Great Circle Vertices

In my time teaching Gen Nav, I have found that many students struggle with Great Circle Vertices.

Wherever we are in the Northern Hemisphere there will be a point on the opposite side of the World which will be in the Southern Hemisphere. These points are known as the Northern and Southern Vertex.

We must remember that a Great Circle goes around the Earth and if we start at say 40^oN 100^oE then that will be the Northern Vertex and we cannot go any further north than this point.

Remember I said we are going round the Earth: so, what are we going to do when we leave the Northern Vertex?

At the Northern Vertex we can only be heading in one of two directions 090^o or 270^o thus we must travel in a southerly direction whether it be easterly or westerly when we leave the northern vertex.

The Southern Vertex is directly opposite the Northern Vertex so it must be at 40^oS. We started at 100^oE so what is the longitude of the Southern Vertex?

The two longitudes must add up to 180^o so:

180 – 100 = 080^oW

It must be west as it is opposite 100^oE.

If we are to do a full circuit and end up back at the Northern Vertex we must cross the Equator twice – the first crossing will be as we head to the Southern Vertex and the second as we head back to the Northern Vertex.

The crossing points will add up to 180^o just like the Vertices one East and one West and they will be 90o away from the Vertices:

100^oE – 90^o = 010^oE

080^oW + 90^o = 170^oW

Just be careful as 100^oE + 90^o = 190^oE which is not possible but becomes 170^oW.

Always draw a diagram:

Now we can work out what direction the GC will cross the Equator. It will always be an angle equal to the latitude of the vertices.

Let’s suppose we are travelling in an Easterly direction from the Northern Vertex of 40oN 100oE. If we are travelling East, we must also be going southerly as we are departing from the Northern Vertex so:

090 + 40 = 130^o

If we now continue travelling East back to the Northern Vertex:

090 – 40 = 050^o

Drawing a diagram will help:

If we were to travel in a westerly direction:

270 – 40 = 230^o to the S Vertex and then

270 + 40 = 310^o back to the N Vertex