Global Positioning System Reference
In-Depth Information
on earth. According to special relativity, moving clocks tick more slowly. If
this theory were not taken into account, a NAVSTAR satellite clock would
fall behind ours by about 7 microseconds (ms) per day. On the other hand,
general relativity says that clocks close to a massive object (the earth) tick
more slowly than clocks that are farther away, and so the NAVSTAR clocks,
at an altitude of 20,200 km, should speed up compared with ours by about
45 ms per day. The net result is that if the designers of GPS did not account
for both forms of relativity, the satellite clocks would gain 38 ms every day
compared with our clocks on earth. That translates into a position error
that increases by more than 11 km per day, which would render GPS
useless. In fact, NAVSTAR clock rates are slowed down to cancel this e√ect.
Software in the receivers accounts for the special relativistic changes that
arise because of the di√erence in speed of a satellite as it passes overhead.
(The 14,000 km hr
-1
figure is an average; the speed relative to a receiver
depends upon satellite position above the receiver.)
Thus, most of the many sources of error for GPS have been anticipated
and eliminated, or else can be mitigated, resulting in an accurate and easy-
to-use system. The advantages for surveying are clear: GPS does not re-
quire a line of sight between two points, and it works at night or in condi-
tions of poor visibility. It can monitor large areas of land at any one time.
GPS has its limitations: it degrades when survey points are beneath a dense
canopy of trees, and it does not work in tunnels or mineshafts. Conse-
quently, theodolites and total systems will be with us for some time, and
yet I hope it is clear from this brief summary that GPS has changed the
game. Surveying and navigating are fundamentally di√erent from what
they were even 30 years ago; the di√erence is greater than that between
1980 and, say, 1680.
Surveying Techniques
So much for the tools of surveying. Now let's look at the techniques that
surveyors adopt when using these measuring instruments for the di√erent
types of surveys that are carried out.
The purpose of surveying is to determine accurately the position of
points on the earth's surface, and the angles and distances between these
points. The application of such information is varied. Traditionally, it has
been used to make maps of coastlines, establish land boundaries, and detail
the assets of newly conquered lands for tax purposes. To carry out their
