
of a large telescope is particularly important, enabling information to be obtained about the Universe
in its remote past.
10.7.5 Extrasolar planets
Of accelerating interest is the possible detection of minute cyclical positional shifts in a star’s position
caused by the presence of planets in orbit about it. The detection of extrasolar planetary systems is
of great importance but it offers extreme technical challenges requiring regular measurements of very
small changes of a star’s coordinates relative to other local field stars.
A feel for the problem can be appreciated by considering our own solar system as providing an
example. Jupiter is the most massive planet orbiting the Sun. The centre of mass based on this twobody
system is approximately at 1 solar radius (696 000 km) from the centre of the Sun. As seen from
a large distance, say at some star, the Sun would appear to move by its diameter over an interval of
time of one-half the orbital period of Jupiter. If the observer were at 10 parsecs (relatively close for a
star), the apparent displacement over this time interval would be
an extremely small angle.
2 × 6·96 × 105
= radian
10 × 30·86 × 1012 4·51 × 10−9
= arc sec
206 265
= 0·′′ 00022