Global Positioning System Reference
In-Depth Information
proposed and brought before them. Anyone who had a sensible suggestion
(and more than a few with nonsensical suggestions, as it turned out) could
be considered. The prize was specified in detail: if a reliable solution
provided a ship's navigator with an estimate of longitude that was in error
by no more than one degree of arc, then the prize would be £10,000. For a
solution accurate to within 40' of arc, the prize would be £15,000, and for a
solution accurate to within 30' of arc, £20,000. (One minute of arc corre-
sponds to a distance of one nautical mile.) In addition, the board could
award discretionary benefits and expenses incurred, including advances
for anticipated expenses.
Such was the extent of the problem—or, to be more precise, the di≈-
culty of providing a workable solution—that the board sat for more than a
century. It finally was dissolved in 1828, and by then there were two
methods that were known to work, and had been known to work for half a
century. The reason for the long interval between finding a reliable method
and disbanding the board was that the solutions needed to be tweaked in
order to make them a√ordable enough that every ship venturing into open
ocean would be able to determine its latitude and longitude.
14
Measuring longitude accurately is equivalent to measuring time accu-
rately because the earth rotates at an angular rate of 15\ per hour.
15
Thus, to
take a simplified hypothetical example, let us say that a navigator on board
an English ship in the Mediterranean Sea looks at his pocket watch (which
is perfectly accurate and which he has not adjusted since he left home port)
and sees that local sunrise occurs at exactly 7:20 a.m. Greenwich Mean
Time. He consults an almanac and reads that, for this day of the year, sun-
rise at Greenwich, London, occurs at exactly 6:00 a.m. GMT. Thus, the ship
is 80 minutes ahead of Greenwich. From the rate at which earth rotates, we
see that this time di√erence converts to a longitude di√erence of exactly
20\. The navigator determines that his ship is 20\ east of Greenwich.
You see the catch: to estimate his longitude, the navigator needs to
know the time at Greenwich more accurately than any pocket watch of the
day could achieve. He can measure the Greenwich Mean Time in a number
of di√erent ways, and we will unpack these di√erent methods over the next
few sections. Note also that a reference longitude is required. It took a very
14. The story of the longitude problem and its solution has been told many times. The
interested reader should consult Howse (1980), Sobel (1996), Taylor (1971), and especially
Andrewes (1993). There are also many articles online.
15. I might also refer to the angular rate of the earth, confusingly, as 15 seconds per
second, or 15& s
-1
. That is, the earth rotates through 15 seconds of arc per second of time.
