A great circle route is the shortest path between two points on the surface of a sphere, such as Earth. It matters because ships, airplanes, and satellites often need the most efficient path over long distances. On a globe, this route looks like a smooth arc that follows part of a circle cutting Earth into two equal halves.
On many flat maps, the same route may look curved or longer than expected because maps distort the round Earth.
Great circle routes work because distance on Earth is measured along the surface, not through the planet. Any plane that passes through Earth’s center cuts the globe in a great circle, and the shortest surface path lies along that circle. The equator is a great circle, but most lines of latitude are not because they do not divide Earth into equal halves.
For example, flights from New York to Tokyo often arc northward on a map because that curved path is shorter on the globe than a straight line drawn across a flat map.
Key Facts
- A great circle is any circle on a sphere whose plane passes through the sphere’s center.
- The shortest surface path between two points on a globe follows a great circle arc.
- The equator is a great circle, but latitude lines such as 30°N and 60°S are small circles.
- Every line of longitude is half of a great circle when paired with the opposite meridian.
- Great circle distance formula: d = R arccos(sin φ1 sin φ2 + cos φ1 cos φ2 cos Δλ).
- For Earth, R ≈ 6371 km, so central angle in radians times 6371 gives distance in kilometers.
Vocabulary
- Great circle
- A great circle is the largest possible circle on a sphere and divides the sphere into two equal halves.
- Great circle route
- A great circle route is the shortest route along the surface of a sphere between two locations.
- Latitude
- Latitude is the angular distance north or south of the equator, measured in degrees.
- Longitude
- Longitude is the angular distance east or west of the prime meridian, measured in degrees.
- Map projection
- A map projection is a method of showing Earth’s curved surface on a flat map, usually with some distortion.
Common Mistakes to Avoid
- Assuming the straight line on a flat map is always shortest, which is wrong because flat projections distort distance and shape.
- Treating all latitude lines as great circles, which is wrong because only the equator passes through Earth’s center and divides Earth into equal halves.
- Ignoring longitude direction when finding Δλ, which is wrong because crossing east or west changes the angular separation between two places.
- Thinking a curved route on a map means a detour, which is wrong because the curve may represent the shortest path on the globe.
Practice Questions
- 1 Two cities lie on the equator at longitudes 20°E and 50°E. Using R = 6371 km, estimate the great circle distance between them. Use d = Rθ, where θ is in radians.
- 2 A flight follows a great circle arc with a central angle of 1.2 radians. Using Earth’s radius as 6371 km, calculate the flight distance in kilometers.
- 3 On a Mercator map, a route from London to Vancouver curves northward instead of appearing as a straight line. Explain why this curved map path can still be the shortest route on the globe.