---
title: "Latitude, Longitude and Time Zones"
book: "Primary & Middle School Earth and Space Sciences"
subject: earth
language: en
chapter: 14
exercises: 12
source: https://one-course.com/books/earth/1/en/chapter/14-latitude-longitude-and-time-zones
license: CC-BY-NC-SA-4.0
credit: "One Earth and Space Sciences Book, One Course (one-course.com)"
---

# Chapter 14 — Latitude, Longitude and Time Zones

Night has fallen on the [ocean](https://one-course.com/books/earth/1/en/chapter/3-water-on-earth#def-g2-water-on-earth-ocean). On the deck of a sailing ship, in the year 1750, the navigator lifts his instrument towards a bright star and measures how high it stands above the [sea](https://one-course.com/books/earth/1/en/chapter/3-water-on-earth#def-g2-water-on-earth-ocean). A few minutes of work, and he knows how far north of the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator) the ship is. But how far east or west? That, he cannot tell. The problem was so serious that in 1714 the British parliament had promised a large prize to whoever found a way to measure it at [sea](https://one-course.com/books/earth/1/en/chapter/3-water-on-earth#def-g2-water-on-earth-ocean). Today, the phone in your pocket gives both answers in one second.

![A navigator of the eighteenth century measures the height of a star above the sea horizon. (AI illustration.)](https://one-course.com/images/onecourse/chapters/earth-1/g6-latitude-longitude/img-865891099639.jpg)

*A navigator of the eighteenth century measures the height of a star above the [sea](https://one-course.com/books/earth/1/en/chapter/3-water-on-earth#def-g2-water-on-earth-ocean) horizon. (AI illustration.)*

**You already know.**

A [globe](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-globe) is a small model of the Earth. The [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator) is the line that runs round the middle of the [globe](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-globe), halfway between the [North Pole](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-poles) and the [South Pole](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-poles); it cuts the Earth into the [northern hemisphere](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator) and the [southern hemisphere](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator) ([Chapter 6](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#ch-g3-continents-and-oceans)). The physics books showed that the Earth turns on itself around an axis through the two [poles](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-poles), once in a day: this turning brings day and night.

## 14.1 Parallels and latitude

To say where a place is on the Earth, we need two numbers, like the row and the column of a seat in a cinema. The first one tells how far north or south of the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator) the place lies.

Imagine the Earth cut in two, through both [poles](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-poles), like an apple cut from the stalk downwards. On the cut face (left, below), the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator) is the horizontal line through the centre. A place P on the surface is seen from the centre at a certain angle above or below that line: this angle is its [latitude](#def-g6-latitude-longitude-latitude).

![](https://one-course.com/images/onecourse/chapters/earth-1/g6-latitude-longitude/fig-2c002eccab5e.svg)

![](https://one-course.com/images/onecourse/chapters/earth-1/g6-latitude-longitude/fig-36830671dfca.svg)

*[Latitude](#def-g6-latitude-longitude-latitude): the angle at the centre of the Earth between the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator) and the place.*

*[Longitude](#def-g6-latitude-longitude-longitude): the Earth seen from above the [North Pole](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-poles). The angle is measured from the [prime meridian](#def-g6-latitude-longitude-longitude), towards the east or towards the west.*

**Definition 14.1 (Parallel and latitude).**

A *parallel* is a circle drawn round the [globe](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-globe) parallel to the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator); all the places on the same parallel are at the same distance from the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator). The *latitude* of a place is the angle, measured at the centre of the Earth, between the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator) and that place. It goes from $0^\circ$ at the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator) to $90^\circ$ at the [poles](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-poles), and we say whether the place is north (N) or south (S) of the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator).

The [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator) is itself a [parallel](#def-g6-latitude-longitude-latitude), the longest one, with [latitude](#def-g6-latitude-longitude-latitude) $0^\circ$. The [parallels](#def-g6-latitude-longitude-latitude) get shorter towards the [poles](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-poles), and each [pole](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-poles) is a single point, at $90^\circ$ N or $90^\circ$ S. Along a line from a [pole](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-poles) to the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator), each degree of [latitude](#def-g6-latitude-longitude-latitude) measures about $111\,\mathrm{km}$.

