Astronomy Principles and Practice Fourth Edition.pdf

Chapter 10
The reduction of positional observations: I
10.1 Introduction
In general, astronomical observations of an object’s position undergo a process of reduction. This
procedure removes known instrumental errors and other systematic effects in order to provide data
about the celestial body that is as objective as possible.
Such reduced observations, independent of the observer’s position, are then suitable for catalogue
purposes or for comparison so that changes in the body’s position with time can be derived. The
raw observations may be the altitude (or zenith distance) and azimuth of the object, its hour angle and
declination, or its position (on a photographic plate or CCD frame) with respect to a stellar background.
In addition, a time is noted at which the observation was made; this time may be a Universal Time (UT)
or a Local Sidereal Time (LST).
If the altitude and azimuth of the object are measured, the first corrections to be applied are known
instrumental errors. This entails a frequent calibration of the observing instrument since such errors
are not, in general, static.
The philosophy behind the correction procedures described here is that they are related to small
effects. They are, therefore, to the first order in small quantities, independent of each other and can be
applied in any order. The end product will usually be a geocentric equatorial position for the object or
a heliocentric ecliptic position or even, in the case of a star cluster or galaxy, a galactocentric equatorial
position.
We now describe the corrections in turn.
10.2 Atmospheric refraction
10.2.1 The laws of refraction
When a ray of light passes from a transparent substance of one density into another transparent
substance of a different density, the ray changes direction. It is said to be refracted and the amount
of the deviation from its original direction depends upon the relative densities of the substances.
Let a ray of light, AB, passing through a vacuum, meet the upper boundary PQ of a plane parallel
slab of glass at an angle i to the normal BN to the slab (figure 10.1). The angle NBA is called the
angle of incidence. The ray is refracted upon entering the slab so that it leaves the lower boundary RS
of the slab at C. Angle MBC,orr, is called the angle of refraction and is less than i. The ray’s path
on leaving at the point C is along the line CD, at an angle ZCD to the normal ZC.
Then the first law of refraction states that the incident ray AB, the normal BN and the refracted
ray BC are coplanar.
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