Astronomy Principles and Practice Fourth Edition.pdf

144 The reduction of positional observations: II
By 15 000 AD, the positions of the north celestial pole and First Point of Aries are P 3 and 3 .
The coordinates of the star are now 12 h ,0 ◦ .
Obviously, after three-quarters of the precessional period has passed, the star’s coordinates will
be 18 h , ε ◦ S, its coordinates returning to their 2000 AD values after one complete precessional period
has elapsed.
The present pole star, Polaris, is about one degree from the north celestial pole and so is a fair
indicator of the pole’s position at the present day. If a star-map is obtained and a circle of radius ε
(∼23 1 2 ◦ ) is traced about the north pole of the ecliptic, this circle will pass through the positions that
have been or will be occupied by the north celestial pole. For example, some 4000 years ago, the bright
star γ Draconis was about 4 ◦ from the pole; and in 12 000 years time, the pole will be within a few
degrees of the bright star α Lyrae (Vega).
Star catalogues give the coordinates of stars with respect to a particular equator and vernal
equinox, i.e. the positions the equator and equinox occupied at a particular epoch, say, the beginning of
the years 1950, 1975 or 2000. The stellar positions in The Astronomical Almanac and other almanacs
are also with reference to the position of the equator and equinox of a certain date—in this case the
beginning of the year for which the almanac has been produced, for example, 2000·0. This equator and
equinox are referred to as the mean equator and mean equinox for 2000·0. Formulas exist, for a time
interval of ten years or so, that can provide the mean coordinates (α 1 ,δ 1 ) of a star at the beginning of
a year either before or after the reference epoch 2000·0. Thus, if (α, δ) are the mean coordinates of the
star at 2000·0, the mean coordinates at 2001·0aregivenby
α 1 − α = 3·s075 + 1·s336 sin α tan δ
δ 1 − δ = 20·′′ 043 cos α. (11.7)
The problem of computing the changes in the mean coordinates due to precession when the time
interval is more than a few years involves a more complicated procedure.
11.10 The cause of precession
Although Hipparchus discovered the phenomena caused by precession in the 2nd century BC, almost
two millennia had to elapse before Newton gave an explanation. Newton showed that it was due to the
gravitational attractions of Sun and Moon on the rotating, non-spherical Earth.
Newton argued on the following lines. If the Earth was perfectly spherical or if the Sun and Moon
always moved in the plane of the celestial equator, their net gravitational attractions would act along
lines joining these bodies to the Earth’s centre and so would produce no tendency to tilt the Earth’s
rotational axis.
The situation is quite different, however. Not only is the Earth an oblate spheroid with an
equatorial bulge but both Sun and Moon move in apparent orbits inclined to the plane of the Earth’s
equator. Let us consider the Sun. Its orbital plane is the plane of the ecliptic. Because of the asymmetry
of the gravitational forces acting upon the Earth’s particles of matter, the resultant solar attraction
does not pass through the Earth’s centre C but acts along the line DF (see figure 11.10). If the
Earth were non-rotating, this force would, in time, tilt the planet until the equator and the ecliptic
planes coincided. The Earth behaves, however, like a spinning-top. The spinning-top’s weight W acts
vertically downwards through its centre of mass G. The axis of spin AB precesses about the vertical
AV, always moving at right angles to the plane instantaneously defined by AB and AV so that the top
precesses, its spin-axis sweeping out a cone (see figure 11.11).
In the case of the Earth, the resultant gravitational pull of the Sun acting along DF causes the
Earth’s axis of rotation QP to sweep out a precessional cone of axis CK, CK being the direction to
the north pole of the ecliptic, K . The north celestial pole, therefore, traces out a small circle about K ,
of radius ε, in the precessional period of 26 000 years.