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Chapter 1: Problem 13

Define a great cirde, great cincle routes, and a small cincle. In terms of these concepts, describe the equator, other parallels, and meridians.

Short Answer

Expert verified
Great circle is the largest circle that can be drawn on a sphere, made by a plane that passes through sphere's center. Great circle routes are shortest paths between two points on a sphere's surface. Small circle is a circle on a sphere's surface with a radius less than sphere's. The equator is a great circle, other parallels are small circles, and meridians are great circles.

Step by step solution

01

Define Great Circle

A great circle of a sphere, also known as an orthodrome, is the intersection of the sphere and a plane that passes through the center point of the sphere. This creates the largest circle that can be drawn on a sphere.
02

Define Great Circle Routes

Great circle routes are the shortest possible path between two points on the surface of a sphere. They are often used in navigation and aviation.
03

Define Small Circle

A small circle is any circle on the surface of a sphere that has a radius smaller than that of the sphere. In other words, a small circle is created when a sphere is intersected by a plane that does not pass through the center of the sphere.
04

Relate Concepts to Equator, Parallels, and Meridian

The equator is an example of a great circle. As it goes around the middle of the earth, the plane that would create the equator does pass through the Earth's center. Other parallels (lines of latitude) are examples of small circles - they do not pass through the Earth's center. Meridians (lines of longitude), however, are all great circles, as they do pass through the Earth's center.

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