Astronomy Principles and Practice Fourth Edition.pdf

The Sun as a position finder 415
Figure 24.10. The intersection of two position lines allows the observer’s position to be determined.
or
In △PZS,wethenhave,
I = z − z ⊙ .
cos z = sin φ D sin δ ⊙ + cos φ D cos δ ⊙ cos H (24.1)
giving z and
sin z cos A = sin δ ⊙ cos φ D − cos δ ⊙ sin φ D cos H (24.2)
giving A.
(iii) The plotting chart. On the plotting chart a suitable scale is chosen, for example, one nautical
mile being represented by one centimetre, remembering that one minute of arc is equivalent to one
nautical mile. The north–south axis is a latitude axis but the east–west axis must be measured as
departure. To convert to difference of longitude, the usual relation is used, namely
departure = difference of longitude × cos(latitude).
In order to find the observer’s position, two position lines must be obtained from observations
made a few hours apart. The intersection of the two position lines (on both of which the observer lies)
will then give the increments in latitude and longitude (corrected from departure) to be applied to the
dead reckoning coordinates φ D and λ D .
It should be noted that if the dead reckoning position D happens to lie within the position circle
(in figure 24.8), the intercept DV will be negative since the observed zenith distance, z, is greater than
the calculated in the distance, z ⊙ . In this case, the intercept must be drawn in the opposite direction to
the azimuth, i.e. in a direction of azimuth 180 ◦ less than the calculated one. Thus, in figure 24.10, we
have a positive intercept, I 1 , and a negative one, I 2 .
The following scheme of instructions and data are taken from an exercise formerly carried out by
first-year students in Astronomy at Glasgow University. In the United Kingdom at that time, British