The shortest distance between two places measured along the surface of the earth, is A. Length of the equator between their longitudes B. Length of the parallel between their longitudes C. Length of the arc of the great circle passing through them D. None of these

The correct answer is C. Length of the arc of the great circle passing through them.

A great circle is the largest circle that can be drawn on a sphere. It is the only circle that divides the sphere into two equal hemispheres. The shortest distance between two points on the surface of the earth is the arc of a great circle that passes through those points.

Option A is incorrect because the length of the equator between two longitudes is not necessarily the shortest distance between those two points. For example, the shortest distance between New York City and London is not along the equator, but rather along a great circle that passes through both cities.

Option B is incorrect because the length of the parallel between two longitudes is not necessarily the shortest distance between those two points. For example, the shortest distance between New York City and Los Angeles is not along the parallel that passes through both cities, but rather along a great circle that passes through both cities.

Option D is incorrect because the shortest distance between two points on the surface of the earth is always the arc of a great circle that passes through those points.