Use the formula in Exercise 1 to calculate the great circle distance between
(a) Washington, D.C. (39° north latitude, 77° west longitude) and Moscow, Russia (56° north latitude, 283° west longitude)
(b) Blountville, Tennessee (36° north latitude, 82° west longitude) and Seattle, Washington (47° north latitude, 123° west longitude)
(c) two of your favorite spots on the earth
Exercise 1
The prime meridian is the great circle arc that passes through the earth’s north pole, south pole, and Greenwich, England. Place the origin of a coordinate system at the center of the earth so that the positive z-axis passes through the north pole and the positive x-axis passes through the intersection of the prime meridian with the equator. We define the longitude of a point on the earth’s surface with spherical coordinates (R, θ, ϕ) to be the angle given by
Θ = 360° – θ,
and the latitude of such a point is
Φ = 90° – ϕ
(where both θ and ϕ are measured in degrees). Find a formula for the great circle distance between one point with latitude and longitude Θ1 and Φ1 and a second with latitude and longitude Θ2 and Φ2. (Take the radius of the earth to be 6370 km.)
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