The navigator of an oil tanker uses the satellites of the Global Positioning System (GPS/NAVSTAR) to find latitude and longitude; see Fig. These are 43⁰36’25.3” N and 77⁰31’48.2” W. If the accuracy of these determinations is ±0.5”, what is the uncertainty in the tanker’s position measured along (a) a north-south line (meridian of longitude) and (b) an east-west line (parallel of latitude)? (c) Where is the tanker?

Now, 0.5’‘ of an arc with respect to the circumference of the Earth is
₀ =
= 3.9 x 10^-7
Substitute 40,000 for S in the equation _0.5S
_0.5S



Then, the range of the error is




Rounding off to two significant figures, the uncertainty in the tanker’s position measured along the north-south line is . 31 m.
(b)
The east-west range is smaller because the distance measured along latitude is smaller than the circumference by a factor of the cosine of the latitude.
Substitute 31m for R₁ and 43.6⁰ for in the equation . R = R₁ cos.
R = R₁ cos
= (31 m) (cos 43.6⁰)
= 22.449 m
Rounding off to two significant figures, the uncertainty in the tanker’s position measured along the east-west line is 22 m.
(c)
The tanker is in Lake Ontario. It is about 20 km off the coast of Hamlin.