Astronomy Principles and Practice Fourth Edition.pdf

142 The reduction of positional observations: II
Figure 11.7. The movement of by precession.
and included in the constellations would, by Hipparchus’ era, be below the horizon; other bright stars,
unseen by the constellation-makers, would, however, have had their declinations changed sufficiently
by the secular phenomenon of precession to appear above Hipparchus’ horizon at nights.
It is seen then that the celestial equator and the vernal equinox change their positions. The problem
arises of knowing at any time where these important references are. A method of achieving this is
outlined in the next section.
11.8 Measuring the positions of and the celestial equator
Use is made of the fact that the Sun’s annual path against the stellar background is the ecliptic. We
know that the value of the Sun’s maximum northerly declination is the obliquity ε. Measurements of
the Sun’s meridian zenith distance z at transit on a number of days around the summer solstice and a
knowledge of the observer’s latitude φ give a set of values for δ by means of the equation
δ = φ − z. (11.6)
The maximum in the graph of δ against time is the value of the obliquity.
If a second set of observations of the Sun’s meridian zenith distance were carried out near an
equinox, its declination will again be calculated from equation (11.6).
From figure 11.8, using the four-parts formula, we obtain
sin α = tan δ cot ε
from which the Sun’s right ascension α at the time of the transit can be found.
At transit, the Sun’s hour angle is zero so that the value of α is the local sidereal time of the hour
angle of . This enables the observatory sidereal clock error to be determined. The sidereal times of
transits of stars may then be noted, giving their right ascensions. Their declinations can also be deduced
from their meridian zenith distances by equation (11.6). In this way the equatorial coordinates of the
stars (i.e. their positions with respect to the celestial equator and the First Point of Aries) can be found
or, using the opposite viewpoint, the positions of the equator and against the stellar background can
be determined at any time.