[Latitude](#def-g6-latitude-longitude-latitude) is the easy number: it can be found from the sky. By day, sailors measured the height of the Sun at noon; at night, in the [northern hemisphere](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator), they measured the height of the Pole Star. That is what the navigator of the opening picture is doing.

The Pole Star sits almost exactly on the line of the Earth’s axis, prolonged beyond the [North Pole](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-poles), and so far away that its light reaches every place on the Earth along parallel lines. At the [North Pole](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-poles) it is straight overhead, at $90^\circ$ above the horizon; at the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator) it lies on the northern horizon, at $0^\circ$. In between, the rule is simple: *the height of the Pole Star above the northern horizon, measured as an angle, is equal to the [latitude](#def-g6-latitude-longitude-latitude)*. The figure below shows why the two angles are the same.

![Why the height of the Pole Star equals the latitude (a sketch, not to scale). The light of the Pole Star arrives parallel to the Earth’s axis (orange). The horizon of the observer is at right angles to the radius through the observer; the axis is at right angles to the equator. So the angle between the horizon and the Pole Star is the same as the latitude, the angle at the centre between the equator and the observer.](https://one-course.com/images/onecourse/chapters/earth-1/g6-latitude-longitude/fig-4e503f14d162.svg)

*Why the height of the Pole Star equals the [latitude](#def-g6-latitude-longitude-latitude) (a sketch, not to scale). The light of the Pole Star arrives parallel to the Earth’s axis (orange). The horizon of the observer is at right angles to the radius through the observer; the axis is at right angles to the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator). So the angle between the horizon and the Pole Star is the same as the [latitude](#def-g6-latitude-longitude-latitude), the angle at the centre between the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator) and the observer.*

**Example 14.2 (A navigator at night).**

A navigator measures the Pole Star at $41^\circ$ above the northern horizon. The ship is at [latitude](#def-g6-latitude-longitude-latitude) $41^\circ$ N, about $41 \times 111
\approx 4550$ km north of the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator). Sailing north, she finds the star a little higher each night; sailing south towards the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator), it sinks towards the horizon. South of the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator) the Pole Star cannot be seen at all, since it stays below the horizon: there, the noon Sun gives the [latitude](#def-g6-latitude-longitude-latitude).

## 14.2 Meridians and longitude

The second number tells how far east or west a place lies. Here there is no natural starting line like the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator): one has to be chosen.

**Definition 14.3 (Meridian, longitude and prime meridian).**

A *meridian* is a half-circle drawn on the [globe](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-globe) from the [North Pole](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-poles) to the [South Pole](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-poles). The *prime meridian* is the meridian chosen as the starting line: the one that passes through the old Royal Observatory at Greenwich, in London. The *longitude* of a place is the angle between the prime meridian and the meridian of that place, seen from the axis of the Earth. It goes from $0^\circ$ at the prime meridian to $180^\circ$, and we say whether the place is east (E) or west (W) of the prime meridian.

All the [meridians](#def-g6-latitude-longitude-longitude) meet at the [poles](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-poles), and they all have the same length. On the opposite side of the Earth from Greenwich, the [meridian](#def-g6-latitude-longitude-longitude) $180^\circ$ E and the [meridian](#def-g6-latitude-longitude-longitude) $180^\circ$ W are the same line.

![A globe with its parallels (blue) and meridians (grey), every 30. The equator is drawn in thick green, the prime meridian in red; they cross in the ocean south of Ghana, at latitude 0, longitude 0. Every meridian runs from pole to pole; every parallel is a circle around the axis. (Land: Natural Earth.)](https://one-course.com/images/onecourse/chapters/earth-1/g6-latitude-longitude/fig-97919e25064f.svg)

