Direction, Latitude and Longitude 1 — Page 8, Lesson 18

Let's begin our study of navigation with the very foundation: how we define a position on the Earth. Navigation, at its core, is the process of directing an aircraft from one position to another. To do that safely and precisely, we need a Position Reference System — a method that defines a position accurately and unambiguously on the Earth's surface. Think about a flat surface first, like a sheet of graph paper. There, we can define any point using Cartesian coordinates, which are the familiar ±x and ±y values measured from two mutually perpendicular axes — the X axis and the Y axis. This system is used in the UK National Grid System, for example on Ordnance Survey Landranger Maps. It works perfectly on a plane. But here's the problem: the Earth is not flat. It's a sphere. So the Cartesian system must be modified to work on that spherical surface. In practice, we replace the linear coordinates x and y with angular coordinates — and those are what we call Longitude and Latitude. Before we can use them, though, we need to define the two mutually perpendicular axes on the sphere, the equivalents of the X and Y axes. And that definition involves two types of circles on the Earth: Great Circles and Small Circles. Let me define a Great Circle precisely, because it's central to everything. A Great Circle is a circle on the surface of the Earth whose centre and radius are those of the Earth itself. In other words, if you cut through the Earth with a plane that passes through its centre, the circle you trace on the surface is a Great Circle. It's called "great" because a disc cut through the Earth in the plane of that Great Circle would have the largest area that can be achieved — no other circle on the surface can enclose a larger area. Now, why does this matter for navigation? Because of a fundamental rule: the shortest distance between two points on the Earth's surface is the shorter arc of the Great Circle joining those two points. That's the path a great-circle route takes — it's the true shortest way between two places on a sphere. One more important property: given two points on the Earth's surface, there will be only one Great Circle joining them — unless the points are diametrically opposed, meaning they're exactly opposite each other on the globe, like the North and South Poles. In that special case, an infinite number of Great Circles pass through both. So hold onto these ideas: Great Circles are the largest possible circles on the Earth, they define the shortest path between two points, and they're unique for any two non-opposite points. These circles are going to be the building blocks for our latitude and longitude axes.