Distance between Cities Find the distance in kilometers between each pair of cities, assuming they lie on the same north-south line. Assume the radius of Earth is 6400 km. See Example 2. Panama City, Panama, 9° N, and Pittsburgh, Pennsylvania, 40° N

Key Concepts

Great Circle Distance

The great circle distance is the shortest path between two points on the surface of a sphere. For cities located along the same north-south line, this distance can be calculated using the difference in their latitudes. The formula involves the Earth's radius and the angular difference in degrees, allowing for a straightforward calculation of distance in kilometers.

Latitude

Latitude is a geographic coordinate that specifies the north-south position of a point on the Earth's surface. It is measured in degrees, with the equator at 0° and the poles at 90° N or S. Understanding latitude is essential for calculating distances between cities that are aligned vertically, as it directly influences the great circle distance.

Earth's Radius

The Earth's radius is the average distance from the center of the Earth to its surface, approximately 6400 kilometers. This value is crucial for calculating distances on the Earth's surface, particularly when using spherical geometry. In the context of the problem, it serves as a constant in the formula to convert angular differences in latitude into actual distances.