# Celestial navigation explained

## Introduction

 It is possible to find your position on Earth just by observing a few stars... Celestial mechanics is precision mechanics and this allows calculating the exact position of a heavenly body (star, planet, moon, sun) in the sky at any given time. Knowing the position of the star in the sky, the measure of the angle between the horizon of the observer and the star, using a sextant, is enough to determine the observer’s position in latitude and longitude (in fact, we will see that at least two measures are needed). Let's show this using an example: imagine you observe a lighthouse from a certain distance. With the sextant, you measure the angle alpha corresponding to the height of the lighthouse seen from your position. If you know the height h, you can find your distance d from the lighthouse. On a chart, you can draw a circle centred on the lighthouse with a radius d. You are somewhere on the circle. This is your circle of position.
 A second observation will give you a second circle of position. You are at the intersection of the circles of position. In fact, there is most often two intersections but your estimated position or a third observation will help you to choose the right one. If you don't observe a lighthouse but the angle between your horizon and a star, you are doing celestial navigation. That's it! Of course, at this stage we need to look a little bit closer at the celestial mechanics to understand how we can calculate the exact position of a heavenly body (star, planet, moon, sun) in your local sky at any given time and which mathematical relation is linking the altitude of a body to a circle of position. Unfortunately, it is not as simple as tan(alpha) = h / d. ## Celestial mechanics - a blueprint Imagine the Earth in space, and surrounded by a celestial sphere on which all the heavenly bodies are moving. This is a quite simple representation of the universe, but this is enough for our purpose. The celestial sphere is centred on Earth with the celestial equator passing through the Earth equator and the axis "Earth centre C to North Pole" defining the axis of reference of the celestial sphere. A plan of reference defined on Earth is also used on the celestial sphere: the Greenwich meridian. On the celestial sphere, we show a star S and its hour circle. The star in the sky is like the lighthouse in the earlier example.