Coaching Centre
Latitude and longitude
The equator, prime meridian, parallels and meridians, writing positions on Earth, differences in latitude and longitude, points due north, south, east or west, and GPS coordinates.
Your phone knows where you are to within a few metres, and it describes that spot with just two numbers. Those numbers are latitude and longitude, a grid of imaginary lines that people have used to navigate for centuries. Long before that grid, Aboriginal and Torres Strait Islander navigators crossed land and sea using the stars, the winds and song lines that carried directions from place to place.
The grid on the globe
- The equator is the circle around the middle of the Earth. It is $0°$ latitude.
- Latitude is the angle north (N) or south (S) of the equator, measured at the Earth's centre. It goes from $0°$ to $90°$, which is a pole. Lines of equal latitude are called parallels.
- The prime meridian (or Greenwich meridian) runs from pole to pole through Greenwich in London. It is $0°$ longitude.
- Longitude is the angle east (E) or west (W) of the prime meridian. It goes from $0°$ to $180°$. Lines of equal longitude are called meridians, and they all meet at the poles.
A position is written latitude first, then longitude: Sydney is at about $(34°\text{S}, 151°\text{E})$. That means $34°$ south of the equator and $151°$ east of Greenwich.
- Tap Sydney, Perth and Darwin. Which has the smallest latitude? What does that tell you about where it is?
- Drag the globe until you can see the yellow prime meridian. Which cities are close to it?
- Find two cities on the globe with almost the same longitude. What do they have in common?
- Press Quiz me and find three cities from their coordinates alone.
Differences in latitude and longitude
If two places are on the same side of the equator, subtract their latitudes. If they are on opposite sides, add them, because you have to go to the equator and then past it. Longitude works the same way around the prime meridian.
Sydney is at $(34°\text{S}, 151°\text{E})$ and Tokyo is at $(36°\text{N}, 140°\text{E})$. Find the difference in (a) latitude (b) longitude.
Longitude has a twist. Going east from $151°$E you reach $180°$, and the next meridian is $179°$W. If adding two longitudes gives more than $180°$, the short way round crosses the $180°$ meridian, and the difference is $360°$ minus that sum.
Find the shortest difference in longitude between Sydney ($151°$E) and Los Angeles ($118°$W).
Points due north, south, east and west
Moving due north or south changes only the latitude. Moving due east or west changes only the longitude.
Perth is at $(32°\text{S}, 116°\text{E})$. Find the position of the point (a) $40°$ due north of Perth (b) $70°$ due east of Perth.
Decimal degrees and GPS
Phones and maps give positions in decimal degrees, using negative numbers for south and west. Sydney's Opera House is near $-33.857, 151.215$. That is $33.857°$S, $151.215°$E. Older maps split degrees into $60$ minutes ($′$), just like hours: $0.857° \times 60 \approx 51′$, so $33°51′$S.
One degree of latitude is always about $111$ km on the ground. (One minute of latitude is one nautical mile, $1852$ m, which is why ships and planes use it.) Degrees of longitude get shorter as you head towards the poles, because the meridians meet there.
Your turn
Hobart is at $(43°\text{S}, 147°\text{E})$ and Port Moresby is at $(9°\text{S}, 147°\text{E})$. Using $1° \approx 111$ km, roughly how far apart are they?
Show the working
Same longitude, so one is due north of the other. Both are south, so the latitude difference is $43 - 9 = 34°$. Distance $\approx 34 \times 111 = 3774$ km.
Latitude measures:
Latitude is an angle north or south of the equator, measured from the Earth's centre.
Darwin is at $12°$S and Hobart is at $43°$S. Find the difference in latitude, in degrees.
Same side of the equator, so subtract: $43 - 12 = 31°$.
Cairo is at $30°$N and Johannesburg is at $26°$S. Find the difference in latitude.
Opposite sides of the equator, so add: $30 + 26 = 56°$.
Perth is at $116°$E and Sydney is at $151°$E. Find the difference in longitude.
Both east, so subtract: $151 - 116 = 35°$.
London is at $0°$ and New York is at $74°$W. Find the difference in longitude.
$74 - 0 = 74°$.
Which point is $30°$ due south of $(10°\text{N}, 50°\text{E})$?
Due south changes only the latitude. $10°$ takes you to the equator and the other $20°$ puts you at $20°$S. The longitude stays $50°$E.
Which city is in both the Southern and Western Hemispheres?
Southern means S latitude and Western means W longitude. Only Rio has both.
What is the largest possible latitude, in degrees?
$90°$, at the North or South Pole.
Exam style: Auckland is at $(37°\text{S}, 175°\text{E})$ and Honolulu is at $(21°\text{N}, 158°\text{W})$. Find the shortest difference in longitude.
East and west, so add: $175 + 158 = 333°$. That is more than $180°$, so go the other way across the $180°$ meridian: $360 - 333 = 27°$.
Exam style: Hobart $(43°\text{S}, 147°\text{E})$ is due south of Port Moresby $(9°\text{S}, 147°\text{E})$. Using $1° \approx 111$ km, estimate the distance between them in kilometres.
Latitude difference $= 43 - 9 = 34°$. Distance $\approx 34 \times 111 = 3774$ km.