Astronomy Principles and Practice Fourth Edition.pdf

114 The reduction of positional observations: I
Figure 10.3. Refraction by the Earth’s atmosphere of light from a star.
10.2.2 Astronomical refraction
Aircraft, balloons, high altitude rockets and artificial satellites have been used to measure the way in
which the density of the Earth’s atmosphere diminishes with the increase of height above the Earth’s
surface. The density is still appreciable enough at 150 km height to produce changes in the orbit of
an artificial Earth satellite due to air-drag. In addition, studies of aurorae show that there is still some
atmosphere up to a height of 800 km. A ray of light entering the Earth’s atmosphere from outer space
will be bent or refracted so that the observed direction of the source of light must be different from
its true direction. It is found, however, that the air-density falls off so swiftly with height that above
the 100 km level, no appreciable refraction takes place. Since the radius of the Earth is 6372 km,
evaluation of atmospheric refraction can neglect the curvature of the atmosphere so long as we deal
with zenith distances less than about 45 degrees.
In figure 10.3, the atmosphere is, therefore, taken to be made up of a large number of thin parallel
layers of different densities, the density being greatest at the Earth’s surface and constant within each
layer. Above the atmosphere is the vacuum of space. A ray of light from a star meets the topmost
layer of the atmosphere at B, the angle of incidence being NBA,ori, and is thereafter refracted in
successive layers until it reaches the observer at O. Its direction in the last layer being LO,thestar
appears to lie in the direction OL, of apparent zenith distance ZOL,orζ . In fact, if OX is drawn
parallel to BA,angleZOX,orz, is the true zenith distance of the star at the time of observation. Since
the direction of increasing density is downwards, the index of refraction also increases in that direction,
so that the star is displaced towards the zenith along the great circle through Z and X, whereX is the
true position of the star.
If n is the index of refraction of the bottom layer we have, from equation (10.2),
sin i = n sin r