← Earth Geometry and Time Zones › Latitude and Longitude
Latitude and Longitude
Key Terms
- Latitude
- measures angular distance north or south of the equator (0° to 90° N or S)
- Longitude
- measures angular distance east or west of the prime meridian (0° to 180° E or W)
- A location is given as (latitude, longitude): e.g., Brisbane ≈ (27.5°S, 153°E)
- Lines of latitude are parallels (they are parallel to each other)
- Lines of longitude are meridians (they all meet at the poles)
- The equator is 0° latitude; the prime meridian (through Greenwich) is 0° longitude
Radius of Earth: R = 6 400 km (use this value unless told otherwise)
Circumference of Earth: C = 2πR ≈ 40 212 km
Arc length along a great circle:
d = R × θ (where θ is in radians)
or d = (2πR × θ°) / 360
Circumference of Earth: C = 2πR ≈ 40 212 km
Arc length along a great circle:
d = R × θ (where θ is in radians)
or d = (2πR × θ°) / 360
Worked Example: Give the coordinates of a location that is 35° north of the equator and 40° east of the prime meridian.
Latitude: 35° N (north of equator)
Longitude: 40° E (east of prime meridian)
Location: (35°N, 40°E)
Latitude: 35° N (north of equator)
Longitude: 40° E (east of prime meridian)
Location: (35°N, 40°E)
Hot Tip: When writing coordinates, always write latitude first, then longitude. Include the direction (N/S and E/W). A common mistake is reversing these.
The Coordinate System on Earth
To locate any point on Earth, we use a coordinate system based on two angles measured from the centre of the Earth:
- Latitude (φ): the angle above or below the equatorial plane. Ranges from 90°S (South Pole) to 90°N (North Pole). The equator is 0°.
- Longitude (λ): the angle east or west of the prime meridian. Ranges from 0° to 180°E and 0° to 180°W.
Parallels and Meridians
Parallels (lines of latitude) form circles on the Earth’s surface. They are parallel to each other and to the equator. The equator is the largest parallel (a great circle); parallels at higher latitudes are smaller.
Meridians (lines of longitude) are semicircles running from pole to pole. All meridians are the same size. Opposite meridians (e.g., 40°E and 140°W or equivalently, the 40°E meridian and its antipodal meridian) together form a great circle.
Key Reference Lines
- Equator: 0° latitude
- Prime Meridian: 0° longitude (through Greenwich, London)
- Tropic of Cancer: 23.5°N
- Tropic of Capricorn: 23.5°S
- Arctic Circle: 66.5°N
- Antarctic Circle: 66.5°S
- International Date Line: 180°
Strategy: When finding the angular difference in latitude between two places, simply subtract (or add if on opposite sides of equator). For longitude differences on the same side: subtract; opposite sides: add (but keep ≤ 180°).
Mastery Practice
- Fluency State the latitude and longitude of: (a) the North Pole (b) a point on the equator directly on the prime meridian (c) a point at 45°S, 90°W.
- Fluency Which is further from the equator: 30°N or 55°S? By how many degrees of latitude?
- Fluency Two cities are at 20°N, 30°E and 20°N, 80°E. What is the difference in their longitudes?
- Fluency Identify the hemisphere (Northern/Southern, Eastern/Western) for the location (42°S, 174°E).
- Understanding Brisbane is approximately (27.5°S, 153°E) and Sydney is approximately (34°S, 151°E). What is the difference in latitude between the two cities? Which is closer to the equator?
- Understanding Two ships are at (0°, 30°W) and (0°, 60°E). They are both on the equator. What is the angular separation between them? If R = 6400 km, what is the distance between them along the equator?
- Understanding A plane flies due north from (10°S, 140°E) to (20°N, 140°E). Through how many degrees of latitude does it travel? Calculate the distance using R = 6400 km.
- Understanding Name two cities or countries you know that are approximately on the same meridian (same longitude). Name two that are on the same parallel (same latitude).
- Problem Solving Point A is at (40°N, 20°W) and point B is at (40°S, 20°W). Both are on the same meridian.
- (a) What is the angular difference in latitude between A and B?
- (b) Calculate the distance from A to B along the meridian (R = 6400 km).
- (c) What fraction of the Earth’s full circumference is this arc?
- Problem Solving The Tropic of Capricorn passes through Australia at approximately 23.5°S. A ship sails due east along this parallel from 115°E to 154°E.
- (a) Through how many degrees of longitude does the ship travel?
- (b) The radius of the circle of latitude at 23.5°S is R cos(23.5°) where R = 6400 km. Calculate the distance travelled.