Great circle

Also called: Great circle route · Topic: Latitude, Longitude and Time · NCERT: Class 11, Ch 3 "Latitude, Longitude and Time"; Class 11, Ch 4 "Map Projections"; Class 12, Ch 7 "Transport and Communication"

Meaning

A great circle is any circle drawn on the globe whose plane passes through the earth's centre, so it cuts the earth into two equal halves. The equator is one example. Every meridian joined with its opposite meridian is another (for example 0° + 180°) [3]. It matters because the shortest path between any two points on the globe lies along a great-circle arc. That is why ships and aircraft follow great-circle routes to save distance, fuel and time [3].

Explanation

What makes a circle "great"

• The test is the circle's plane. Picture a flat sheet slicing through the globe along the circle.
• If the sheet passes through the earth's centre, the circle is a great circle.

• If it misses the centre, the circle is a small circle.

• Two results follow:

• A great circle always cuts the earth into two equal halves (hemispheres, meaning half-globes).

• It is the largest circle you can draw on a sphere [3].

• You can draw as many great circles as you like. Through any two points on the globe (if they are not exactly opposite each other), only one great circle passes.

Great circles in the latitude–longitude grid

• Parallels of latitude (east–west circles):
• The equator (0°) is the only parallel that is a great circle. It is the earth's only east–west great circle [3].

• Every other parallel is a small circle, such as the Tropic of Cancer (23½°N) and the Arctic Circle (66½°N) [2]. Parallels get smaller towards the poles.

• Meridians of longitude (north–south lines):

• All meridians meet at the poles.

• A single meridian is only a half-circle. A meridian joined with its opposite meridian forms a full great circle, for example 0° with 180° [3].

• Size is not the same for all great circles:

• The equator measures about 40,075 km around [3].
• Great circles that pass through the poles measure about 40,000 km [3].
• The equator is longer because of the equatorial bulge. The earth is an oblate spheroid (a slightly squashed ball, wider at the equator and flatter at the poles) [3].

Why the great-circle route is the shortest

• Cause: the earth is a sphere, not a flat sheet. So a straight line drawn on a flat map is not the shortest path on the globe.
• Process: the shortest path between two points on a sphere always runs along the arc of the great circle that passes through both points [3].
• Result: ships and aircraft follow great-circle routes to save distance, fuel and time [3].

• Pilots still change these routes to deal with weather and winds [3].

• How it looks on a map:

• On many flat map projections (ways of drawing the round earth on flat paper), a great-circle route looks curved. It bends towards the pole.
• So the projection you choose decides whether a route looks straight or curved. This is why projection matters when you show routes on a map.

Where it occurs

• Equator: the great circle that divides the earth into the Northern Hemisphere and the Southern Hemisphere [2][3].
• Prime Meridian (0°, Greenwich) + 180° meridian: together they form one great circle [3].
• India's standard meridian (82°30'E): this is the meridian used for Indian Standard Time. Joined with its opposite meridian, it also forms a great circle.
• North Pacific sea route (NCERT Class 12): the route from Vancouver (Canada) to Yokohama (Japan) follows a great-circle arc. That is why North Pacific shipping lanes curve northwards.
• Atlanta (USA)–Athens (Greece): flights between these cities are planned along a great circle [3].
• Asia–North America flights: many of them pass over the Arctic, because the great-circle arc between these continents runs close to the North Pole.

Don't confuse with

• Small circle: its plane does not pass through the earth's centre, so it does not cut the earth into equal halves. Every parallel except the equator is a small circle. The Tropics and the Arctic Circle are small circles, not great circles.
• A single meridian: one meridian is only a half great circle, running from pole to pole. It becomes a full great circle only when joined with its opposite meridian (for example 0° + 180°) [3].
• Straight line on a flat map: a straight line on most map projections is not the shortest route. The shortest route is the great-circle arc, and it usually looks curved on the map, bending towards the pole.
• Equator vs meridian great circles: both are great circles, but they differ in length. The equator is about 40,075 km and the pole-to-pole great circles are about 40,000 km, because of the equatorial bulge [3].

Prelims Hooks

• The equator is the only parallel that is a great circle. All other parallels, including the Tropic of Cancer and the Arctic Circle, are small circles [3].
• Every meridian taken with its opposite meridian (for example 0° and 180°) forms a great circle [3].
• A great circle is the largest circle that can be drawn on a sphere, and it always cuts the earth into two equal halves [3].
• The shortest route between two points on the globe is a great-circle arc. NCERT example: Vancouver–Yokohama across the North Pacific.
• Trap: "All great circles on earth are equal in length." This is false. The equator (about 40,075 km) is longer than the pole-to-pole great circles (about 40,000 km) because of the equatorial bulge [3].
• On many flat map projections, a great-circle route looks curved and bends towards the pole, even though it is the shortest path.

Mains Points

• Great-circle navigation in transport (GS-I/GS-III):
• Air and shipping routes follow great-circle arcs to cut distance, fuel use and emissions [3].
• So many Asia–North America flights cross the Arctic, and North Pacific shipping lanes (such as Vancouver–Yokohama) curve northwards.

• Real routes still shift with weather, jet streams (fast, narrow bands of wind high in the atmosphere) and airspace limits [3].

• Earth's shape and measurement:

• The earth is an oblate spheroid. This is why the equatorial great circle (about 40,075 km) is longer than the meridian great circles (about 40,000 km) [3].

• Geodesy (the science of measuring the earth's shape and size) builds on this. It supports mapping by the Survey of India and satellite positioning.

• Map projections and correct map reading:

• The shortest route looks curved on many flat maps, so a planner who reads a map without knowing its projection can misjudge distances and routes.
• Choosing the right projection is therefore key for showing air and sea routes accurately.

Related concepts

• Parallels of latitude
• Equator
• Small circle
• Length of a degree of latitude and longitude

Read more

• Parallels of latitude: equator, great and small circles, length of a degree