*A [globe](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-globe) with its [parallels](#def-g6-latitude-longitude-latitude) (blue) and [meridians](#def-g6-latitude-longitude-longitude) (grey), every $30^\circ$. The [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator) is drawn in thick green, the [prime meridian](#def-g6-latitude-longitude-longitude) in red; they cross in the [ocean](https://one-course.com/books/earth/1/en/chapter/3-water-on-earth#def-g2-water-on-earth-ocean) south of Ghana, at [latitude](#def-g6-latitude-longitude-latitude) $0^\circ$, [longitude](#def-g6-latitude-longitude-longitude) $0^\circ$. Every [meridian](#def-g6-latitude-longitude-longitude) runs from [pole](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-poles) to [pole](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-poles); every [parallel](#def-g6-latitude-longitude-latitude) is a circle around the axis. (Land: Natural Earth.)*

**History — Choosing the prime meridian.**

For a long time, each country drew its [maps](https://one-course.com/books/earth/1/en/chapter/4-from-a-drawing-to-a-map#def-g2-drawing-to-map-map) with its own starting [meridian](#def-g6-latitude-longitude-longitude): London, Paris and other places were all used. In October 1884, delegates of many countries met in Washington to choose one [meridian](#def-g6-latitude-longitude-longitude) for the whole world. On 13 October, they voted to propose the [meridian](#def-g6-latitude-longitude-longitude) passing through the observatory of Greenwich: 21 countries voted for it, one against, and two did not vote.

## 14.3 Finding a place by its two angles

With its [latitude](#def-g6-latitude-longitude-latitude) and its [longitude](#def-g6-latitude-longitude-longitude), any place on the Earth can be found, on a [map](https://one-course.com/books/earth/1/en/chapter/4-from-a-drawing-to-a-map#def-g2-drawing-to-map-map) or on a [globe](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-globe). We write the [latitude](#def-g6-latitude-longitude-latitude) first: Cairo, for example, is at about $30^\circ$ N, $31^\circ$ E.

![Thirteen cities on a world map with a grid every 30. The equator is drawn in green, the prime meridian in red. (Coastlines and cities: Natural Earth.)](https://one-course.com/images/onecourse/chapters/earth-1/g6-latitude-longitude/fig-8b535c7e7248.svg)

*Thirteen cities on a [world map](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-world-map) with a grid every $30^\circ$. The [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator) is drawn in green, the [prime meridian](#def-g6-latitude-longitude-longitude) in red. (Coastlines and cities: Natural Earth.)*

**Method 14.4 (Locating a place by its coordinates).**

1. [Latitude](#def-g6-latitude-longitude-latitude) : start from the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator) and go north (N) or south (S), counting the [parallels](#def-g6-latitude-longitude-latitude) , up to the right number of degrees.
2. [Longitude](#def-g6-latitude-longitude-longitude) : start from the [prime meridian](#def-g6-latitude-longitude-longitude) and go east (E) or west (W), counting the [meridians](#def-g6-latitude-longitude-longitude) , up to the right number of degrees.
3. The place is where the [parallel](#def-g6-latitude-longitude-latitude) and the [meridian](#def-g6-latitude-longitude-longitude) cross. Between two lines of the grid, estimate: halfway between $30^\circ$ and $60^\circ$ is $45^\circ$ .

**Example 14.5 (Reading the coordinates of Sydney).**

On the [map](https://one-course.com/books/earth/1/en/chapter/4-from-a-drawing-to-a-map#def-g2-drawing-to-map-map), Sydney lies below the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator): it is in the [southern hemisphere](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator), a little above the [parallel](#def-g6-latitude-longitude-latitude) $30^\circ$ S, closer to $30^\circ$ than to $60^\circ$; its [latitude](#def-g6-latitude-longitude-latitude) is about $34^\circ$ S. It lies to the right of the [prime meridian](#def-g6-latitude-longitude-longitude), a little beyond the [meridian](#def-g6-latitude-longitude-longitude) $150^\circ$ E; its [longitude](#def-g6-latitude-longitude-longitude) is about $151^\circ$ E. We write: Sydney, $34^\circ$ S, $151^\circ$ E.

