If the Earth were flat, rectangular coordinates (x,y) would be sufficient to describe the locations of points on its surface. However, Earth is a sphere with no sides, and a special frame of reference is needed. The poles of Earth provide this reference frame.
The equator is an imaginary circle around the Earth located halfway between the north and south poles. Other lines drawn parallel to the equator but shifted to the north or south are called lines of latitude. At the equator the latitude is 0°, halfway to the pole it is 45°, and at the poles it is 90°
Lines running north/south through the poles are called lines of longitude (or meridians). Longitude is the number of degrees east or west of the prime meridian (0°) which passes through Greenwich, England.
Lines of Latitude | Lines of Longitude | |
Hawaii is in the northern hemisphere and is located 20° north of the equator and 155° west of the Prime Meridian (Greenwich, England) as shown on the cutaway globe to the right.
To the left is a map of the East Pacific ocean between Hawaii and the southwestern U.S. with latitude and longitude marked on its edges. The coordinates of Hawaii (20°N, 155°W) and Los Angeles (34°N, 118°W) are labeled. A red line connects these two points.
The distance between Hawaii and Los Angeles (the red line on the map above) can be calculated from their latitudes and longitudes.
A: Hawaii (20°N, 155°W)
B: Los Angeles (34°N, 118°W)
Latitude (phi) and longitude (theta) are related to
rectangular coordinates (x,y,z) by the relationship
(x,y,z) = (Rsin(theta)cos(90° - phi), Rsin(theta)sin(90° - phi), Rcos(theta) ) (1)
where R is the radius of the sphere.
Using these concepts, the distance, D, between Hawaii and Los Angeles can be calculated from the formula
D = R (0.7861)
Using the formula for D above, calculate the distance between Los Angeles and Hawaii. The radius of the Earth is R = 6370 km (3960 miles ).
Check your answer below, choose the distance closest to your number.