Great circle

Great circle, axis, and poles

Great circle hemispheres.png

Great circle

A great circle is the largest possible circle that can be drawn on a sphere. It is formed by the intersection of the sphere with a plane that passes through the center of the sphere. Great circles are significant in various fields such as geography, navigation, and astronomy.

Properties

Great circles have several important properties:

• They divide the sphere into two equal hemispheres.
• The shortest path between any two points on the surface of a sphere lies along the arc of a great circle. This is known as a geodesic.
• All great circles have the same circumference, which is equal to the circumference of the sphere.

Applications

Navigation

In navigation, great circles are used to find the shortest route between two points on the Earth's surface. This is particularly important in aviation and maritime navigation. The great circle route is often referred to as the orthodromic route.

Geography

In geography, the Equator and all lines of longitude are examples of great circles. The Equator is the only line of latitude that is a great circle. Other lines of latitude are smaller circles and are called parallels.

Astronomy

In astronomy, great circles are used to define the celestial sphere. The celestial equator and the ecliptic are examples of great circles on the celestial sphere.

Mathematical Representation

A great circle on a sphere of radius \( R \) can be represented mathematically by the equation: \[ x^2 + y^2 + z^2 = R^2 \] where \( (x, y, z) \) are the coordinates of a point on the sphere.

See Also

• Geodesic
• Orthodromic route
• Equator
• Longitude
• Celestial sphere
• Ecliptic