Question

Earth has been charted with vertical and horizontal lines so that points can be named with coordinates. The horizontal lines are called latitude lines. The equator is latitude line 0. Parallel lines are numbered up to pi/2 to the north and to the south. If we assume Earth is spherical, the length of any parallel of latitude is equal to the circumference of a great circle of Earth times the cosine of the latitude angle. a. The radius of earth is about 6400 kilometers. Find the circumference of a great circle. b. Write an equation for the circumference of any latitude circle with angle theta c. Which latitude circle has a circumference of about 3593 kilometers? d. What is the circumference of the equator?

Answer 1

a. The radius of earth is about 6400 kilometers. Find the circumference of a great circle.

Circumference = 2π(radius) = 2π(6400 km) = 40.212,39 km

b. Write an equation for the circumference of any latitude circle with angle theta

As stated, the length of any parallel of latitude (this is the circumference of corresponding circle) is equal to the circumference of a great circle of Earth times the cosine of the latitude angle:

=> Circumference = 2π*radius* cos(Θ) = 2 π*6400km*cos(Θ) = 40,212.39 cos(Θ)

Answer: circumference = 40,212.39 cos(Θ) km

c. Which latitude circle has a circumference of about 3593 kilometers?

Make 40,212.39 cos(Θ) km = 3593 km

=> cos(Θ) = 3593 / 40,212.39 = 0.08935 => Θ = arccos(0.08935) = 84.5° = 1.48 rad

Answer: 1.48

d. What is the circumference of the Equator?

For the Equator Θ = 0°

=> circumference = 40,213.49cos(0°) km = 40,212.49 km

Answer: 40,212.49 km