What term describes any circle on the Earth's surface made by a plane passing through its center?

The term that accurately describes any circle on the Earth's surface made by a plane passing through its center is a great circle. Great circles have specific characteristics: they are the largest circles that can be drawn on a sphere and divide the sphere into two equal halves. The equator is an example of a great circle, as well as the lines of longitude when considering them as the full circles they form around the Earth.

Small circles, in contrast, are circles that do not divide the sphere into two equal halves and do not pass through the center; an example would be circles of latitude like those found north or south of the equator. The equatorial circle refers specifically to the equator itself, which is indeed a great circle but does not encompass all circles made through the Earth's center. The term orbital circle does not apply directly to the geometric description of the Earth’s regions but rather refers to circular paths taken by celestial bodies.

Understanding these distinctions is key to grasping fundamental concepts in spherical geometry and navigation.