## 14.4 The turning Earth and the time zones

The Earth turns on itself once a day, from west to east. As it turns, the Sun seems to cross the sky from east to west. When the Sun is at its highest in the sky, it is noon. But it is not noon everywhere at the same moment: when it is noon in London, it is already afternoon in Cairo, further east, and still morning in New York, further west.

How much does the Earth turn in one hour? A whole turn is $360^\circ$, and it takes 24 hours:

$$
360^\circ \div 24 = 15^\circ \text{ per hour.}
$$

So two places $15^\circ$ of [longitude](#def-g6-latitude-longitude-longitude) apart have their noon one hour apart: the place further east has it first. One degree takes 4 minutes.

**Definition 14.6 (Time zone).**

A *time zone* is a band of the Earth, from [pole](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-poles) to [pole](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-poles), where all the clocks show the same time. Ideally, each zone is $15^\circ$ of [longitude](#def-g6-latitude-longitude-longitude) wide, so that there are 24 zones, one for each hour; going one zone to the east, the clocks show one hour more.

In the ideal zones, the zone of a place is its [longitude](#def-g6-latitude-longitude-longitude) divided by $15$, rounded to the nearest whole number: east of Greenwich we add that many hours to the time at Greenwich, west of it we subtract them. Tokyo, at $140^\circ$ E: $140 \div 15 \approx 9.3$, so the zone is $+9$: when it is noon at Greenwich, it is 9 p.m. in Tokyo. Real [time zones](#def-g6-latitude-longitude-time-zone) are not straight bands: they follow the borders of countries and regions, so that a whole country, or a whole region, keeps the same time.

![The 24 ideal time zones, each 15 wide, with the number of hours to add to the time at Greenwich (the black line in the middle). The date line runs along the 180 meridian, which this map cuts in two: it is both the left and the right edge. Roll the map into a tube, and the two red lines become one. The zone on each side of the date line is half a zone wide.](https://one-course.com/images/onecourse/chapters/earth-1/g6-latitude-longitude/fig-246019cedc07.svg)

*The 24 ideal [time zones](#def-g6-latitude-longitude-time-zone), each $15^\circ$ wide, with the number of hours to add to the time at Greenwich (the black line in the middle). The [date line](#def-g6-latitude-longitude-date-line) runs along the $180^\circ$ [meridian](#def-g6-latitude-longitude-longitude), which this [map](https://one-course.com/books/earth/1/en/chapter/4-from-a-drawing-to-a-map#def-g2-drawing-to-map-map) cuts in two: it is both the left and the right edge. Roll the [map](https://one-course.com/books/earth/1/en/chapter/4-from-a-drawing-to-a-map#def-g2-drawing-to-map-map) into a tube, and the two red lines become one. The zone on each side of the [date line](#def-g6-latitude-longitude-date-line) is half a zone wide.*

**The date line.** Travel east from Greenwich, adding one hour per zone: at $180^\circ$ you are 12 hours ahead. Travel west, subtracting one hour per zone: at $180^\circ$ you are 12 hours behind. The two travellers meet on the same [meridian](#def-g6-latitude-longitude-longitude) with clocks showing the same hour, but a whole day apart! One of them must change the date.

**Definition 14.7 (International date line).**

The *international date line* is the line, in the middle of the Pacific [Ocean](https://one-course.com/books/earth/1/en/chapter/3-water-on-earth#def-g2-water-on-earth-ocean), where the date changes. It follows the $180^\circ$ [meridian](#def-g6-latitude-longitude-longitude), with a few bends so as not to cut a country in two. Crossing it towards the west, we move to the next day; crossing it towards the east, we go back to the day before.

**History — Harrison’s sea watch.**

![](https://one-course.com/images/onecourse/chapters/earth-1/g6-latitude-longitude/img-372b9eb654a7.jpg)

*Harrison’s H4, National Maritime Museum, Greenwich. (Photo: Colonel Warden, CC BY-SA 3.0, via Wikimedia Commons.)*

To find his [longitude](#def-g6-latitude-longitude-longitude), a navigator compares two times: the local time on the ship, read from the Sun, and at the same moment the time at a home port. Each hour of difference means $15^\circ$ of [longitude](#def-g6-latitude-longitude-longitude). The difficulty was to carry the home time across the [ocean](https://one-course.com/books/earth/1/en/chapter/3-water-on-earth#def-g2-water-on-earth-ocean): even the best watches of the time were not accurate enough. The English clockmaker John Harrison spent decades on the problem, aiming at a clock that would not gain or lose more than 3 seconds a day. His fourth [sea](https://one-course.com/books/earth/1/en/chapter/3-water-on-earth#def-g2-water-on-earth-ocean) timekeeper, called H4, looks like a large pocket watch and ticks five times a second. In 1761, his son William took it on a voyage to Jamaica to test it.

