What defines a great circle?

A great circle is defined as the shortest path between two points on the surface of a sphere. This is because a great circle divides the sphere into two equal halves and represents the largest possible circle that can be drawn on a sphere. When traveling between two locations, the great circle route minimizes the distance traveled, which is crucial for navigation and flight planning.

Understanding this concept is important in fields such as aviation and geography, where efficient travel routes are essential. For instance, when plotting the flight path of an aircraft, pilots and navigators use great circles to determine the optimal route, ensuring they take the shortest distance possible between destinations.

In contrast, the other options do not accurately represent the definition of a great circle. For example, while a constant direction track may refer to a rhumb line, it does not provide the shortest distance between two points; and a circular path around the north pole does not encompass all potential great circles, as multiple great circles pass through different pairs of points on a sphere. Thus, recognizing that the great circle is fundamentally about minimizing distance is key to understanding its significance.