How We Came to Know the Cosmos: Space & Time

# Chapter 2. Latitude and Longitude

## 2.1 Latitude and longitude

People split the Earth into lines of latitude and longitude 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. The latitude is 0° at the equator and 90° at the poles. Longitude lines, or meridians, circle the Earth from east to west, and a person’s longitude determines how far east or west they are in degrees. The meridian that passes through Greenwich, in London, is set at 0° longitude for historical reasons.

 Figure 2.1Image credit Latitude and longitude lines.

## 2.2 Measuring latitude

You can work out your latitude by measuring the angle of the Sun at noon, when the Sun is highest in the sky. You can do this by placing a stick in the ground and looking at the angle of its shadow.

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 would be standing at a 90° angle to how you would be standing on the equator. This is not strictly true, however, because the Earth is tilted at an angle of about 23.4°.

 Figure 2.2Image credit An illustration of the effects of a spherical Earth on shadows, where the yellow lines represent individual rays of the Sun, and the brown 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°.
 Figure 2.3Image credit The tilt of the Earth.

### 2.2.1 Seasons and the tilt of the Earth

The tilt of the Earth means 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 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’s tilted towards the Sun, and winter on the side that’s tilted away.

 Figure 2.4Image credit The seasons are caused by the tilt of the Earth.

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 and hotter (as discussed in Book II) - when it travels through less atmosphere.

The summer solstice occurs when the part of the Earth that 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 that 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.

 Figure 2.5Image credit Eratosthenes measured the Earth’s axial tilt by measuring the angle of the Sun on the summer and winter solstices.

### 2.2.2 Eratosthenes and the tilt of the Earth

The 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 is tilted by about 23.4°, and so to find your latitude on the summer solstice you need to add 23.4° to the angle you measure. 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.

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.

## 2.3 Measuring longitude

Longitude is much harder to calculate than latitude. The Earth rotates 360° per day, which is 15° per hour, and so there’s a direct relationship between longitude and the time that the Sun rises and sets. The Greenwich meridian is designated 0° longitude; the Sun sets an hour earlier every 15° east of this and one hour later every 15° west.

 Figure 2.6Image credit Time zones are caused by the rotation of the Earth.

If you know the difference between the time of the sunset in your location and another known location, then you can work out how far east or west you are from there.

Hipparchus suggested that longitude could be measured by comparing the time of a lunar eclipse at different locations in about 127 BCE, but timekeeping devices were too inaccurate to actually do this.[2]

### 2.3.1 The first mechanical clocks

Early clocks included sundials, which can be used to measure the movement of the Sun across the sky by marking where a shadow falls, and sand clocks, candles, incense sticks, and water clocks, which are all used to measure constant time durations.

Water clocks measure how long it takes for water to flow from one place to another. These existed in ancient Egypt, Babylon, India, and China.

Mechanical clocks were first built in 13th century Europe. These use an escapement mechanism, which was first designed by the Chinese polymath Su Song in 1088. An escapement is a device that supplies energy to the timekeeping element and allows each cycle to be counted. In Song’s clock, it was driven by water.[3]

In medieval clocks, the escapement mechanism is composed of a verge and foliot, where verge refers to a vertical rod connecting a wheel, shaped like a crown, to the foliot. The foliot is a horizontal beam with weights attached to either side. The rod has two metal plates, the pallets, which are placed at the top and bottom of the wheel.

 Figure 2.7Image credit A verge and foliot escapement mechanism.

The foliot moves back and forth, which causes the verge and pallets to rotate. This turns the wheel, which can be attached to the hands on the clock via a series of wheels, so the hands on the clock move every time the foliot swings.

The Ottoman Turkish polymath Taqi al-Din invented the first known alarm clock, the first watch, and the first clocks that measure time in minutes and seconds. In 1551, he invented a rudimentary steam engine.[4]

### 2.3.2 The first pendulum clocks

The Italian natural philosopher Galileo Galilei became the first person to suggest using a pendulum to measure time in 1602. Galileo discovered that the time it takes for a pendulum to swing back and forth, its period, does not depend on how far it swings or how massive the pendulum is. The time it takes is, however, proportional to the square root of the length of the pendulum.[5]

 P ∝ √ ℓ (2.1)

Here, P is the period of the pendulum and is the length of the pendulum.

