Distances and Movement of the Stars
ATLAS OF THE UNIVERSE
I
t is very easy to take an attractive star picture. All you
need is a camera capable of giving a time exposure.
Using a reasonably fast film, open the shutter and point
the camera skywards on a dark, clear night. Wait for half
an hour or so – the exact timing is not important – and
end the exposure. You will find that you have a picture
showing the trails left by the stars as they crawl across the
field of view by virtue of the Earth’s rotation, and you
may be lucky enough to catch a meteor or an artificial
satellite. Perhaps the most rewarding effects are obtained
by pointing the camera at the celestial pole.
The first successful measurement of the distance of
a star was made in 1838 by the German astronomer
Friedrich Bessel. His method was that of parallax; the
principle was the same as that used by surveyors who want
to find the distance of some inaccessible object such as a
mountain top. They measure out a baseline and observe
the direction of the target from its opposite ends. From this
they can find the angle at the target, half of which is
termed the parallax. They know the length of the baseline,
and simple trigonometry will enable them to work out the
distance to the target, which is what they need to know.
With the stars, a much longer baseline is needed, and
Bessel chose the diameter of the Earth’s orbit. A now rep-
resents the position of the Earth in January and B the posi-
tion of the Earth in June, when it has moved round to the
other side of its orbit; since the Earth is 150 million kilo-
metres (93 million miles) from the Sun (S) the distance
A–B is twice this, or 300 million kilometres (186 million
miles). X now represents the target star, 61 Cygni in the
constellation of the Swan, which Bessel calculated because
he had reason to believe that it might be comparatively
close. He worked out that the parallax is 0.29 of a second
of arc, corresponding to a distance of 11.2 light-years.
The parallax method works well out to a few hundreds
of light-years, but at greater distances the annual shifts
become so small that they are swamped by unavoidable
errors of observation, and we have to turn to less direct
methods. What is done is to find out how luminous the
star really is, using spectroscopic analysis. Once this has
been found, the distance follows, provided that many
complications have been taken into account – such as the
absorption of light in space.
A star at a distance of 3.26 light-years would have a
parallax of one second of arc, so that this distance is
known as a parsec; professional astronomers generally use
it in preference to the light-year. In fact, no star (apart
from the Sun, of course) is within one parsec of us, and
our nearest neighbour, the dim southern Proxima Centauri,
has an annual parallax of 0.76 of a second of arc, corres-
ponding to a distance of 4.249 light-years. Another term in
common use is absolute magnitude, which is the apparent
magnitude that a star would have if it could be viewed
from a standard distance of 10 parsecs or 32.6 light-years.
The absolute magnitude of the Sun is 4.8, so that from the
standard distance it would be a dim naked-eye object. Sirius
has an absolute magnitude of 1.4, but the absolute mag-
nitude of Rigel in Orion is 7.1, so that if it could be seen
from the standard distance it would cast strong shadows.
(En passant, the distances and luminosities of remote
stars are rather uncertain, and different catalogues give
different values. In this Atlas, I have followed the authori-
tative Cambridge catalogue. At least we may be sure that
Rigel qualifies as a cosmic searchlight. Hipparcos, the
‘astrometric satellite’, has revised the star distances some-
what, but the general principles remain the same.)
Though the individual or proper motions of the stars
are slight, because of the tremendous distances involved, Trigonometrical
parallax. A represents
the Earth in its position
in January; the nearby
star X, measured against
the background of more
remote stars, appears at X 1.
Six months later, by July,
the Earth has moved to
position B; as the Earth is
150 million km (93 million
miles) from the Sun, the
distance A–B is twice
150 300 million km
(186 million miles). Star X
now appears at X 2. The
angle AXS can therefore
be found, and this is known
as the parallax. Since the
length of the baseline A–B
is known, the triangle can
be solved, and the distance
(X–S) of the star can be
calculated.▼ Proper motion of Proxima
Centauri. Proxima, the
nearest star beyond the Sun
(4.249 light-years) has the
very large proper motion
of 3”.75 per year. These
two pictures, one taken in
1897 and the other in 1940,
show the shift very clearly
(Proxima is arrowed).E152-191 UNIVERSE UK 2003mb 7/4/03 5:47 pm Page 170