Because any 'Great Circle' is the shortest distance across a sphere.
Where the Earth is concerned , all the meridians and the Equator are Great Circles.
The Plane of a 'Great Circles ' 'cut' the sphere into two equally sized hemispheres.
NB Other than the Equator all the latitudes are NOT great Circles.
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Because on a globe, a great-circle route is the shortest route between two places.
Let's be very careful here: The "great circle" of a sphere is a circle that lies on the surface ofthe sphere, so there's no way the great circle can "pass through" the sphere's center.However, in order for the circle to be a "great circle", its center must be the center of the sphere.
Yes the great circle formula is the same formula for any other circle.
Say you're planning a plane flight from Chicago, Illinois to Tokyo, Japan. If you use a flat map, your shortest distance may require a fuel stop, or two. If you use the great circle, you might be able to make it in one flight, and also save several hours of flight time. Navigation, fuel conservation, living in a 3D world.
Pi can be used to calculate the area of a circle Pi can be used to calculate the circumference of a circle