The Sun as a position finder
 

At any particular instant, the apparent position of the Sun in the sky depends on the longitude and latitude of the observer. If positional measures of the Sun are used to determine the location with some degree of accuracy, an observer needs to use an optical instrument such as a theodolite or sextant and corrections such as those for refraction effects of the Earth’s atmosphere must be applied. Nowadays, an observer’s location on the Earth can be obtained to extreme accuracy by using GPS devices. Previous to the advent of such satellite technology, location fixes were derived from measurements by optical instruments.
It is of interest to note just how much GPS technology has improved the accuracy in respect of the location determination. Consider a simple situation of measuring the altitude of the Sun,, when
it is exactly on the meridian. The determination of the latitude of the observer based on this altitude measurement above would involve the relation

Any error made in the measurement is directly translated into a location error along the line of longitude, i.e. the determined value of ∅ will be displaced either N or S relative to the true position.
Suppose that optical measurements carry measurement uncertainties δ_θ = ±10 arc sec—this being typical of what can be achieved using simple optical equipment. In terms of the error, δd, in distance along the meridian, this corresponds to

where R_⊕ is the radius of the Earth. By substituting the appropriate value, δd ≈ 0·3 km.
By similar reasoning, an error in the knowledge of   or in the calculation of the refraction
correction to  of ±1'' introduces uncertainties in position of approximately ±0·03 km or ±30 m.
Currently available GPS devices provide positional determinations to accuracies more than 10 times better than this last figure, i.e. positional fixes to ±3 m are readily achieved, and it is very obvious why location by optical instruments has been abandoned. Such weather-dependent systems with their associated labour of subsequent numerical calculations are things of the past. It is, however, very instructive to use old optical devices to obtain data on the Sun’s position in the sky and on its apparent movement. In addition to providing data and gaining familiarity with various reduction procedures, their application gives some feel as to the accuracy to which simple hand-held optical instruments provide positional fixes of the Sun and how these are translated to a determination of the observer’s location on the Earth.
If such exercises are now attempted, it will be noted that The Astronomical Almanac or AA has evolved in ways more related to modern positional astronomy. Certain kinds of information are now presented differently relative to times past when positional determinations were regularly obtained from optical measurements. For example, the positions of the Sun (RA and δ) were formerly given for each day at 00^h UT rather than 00^h TDT as they are done currently. The examples provided here are from measurements obtained in recent times. Consequently, the presented numerical correction procedures are related to the present forms of the data tables and are slightly different than in the previous era.