Astronomy Principles and Practice Fourth Edition.pdf

344 Modern telescopes and other optical systems
Figure 20.12. Measurements of two stars on the meridian using the zenith tube.
screw so that the transit is made along the same wire. The difference between the settings of the wire
is read off the micrometer and this is then converted to angular measure.
Suppose that two stars have declinations δ 1 and δ 2 and appear on the meridian at a particular site
when the zenith distances are z 1 and z 2 (see figure 20.12). The measurements made by the zenith tube
provide a value for (z 2 − z 1 ).
By considering sections 8.2 and 8.3, it is readily seen from figure 20.12 that the latitude, φ,ofthe
observing station is given by
φ = δ 1 + z 1 . (20.4)
It can also be seen from the same figure that
δ 2 = δ 1 + z 1 + z 2 = δ 1 + 2z 1 + (z 2 − z 1 ).
Therefore,
z 1 = (δ 2 − δ 1 )
2
By substituting equation (20.5) into (20.4), we have
φ = δ 1 + (δ 2 − δ 1 )
2
− (z 2 − z 1 )
. (20.5)
2
− (z 2 − z 1 )
2
or
φ = (δ 1 + δ 2 )
− (z 2 − z 1 )
. (20.6)
2 2
Thus, the latitude of the observing station is the mean of the stars’ declinations, corrected for half
the difference of their zenith distances.
Accurate positions of longitude may be determined if the transit times are also recorded.
20.7 Portable positional instruments
20.7.1 The theodolite
For some purposes, such as surveying, it is useful to have some kind of portable instrument which is
capable of determining the position of an observer from measurements made of astronomical objects.
Such an instrument is the theodolite.