The pendulum was the first harmonic oscillator to be studied scientifically. A harmonic oscillator is a system that, when moved from equilibrium, experiences a force that restores it to its original position. If the restoring force is the only force involved, then it is called a simple harmonic oscillator. The Dutch natural philosopher Christiaan Huygens built the first pendulum clock in 1656.[6]

 Figure 2.8Image credit A diagram of Christiaan Huygens’ pendulum clock by Huygens, 1673.

In 1660, the English natural philosopher Robert Hooke showed that a spring acts similarly to a pendulum, where the force needed to compress a spring is proportional to the length you compress. Hooke used a pendulum to model the orbits of the planets, and in about 1666, he suggested that the pendulum could be used to measure the acceleration due to gravity (g).

 P = 2π √ℓ/g (2.2)

This equation would later be explained by the English natural philosopher Isaac Newton’s theory of gravitation, which was published in 1687 (discussed in Chapter 5).

In 1671, the French astronomer Jean Richer noticed that his pendulum clock was over two minutes slower every day that he was in Cayenne, in South America, compared to when he was in Paris, in Europe. He realised that the force of gravity must be lower in Cayenne, allowing the pendulum to swing further.[7] Newton later showed that this is because the centrifugal force, the outward force caused by rotation, is stronger at the equator. This is why the Earth and all other rotating spheres are slightly elongated there. Richer's discovery meant that gravity maps of the Earth could be made by taking pendulums around the world.

 Figure 2.9Image credit The Earth’s equatorial diameter is slightly larger than its polar diameter because the centrifugal force is strongest at the equator.

### 2.3.3 The Royal Observatory at Greenwich

In 1514, the German mathematician Johannes Werner had suggested that time could be measured by observing the position of the Moon.[8] He may have been inspired by the Italian explorer Amerigo Vespucci, who wrote in 1502 that the Moon moves west at about 11.5° per hour, which is slightly less than the movement of the stars.[9] This is because the Moon is also orbiting the Earth, completing one full orbit a month. Once an observer knew the position of the Moon, they could determine the time at Greenwich using a prepared table of lunar distances and times, and then compare this to the local time.

The French explorer Jean-Paul Le Gardeur informed King Charles II of England of Werner’s technique in 1674. The King consulted his royal commissioners, who included Hooke, and they asked the English astronomer John Flamsteed.

Flamsteed said that they didn’t have the means to measure the positions of the stars and Moon accurately enough to determine longitude in this way, and so King Charles II established the Royal Observatory at Greenwich and appointed Flamsteed as the first Astronomer Royal.[10]

### 2.3.4 The Board of Longitude

Werner’s method was modified to account for Newton’s theory of gravity, but errors in navigation led to so many shipwrecks that in 1714, the British government established the Board of Longitude. The Board promised to reward the first person who showed how longitude could be accurately calculated, following similar schemes in France, Spain, and Holland.

The German astronomer Tobias Mayer and the Swiss mathematician Leonhard Euler created a set of tables that predicted the position of the Moon more accurately than ever before. This allowed people to calculate their longitude to within half a degree.

Euler and Mayer submitted these to the Board of Longitude in 1755, and the British astronomer Nevil Maskelyne, the fifth Astronomer Royal, suggested that tables like these should be published annually in an official book known as a nautical almanac. The nautical almanac was ready for 1767 and became the standard set of tables used worldwide.[11] The Greenwich meridian was designated 0° longitude, and this was accepted internationally in 1884.[12]

### 2.3.5 The marine chronometer

People were able to measure longitude more accurately after the English clockmaker John Harrison devised a clock that works at sea. This is known as a marine chronometer. Harrison made several attempts before he solved the problem in 1759. Harrison’s fourth design, known as H4, was only 13 cm wide and looked like a large pocket watch.[5]

 Figure 2.10Image credit Harrison’s H4 chronometer.

Harrison had to fight for the prize offered by the Board of Longitude, eventually gaining the prize money in 1773, after appealing to King George III. Harrison’s clocks were used by explorers like Captain James Cook, but they were expensive, and so they did not become standard for another few decades.[5]

The British Nautical Almanac published lunar distance tables until 1906, two years after the time in any particular location was first broadcast by radio.