# Latitude

## 1. Latitude and longitude ↑

People split the Earth into lines of latitude and longitude in order to help with navigation. Latitude lines are lines around the Earth moving from north to south, and a person's latitude determines how far north or south they are in degrees. At the equator, the latitude is 0° and it is 90° at the poles. Longitude lines, or meridians, circle the Earth from east to west.

Latitude and Longitude. Image credit: Djexplo/Public domain.

## 2. Measuring latitude ↑

You can work out your latitude by measuring the angle of the Sun, relative to a stick placed vertically in the ground at noon, when the Sun is highest in the sky.

At the equator, the Sun will be perpendicular to the ground, but as you move away, the Sun will seem tilted because you are on a surface that is tilted. At the pole, you are standing at a 90° angle to how you would be standing on the equator.

An illustration of the effects of a spherical Earth on shadows, where the dark yellow lines represent individual rays of the Sun, and the red lines represent objects that block the light. The effects of a spherical Earth on the atmosphere are also shown, where light travels through more of the atmosphere at sunrise and sunset. This makes the light appear redder. This is an approximation because the Earth is tilted by about 23.4°. Image credit: modified by Helen Klus, original image by NASA/Public domain.

This is not strictly true, however, because the Earth is titled at an angle of about 23.4°.

### 2.1 Seasons and the tilt of the Earth ↑

There is an angle of about 23.4° between the ecliptic, the path the Sun and planets appear to travel through, and the celestial equator, which runs through the centre of the Earth between the North and South Poles. This angle is known as the obliquity of the ecliptic.

The tilt of the Earth. Image credit: modified by Helen Klus, original image by Andrea Pittalis/CC-SA.

The tilt of the Earth means that the light of the Sun arrives from different angles over the course of a year. This causes the seasons to change, where summer occurs on the side of the Earth that is tilted towards the Sun, and winter on the side that is tilted away.

Image credit: modified by Helen Klus, original image by Tfr000/CC-SA.

It's hotter in the summer for the same reason that it's hotter at the equator: light loses less energy - meaning it has a shorter wavelength and is therefore bluer - when it travels through less atmosphere.

The summer solstice occurs when the part of the Earth you are on is tilted towards the Sun at the highest possible angle; this occurs on June 21st in the northern hemisphere, and on December 21st in the southern hemisphere.

The winter solstice occurs when the part of the Earth you are on is tilted towards the Sun at the lowest possible angle; this occurs on December 21st in the northern hemisphere, and on June 21st in the southern hemisphere.

### 2.2 Eratosthenes ↑

In order to measure your true latitude, you need to know the angle the Earth is tilted by.

Ancient Greek astronomer Eratosthenes first measured the tilt of the Earth in about 240 BCE[1]. He did this by measuring the angle of the Sun on the summer and winter solstices, where the difference between these two values is twice the angle that the Earth is tilted by.

The Earth's axial tilt. Image credit: Helen Klus/CC-NC-SA.

The Earth is tilted by about 23.4°, and so to find your latitude at the summer solstice, you need to add 23.4° to the angle you measure in order to get your correct latitude. During the winter solstice, you need to deduct 23.4°, and at any date in between, you need to work out the angle, knowing that it changes by 23.4° every six months, and therefore about 0.13° per day.

In the northern hemisphere, you can also calculate the tilt of the Earth, and therefore your latitude, by looking at the angle of the North Star. At the North Pole, it will be straight above you, 90° from the horizon, and at the equator, it will be straight ahead, 0° from the horizon.

In order to know your full position, however, you need East-West as well as North-South coordinates, and for this, you need to know your longitude.

## 3. References ↑

1. Agarwal, R. and Sen, S., 2014, 'Creators of Mathematical and Computational Sciences', Springer.