Earth's Shape and Coordinate Systems
The Earth Model
For navigation the Earth is treated as an oblate spheroid flattened at the poles: the polar radius is about 6,357 km and the equatorial radius about 6,378 km. The difference matters for long-range work; for short legs a sphere is adequate. Positions are given as latitude (0° to 90° N or S of the equator) and longitude (0° to 180° E or W of Greenwich).
Latitude, Longitude and Distance
One minute of latitude is always one nautical mile (1,852 m). One minute of longitude equals one nautical mile only at the equator, shrinking as the cosine of latitude, so at 60° it is half a mile. This asymmetry is the single most examined idea in this domain.
Great Circles and Rhumb Lines
A great circle is the intersection of the Earth's surface with a plane through its centre; it is the shortest surface distance between two points and, except for the equator and meridians, crosses each meridian at a changing angle. A rhumb line cuts every meridian at the same angle; it is a straight line on a Mercator chart but is longer than the great circle except on the equator or a meridian. The vertex is the point of highest latitude on a great circle.
Traps
Questions often ask for the highest latitude reached (the vertex), the change of heading along a great circle, or the longitude spacing for a given distance. Remember convergence: meridians meet at the poles, so a constant heading does not give a straight ground track.
Rule of Thumb
Departure (nm) = change of longitude in minutes × cos(latitude). Example: 10° of longitude at 30°N = 600 × cos 30° = 600 × 0.866 = 520 nm.