Astronomy Principles and Practice Fourth Edition.pdf

The Sun as a position finder 413
Figure 24.7. The position of the sub-solar point.
The Sun’s geocentric zenith distance, z ⊙ , is found at this time by applying corrections for
sextant errors, refraction, semi-diameter and geocentric parallax to the observed altitude of the Sun
as measured by the sextant. Then it is readily seen that the observer must have been on the small circle
centred at L, found by drawing a circle of radius z ⊙ , centre S and allowing the cone it makes with the
Earth’s centre to intersect the Earth’s surface in a circle. This small circle is called a position circle.
Let us suppose that the observer’s position (i.e. latitude and longitude) does not change with time.
Some hours later, a second observation of the Sun’s altitude will provide a second position circle. The
observer must be at one of the two points of intersection of these circles when they are drawn on a
map. Since the points are usually hundreds of nautical miles apart, the observer usually has no doubt
as to which is the correct position.
The required information of the Sun’s Greenwich hour angle and declination can be derived from
The Astronomical Almanac, using the corrected chronometer times of the observations.
(ii) The position line. In practice, the observer makes use of the knowledge of the latitude and
longitude, φ D and λ D respectively, of the approximate position D (the so-called dead reckoning
position). This position will lie in the vicinity of the position circle. The line from D to the centre, L,
of the position circle will, therefore, cut it at some point V (see figure 24.8).
In the vicinity of V , we can use a straight line as an approximation to the position circle. Then the
observer will be on the straight line FJ tangential to the position circle at V and at a distance DV from
the dead reckoning position. If the length DV and the value of the azimuth, pDV, measured east of
north, can be found, then on a chart the position line, asFJ is called, can be plotted. The distance
DV is called the intercept (see figure 24.9). The angle pDV is obviously equal to PZS.Also
PZS = 360 ◦ − A
where PZS is within △PZS. Angle SPZ is the Sun’s hour angle H measured from the observer’s
meridian for the dead reckoning position D.
DV = ZW = SZ − SW.