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

I want to walk you through the foundation of how we define position on the Earth for navigation. Let's start with the big idea. Navigation is the process of directing an aircraft from one position to another. To do that, we need a Position Reference System — a way to define any position on the Earth's surface accurately and unambiguously, so there's no confusion about where we are or where we're going. Now, on a flat surface — like a sheet of graph paper — we can do this easily using Cartesian coordinates. That means we have two mutually perpendicular axes, an X axis and a Y axis, and we define a point by its distances ±x and ±y from where those axes cross. A real-world example of this is the UK National Grid System, used on Ordnance Survey Landranger Maps. That works perfectly on a flat plane. But the Earth is not flat — it's a sphere. So the Cartesian system has to be modified to work on a spherical surface. Instead of linear distances x and y, we replace them with angular coordinates. Those angular coordinates are called Longitude and Latitude. The first thing we need for this spherical system is to define the two mutually perpendicular axes — the equivalents of the X and Y axes on the flat system. And to define and use those axes, we need to understand two types of circles on the Earth: Great Circles and Small Circles. Let's focus on the Great Circle first. A Great Circle is a circle on the surface of the Earth whose centre and radius are exactly the same as the centre and radius of the Earth itself. It's called 'great' because if you cut a disc through the Earth in the plane of that Great Circle, that disc would have the largest possible area you can achieve — no other circle cut through the Earth can have a bigger cross-section. Here's the key practical fact for navigation: the shortest distance between any two points on the Earth's surface is the shorter arc of the Great Circle that joins those two points. That's why aircraft fly Great Circle routes — they're the most efficient path. Also, given any two points on the Earth's surface, there is only one Great Circle that joins them — unless those two points are diametrically opposed, meaning they're exactly opposite each other on the globe. In that special case, there are infinitely many Great Circles that pass through both points. So to summarise: we start with a flat Cartesian system using X and Y axes, then adapt it to a sphere using angular coordinates called Longitude and Latitude. The foundation of that spherical system is the Great Circle — a circle centred at the Earth's centre with the Earth's radius, giving us the shortest path between two points.