## 14.5 Exercises

**Exercise 14.1 ★.**

Copy and complete: “[Latitude](#def-g6-latitude-longitude-latitude) is measured from the … and goes from $0^\circ$ to …; [longitude](#def-g6-latitude-longitude-longitude) is measured from the … [meridian](#def-g6-latitude-longitude-longitude) and goes from $0^\circ$ to …”

**Solution of Exercise 14.1.**

“[Latitude](#def-g6-latitude-longitude-latitude) is measured from the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator) and goes from $0^\circ$ to $90^\circ$ (north or south); [longitude](#def-g6-latitude-longitude-longitude) is measured from the [prime meridian](#def-g6-latitude-longitude-longitude) and goes from $0^\circ$ to $180^\circ$ (east or west).”

**Exercise 14.2 ★.**

What is the [latitude](#def-g6-latitude-longitude-latitude) of the [North Pole](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-poles)? Of the [South Pole](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-poles)? Of a town on the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator)?

**Solution of Exercise 14.2.**

The [North Pole](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-poles): $90^\circ$ N. The [South Pole](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-poles): $90^\circ$ S. A town on the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator): $0^\circ$.

**Exercise 14.3 ★.**

Using the [map](https://one-course.com/books/earth/1/en/chapter/4-from-a-drawing-to-a-map#def-g2-drawing-to-map-map) of the thirteen cities, say in which [hemisphere](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator), northern or southern, and on which side of the [prime meridian](#def-g6-latitude-longitude-longitude), east or west, each of these cities lies: Sydney, New York, Cairo, Rio de Janeiro.

**Solution of Exercise 14.3.**

Sydney: [southern hemisphere](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator), east. New York: [northern hemisphere](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator), west. Cairo: [northern hemisphere](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator), east. Rio de Janeiro: [southern hemisphere](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator), west.

**Exercise 14.4 ★.**

True or false? Correct the false sentences. (a) All the [meridians](#def-g6-latitude-longitude-longitude) meet at the [poles](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-poles). (b) All the [parallels](#def-g6-latitude-longitude-latitude) have the same length. (c) The [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator) is a [parallel](#def-g6-latitude-longitude-latitude). (d) The [prime meridian](#def-g6-latitude-longitude-longitude) passes through Paris.

**Solution of Exercise 14.4.**

(a) True. (b) False: the [parallels](#def-g6-latitude-longitude-latitude) get shorter towards the [poles](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-poles); the longest is the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator). (c) True. (d) False: it passes through Greenwich, in London.

**Exercise 14.5 ★★.**

Using the [map](https://one-course.com/books/earth/1/en/chapter/4-from-a-drawing-to-a-map#def-g2-drawing-to-map-map) of the thirteen cities, which city lies at about $30^\circ$ N, $31^\circ$ E? Which one at about $41^\circ$ N, $74^\circ$ W? Give the approximate coordinates of Tokyo.

**Solution of Exercise 14.5.**

Cairo. New York. Tokyo is at about $36^\circ$ N, $140^\circ$ E (a little above the [parallel](#def-g6-latitude-longitude-latitude) $30^\circ$ N, a little beyond the [meridian](#def-g6-latitude-longitude-longitude) $120^\circ$ E, short of $150^\circ$ E).

**Exercise 14.6 ★★.**

Town A is at [longitude](#def-g6-latitude-longitude-longitude) $0^\circ$ and town B at [longitude](#def-g6-latitude-longitude-longitude) $45^\circ$ E. How many hours apart are their noons? In which town is it noon first?

