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 0
c. Which latitude circle has a circumference of about 3593 kilometers?
d. What is the circumference of the equator?

Answer 1

a) circumference of great circle=40212.4km

b) circumference of latutude circle=40212.4cos
`\theta` kilometers

c)The latitude circle is at an angle of 84.9°

d)Circumference of equator=40212.4km

Explanation:

Refer to the figure shown below, we are given that earth has been charted with vertical and horizontal line and horizontal lines are called latitude lines.

So every horizontal line corresponds to a circle.

So the great circle will have radius equal to earth radius.

a)we are given with earth radius=6400km.

Hence circumference of a great circle= 2πX6400=40212.4km

b)At a latitude with angle x=
`\theta`, the circumference of latitude circle =
`40212.4cos\theta`

c)If a latitude circle has a circumference of about 3593km,

then
`40212.4cos\theta=3593`

`cos\theta=(3593)/(40212.4) =0.0894`

`\theta=cos^(-1)(0.0894)`=84.9°

Hence the latitude circle is at an angle of 84.9°

d) At equator angle is 0.

Hence circumference of equator=40212.4cos(0)=40212.4km