Shortest Distance from Chicago to Honolulu Find the shortest distance from Chicago, latitude41,50N
longitude87,37W
to Honolulu, latitude 21,18N
longitude 157,50W
. Round your answer to the nearest mile.
The Correct Answer and Explanation is:
The shortest distance is 4,254 miles.
The shortest distance between two points on a spherical surface like the Earth is not a straight line as depicted on a flat map. Instead, it is an arc of what is known as a great circle. A great circle is any circle drawn on the globe with a center that coincides with the center of the Earth. The equator is a prime example of a great circle. This path, often called the great circle route, is the most direct and efficient trajectory for long distance travel, which is why airplanes typically follow these routes to conserve fuel and time.
To calculate this distance, a mathematical formula called the Haversine formula is used. This formula is specifically designed to determine the great circle distance between two points on a sphere from their latitudes and longitudes. The calculation requires several key inputs: the latitude and longitude coordinates for both Chicago (41.50° N, 87.37° W) and Honolulu (21.18° N, 157.50° W), along with the average radius of the Earth, which is approximately 3,959 miles.
The formula first computes the differences in latitude and longitude. It then uses trigonometric functions to calculate the central angle between the two cities. This is the angle created by drawing lines from each city’s location on the surface to the Earth’s core. Once this central angle is found, it is multiplied by the Earth’s radius. This final step converts the angular separation into a real world distance. The resulting calculation reveals that the arc connecting Chicago and Honolulu along this great circle path measures approximately 4,254 miles when rounded to the nearest mile, representing the true shortest distance between the two locations.