**Solution of Exercise 14.6.**

$45 \div 15 = 3$: their noons are 3 hours apart. It is noon first in town B, which is further east.

**Exercise 14.7 ★★.**

Mumbai is at about $73^\circ$ E. Work out its ideal [time zone](#def-g6-latitude-longitude-time-zone). When it is noon at Greenwich, what time is it in Mumbai, in the ideal zones?

**Solution of Exercise 14.7.**

$73 \div 15 \approx 4.9$, rounded to 5: the zone is $+5$. When it is noon at Greenwich, it is $12 + 5 = 17$, that is 5 p.m., in Mumbai.

**Exercise 14.8 ★★.**

Each degree of [latitude](#def-g6-latitude-longitude-latitude) measures about $111\,\mathrm{km}$. How far from the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator) is a town at $30^\circ$ N, measured along its [meridian](#def-g6-latitude-longitude-longitude)? How far is the [North Pole](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-poles) from the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator)?

**Solution of Exercise 14.8.**

$30 \times 111 = 3\,330$ km. The [North Pole](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-poles) is at $90^\circ$: $90 \times 111 = 9\,990$ km, about 10 000 km.

**Exercise 14.9 ★★.**

New York is in the zone $-5$ and Tokyo in the zone $+9$. How many hours apart are their clocks? When it is 8 a.m. on Monday in New York, what time and what day is it in Tokyo?

**Solution of Exercise 14.9.**

$9 - (-5) = 14$ hours apart. $8 + 14 = 22$: it is 10 p.m. on Monday in Tokyo.

**Exercise 14.10 ★★.**

Lena says: “The Sun rises in the east, so the towns in the east see the Sun rise before the towns in the west.” Is she right? Explain with the turning of the Earth.

**Solution of Exercise 14.10.**

She is right. The Earth turns from west to east, so the towns in the east are carried towards the Sun first: they see it rise, reach its highest point and set before the towns further west.

**Exercise 14.11 ★★★.**

A ship’s clock gains 3 seconds a day (it runs too fast). (a) How many seconds fast is it after a voyage of 42 days? (b) The Earth turns one degree in 4 minutes, that is 240 seconds. What error, in degrees of [longitude](#def-g6-latitude-longitude-longitude), does the clock’s error make? (c) At the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator), one degree of [longitude](#def-g6-latitude-longitude-longitude) measures about $111\,\mathrm{km}$. About how many kilometres is the navigator wrong, at the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator)?

**Solution of Exercise 14.11.**

(a) $42 \times 3 = 126$ seconds, a little more than 2 minutes. (b) $126 \div 240 \approx 0.5$: about half a degree of [longitude](#def-g6-latitude-longitude-longitude). (c) $0.5 \times 111 \approx 55$ km (with $0.525$: about 58 km). A mistake of about fifty kilometres: enough to miss an island, or to run onto a [coast](https://one-course.com/books/earth/1/en/chapter/2-landscapes-around-us#def-g1-landscapes-around-us-water) thought to be far away.

**Exercise 14.12 ★★★.**

A plane leaves Tokyo (zone $+9$) at 6 p.m. on Monday and flies east across the Pacific to Los Angeles (zone $-8$). The flight lasts 10 hours. (a) What time is it at Greenwich when the plane leaves? (b) What time is it at Greenwich when it lands? (c) What is the local time and the day in Los Angeles when it lands? Why do travellers say that on this flight “you land before you took off”?

**Solution of Exercise 14.12.**

(a) $18 - 9 = 9$: 9 a.m. on Monday at Greenwich. (b) $9 + 10 = 19$: 7 p.m. on Monday at Greenwich. (c) $19 - 8 = 11$: 11 a.m. on Monday in Los Angeles. The plane left at 6 p.m. on Monday (Tokyo time) and lands at 11 a.m. on the same Monday (Los Angeles time): the clocks at arrival show an earlier time than the clocks at departure, because the plane crossed the [date line](#def-g6-latitude-longitude-date-line) towards the east and went back one day.

