Q1. A great circle has its North vertex at 70N130E, at what longitude and in what direction would the great circle cross the equator assuming:
a. Initial direction is east from the northern vertex{ans-140W 160{T}}
b. Initial direction is west frm northern vertex{ANs-040E200{T}}
The centre of any great circle is at the centre of the Earth. This means that.
1. The vertices are at diametrically opposite latitudes. With one at 70N the other must be at 70S.
2. The vertices are at 180 degrees of longitude apart. With one at 130E the other must be at 050W.
3. The great circle crosses the Equator midway between the two vertices. With one vertex at 130E and the other at 050W the great circle crosses the equator at 040E. The second crossing point is 180 degrees of longitude away, which is at 140W.
The two vertices are at 70N and 70S, so a straight line (great circle) between the two crosses the Equator at an angle of 70 degrees (this is based on the definition of latitude).
This means that the great circle crosses the local meridians at the Equator at an angle of 20 degrees (which is 90 – 70 = 20).
This in turn means that the true tracks at the equator are 180 + 20 = 200 and 180 – 20 = 160.
If you do a simple sketch of the situation you should be able to see that the answers are as stated in your question.
Q2. Given that the compression value of the earth is 1/297 and that the semi major axis of the earth,measured at the axisof equator is 6378.4km,what is the semi major axis of the earth measured at the axis of the poles?
A compression of 1/297 means that the smaller axis is 296/297 of the larger axis.
So the answer is 6378.4 km x 296/297 = 6356.9 km.
Last edited by keith williams; 13th Oct 2011 at 13:54.