### Great Circles

In this lesson we will be discussing about Great Circles, their properties and importance. Great circles are circles drawn on the surface of earth with their centre & radius same as that of the earth. Equator is an example of a great circle with the centre and radius same as that of the earth.

One of the important properties of a great circle is that, the plane of the great circle divides earth into two equal halves. Also, only one great circle can be drawn between any two points two points. There is only one exception to this rule. The exception is, when the selected points are diametrically opposite to each other, infinite great circles can be drawn joining those points.

### Great Circle Distance

Let us understand a little about Great circle distances. Great Circle distance is the shorter arc of the great circle joining the selected points. Imagine that the two selected points are your departure and destination. The shorter arc of the great circle drawn between those two points would be the shortest distance between two points on earth’s surface.

In the later chapters on distances and nautical miles you would realise that the complete diameter of the Great circle will be equal to the circumference of the earth. Earths circumference is equal to 40,000 KM or 21,600 NM.

### Vertices of a Great Circle

Northern vertex is the northern-most point of a great circle and the Southern vertex is the southern-most point of a great circle. The northern & southern vertices of a great circle are antipodal. The word anti-podal means diametrically opposite to each other. So, if you are flying a great circle track between two points the you would be closest to the north pole when you are at the northern vertex and closest to the south pole when you at the southern vertex. Distance between the northern and southern vertices is exactly half the total length of a great circle, hence would be half of 21,600 which would be 10,800 NM

### Properties of Vertices

Vertices of a great circle has certain peculiar properties. The northern and southern vertices lie on the same latitude on opposite hemispheres. Let’s say the northern vertex lies at 50-degree North latitude, then its southern vertex will have to be at 50-degree South. The vertices of a great circle will be placed in the respective meridian & anti-meridians. If the northern vertex of a great circle is at 000 meridian, then its corresponding southern vertex would be in 180 EW meridian. Great circle direction at either vertex will be easterly (090) or westerly (270)

### Equatorial Crossing of a Great Circle

Let us discuss what will be the position and orientation of a Great circle when it crosses over the equator. All great circles will cut equator at two points only. When the great circle crosses the equator, the angle made between the equator and great circle will be equal to the latitude of the point. Similarly, the longitude at which the great circle crosses the equator would be 90 degrees removed from its vertex longitude.

### Example of Vertex

Let us talk with an example. If a great circle has its northern vertex at 50 N 000 EW its southern vertex would be at 50 W 180 EW. This great circle would cross the equator 090 E and 270 W and the angle made between the great circle and plane of equator would be equal to 50 degrees

### Meridians and Equator

Meridians are also great circles with vertices at 90 North & 90 South. In short, the North and South Poles would be the vertices of meridians. Meridians will cut equator at directions of 000 & 180 degrees; that’s northerly and southerly directions. Logically correct, since their angle with plane of equator will be 90 degrees which are same as that of their vertices at 090 north and south.

Equator is also a great circle with vertices at 0 degrees. As we had discussed the direction of any great circle at their vertices is always easterly that is 090 or westerly that is 270 degrees. Equator is a unique great circle since all the points on equator are its vertices meaning their northern and southern most points