## 14.6 Problem: A video call around the world

**Problem 14.1.**

Weekend problem — five friends, four time zones and one date line: what time is it in Auckland when the call starts?

Lena lives in London. She wants to organise a video call with four friends she met on holiday: Ana in Rio de Janeiro, Kenji in Tokyo, Mia in Auckland and Sam in Los Angeles. In this problem, we use the ideal [time zones](#def-g6-latitude-longitude-time-zone).

| friend | city | coordinates |
| --- | --- | --- |
| Lena | London | $52^\circ$ N, $0^\circ$ |
| Ana | Rio de Janeiro | $23^\circ$ S, $43^\circ$ W |
| Kenji | Tokyo | $36^\circ$ N, $140^\circ$ E |
| Mia | Auckland | $37^\circ$ S, $175^\circ$ E |
| Sam | Los Angeles | $34^\circ$ N, $118^\circ$ W |

**Part I — Where the friends live.**

1. Which friends live in the [southern hemisphere](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator) ?
2. Which friends live west of the [prime meridian](#def-g6-latitude-longitude-longitude) ?
3. Which friend lives farthest from the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator) ?
4. Which friend lives closest to the $180^\circ$ [meridian](#def-g6-latitude-longitude-longitude) ? How many degrees of [longitude](#def-g6-latitude-longitude-longitude) away from it?

**Part II — What time is it?**

5. How many degrees does the Earth turn in one hour?
6. Work out the ideal [time zone](#def-g6-latitude-longitude-time-zone) of each friend’s city.
7. Lena proposes to start the call on Friday at 8 p.m., London time. What time and what day is it then in Rio de Janeiro? In Tokyo?
8. Kenji answers that he will be asleep. Explain why it is already Saturday in Tokyo.

**Part III — Crossing the date line.**

9. What time and what day is it in Los Angeles when the call starts?
10. How many hours ahead of Los Angeles are the clocks of Auckland?
11. Sailing east from Auckland to Los Angeles, a ship crosses the [date line](#def-g6-latitude-longitude-date-line) . Does it go forward to the next day or back to the day before?
12. What is the local time, and the day, in Auckland when the call starts?

**Solution of Problem 14.1.**

**1.** Ana (Rio de Janeiro, $23^\circ$ S) and Mia (Auckland, $37^\circ$ S).

**2.** Ana and Sam ($43^\circ$ W and $118^\circ$ W). Lena is on the [prime meridian](#def-g6-latitude-longitude-longitude).

**3.** Lena: London is at $52^\circ$ N, farther from the [equator](https://one-course.com/books/earth/1/en/chapter/6-the-globe-continents-and-oceans#def-g3-continents-and-oceans-equator) than all the others.

**4.** Mia: Auckland is at $175^\circ$ E, only $180 - 175 = 5$ degrees from the $180^\circ$ [meridian](#def-g6-latitude-longitude-longitude).

**5.** $360^\circ \div 24 = 15^\circ$.

**6.** London: $0$. Rio de Janeiro: $43 \div 15 \approx 2.9$, west, so $-3$. Tokyo: $140 \div 15 \approx 9.3$, east, so $+9$. Auckland: $175 \div 15 \approx 11.7$, east, so $+12$. Los Angeles: $118 \div 15 \approx 7.9$, west, so $-8$.

**7.** Rio de Janeiro: $20 - 3 = 17$, 5 p.m. on Friday. Tokyo: $20 + 9 = 29$; $29 - 24 = 5$: 5 a.m. on Saturday.

**8.** Tokyo is far to the east: its clocks are 9 hours ahead of London’s. At 8 p.m. in London, Tokyo has already passed midnight, so its Saturday has begun.

**9.** $20 - 8 = 12$: noon on Friday.

**10.** $12 - (-8) = 20$ hours ahead.

**11.** Crossing the [date line](#def-g6-latitude-longitude-date-line) towards the east, the ship goes back to the day before.

**12.** $20 + 12 = 32$; $32 - 24 = 8$: when the call starts, it is **8 a.m. on Saturday** in Auckland. Mia joins the call at breakfast time, while Sam has his lunch on Friday.