Find the shortest distance from Honolulu to Melbourne, Australia, latitude 37°47'S, longitude 144°58'E. Round your answer to the nearest mile.

The shortest distance between two points on Earth's surface can be determined from the latitude and longitude of the two locations. For example, if location 1 has (lat, lon) = (α₁, β₁) and location 2 has (lat, lon) = (α₂, β₂), the shortest distance between the two locations is approximately

d = rcos^-1[(cos α₁ cos β₁ cos α₂ cos β₂) + (cos α₁ sin β₁ cos α₂ sin β₂) + (sin α₁ sin α₂)]

where r = radius of Earth ≈ 3960 miles and the inverse cosine function is expressed in radians Also N latitude and E longitude are positive angles while S latitude and W longitude are negative angles.