the equatorial coordinate system
Because the altitude and azimuth of a star are constantly changing, it is
not possible to use the horizontal
coordinate system in a catalogue of positions.
A more convenient coordinate system for cataloguing purposes is one based
on the celestial equator and the
celestial poles and defined in a
manner to latitude and
longitude on the surface of the
Earth. In this system, known as the equatorial coordinate
system, the analogue of latitude is the
The declination of a star is its
angular distance in degrees measured from the celestial equator along the
through the star. It is measured north and south of the
celestial equator and ranges from 0° at the celestial equator
to 90° at the celestial poles,
being taken to be positive when north of the celestial equator and
negative when south. In Figure 15, the
declination of the star X is given by the angle between
Y and X.
The analogue of longitude in the equatorial system is the
hour angle, H (you may also see the symbol
HA used). Defining the observer's meridian
as the arc of the great circle which passes from the north celestial
pole through the zenith to the south celestial pole, the hour angle
of a star is
measured from the observer's meridian westwards (for both northern
and southern hemisphere observers) to the meridian through the star (from
0° to 360°). Because of the rotation of the Earth, hour angle
increases uniformly with time, going from 0° to 360° in 24 hours.
The hour angle of a particular object is therefore a measure of the time
since it crossed the observer's meridian - hence the name. For this reason
it is often measured in hours, minutes and seconds of time rather than in
(just like longitude).
In Figure 15, the
hour angle of the star X is given by the angle
Z-NCP-X. Note that all stars attain their maximum altitude above
the horizon when they transit (or attain upper culmination on, in the case
of circumpolar stars) the observer's meridian.
The declination of a star does not change with time. The hour angle does,
and hence it is not a suitable coordinate for a catalogue. This problem
is overcome in a manner analogous to the way in which the
has been (arbitrarily) selected as the zero point for the measurement
of longitude. The zero point chosen on the celestial sphere is the
first point of Aries,
and the angle between it and the intersection of the
meridian through a celestial object and the celestial equator is called
the right ascension (RA) of the object. Right ascension is
denoted by the Greek letter
measured from 0h to 24h along the celestial
from the first point of Aries, that
is, in the opposite direction to that in which hour angle is measured. Like
the definition of hour angle, this convention holds for observers in both
northern and southern hemispheres.
In Figure 15, the
right ascension of the star X is given by the angle
The equatorial coordinate system.
As described previously,
most modern research telescopes do not
use equatorial mounts due to their higher cost and lower stability. This
is at the expense of the simplicity of telescope tracking - an
equatorially-mounted telescope need only move its right ascension axis
in order to track the motion of the celestial sphere.
Figure 16 shows an example of an
An equatorially mounted telescope - the 3.9 m Anglo-Australian
Telescope (AAT) in Australia.
In the above discussions on coordinate systems and the celestial sphere
we make the assumption that the stars are fixed on the celestial sphere
and never move. For accurate positional work on long timescales, this
assumption does not hold - the stars do move on the celestial sphere.
The Earth's axis of rotation is not fixed in direction, but precesses
slowly in space, like a spinning top, due to the gravitational attractions
of the Sun and Moon on the rotating, non-spherical Earth (see page 144 of
Roy and Clarke for a detailed description). Because of this, the north
celestial pole traces out a small circle with a radius equal to the
obliquity of the ecliptic,
This also causes the celestial equator to
move, and as a result the first point of Aries is not actually a fixed
reference point; it moves gradually backwards along the ecliptic, by about
50 arcseconds per year, and is in fact currently in the neighbouring
constellation of Pisces. This motion is known as the
precession of the equinoxes and it means
that even right ascension and declination
are not quite fixed coordinates and catalogues of star positions have to
specify the date (e.g. 1950.0 or 2000.0) to which they refer. More
precisely, the coordinate frame used for catalogue positions is defined by
the position of the vernal equinox (the first point of Aries) on a
particular date, so
astronomers talk about positions referred to (for example) the equinox of
2000.0. Although the pole
takes some 26 000 years to make one revolution, the effect of precession
is much larger than the uncertainties in the positions of objects, so all
positional measurements must be corrected for precession.
Precession only rotates the reference frame, and has no effect on the
relative positions of stars. However, the stars are not stationary in space;
they are all moving around the centre of the Galaxy, in different orbits,
and the effect is that nearby stars have measurable motions relative to the
Sun. The projections of these motions onto the celestial sphere are known
as the stars' proper motions, usually given the symbol
, and they do cause changes
in the relative positions of stars.
For stars with significant proper motion, it is therefore necessary to
specify both the proper motion and the date of the observation (known as
the epoch), as well as the catalogue position and the equinox to
which it refers.
If no epoch is given for a position, it is
assumed that the epoch is the same as the
equinox of the reference frame.
There are a number of other, generally smaller, corrections
astronomers need to
make to the coordinates of an astronomical object before doing accurate
positional work. These include atmospheric refraction,
stellar aberration and nutation, which
are all described in Chapters 10 and 11 of Roy and Clarke.
You should now be able to understand a page out of a
star catalogue, an example of which is shown in
An extract from a typical star catalogue.
Using the position of the first point of Aries as the basis of the
equatorial coordinate system is inappropriate for high-precision
positional astronomy. This is due to the fact that the theories of
motion of the Earth that define how the celestial equator and ecliptic
(and hence the first point of Aries) move are imperfect. Even if these
planes are defined without any reference to the motions of the Earth,
there is no way to magically paint them on the celestial sphere at any
particular time. Therefore, in practice, a set of fiducial objects
with assigned coordinates are used to define the coordinate system.
The axes of the International Celestial Reference System
(ICRS), the current standard celestial reference system, are defined
by the adopted positions of a specific set of extragalactic objects
(mainly quasars observed in the radio), which are assumed to have no
measurable proper motions. The ICRS axes are consistent to better than
0.1 arcseconds with the equinox of 2000.0 defined by the dynamics of
the Earth. However, the ICRS axes are meant to be regarded as fixed
directions in space that have an existence independent of the dynamics
of the Earth or the particular set of objects used to define them at
any given time.
©Vik Dhillon, 30th September 2009