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

Detail

What latitude is

• Latitude is a place's angle north or south of the equator.
• The angle is measured at the earth's centre, along the place's meridian.

• So latitude is an angle in degrees, not a distance in kilometres.

• Parallel of latitude: a circle that joins all places with the same latitude. Parallels run east–west.

• Each degree (°) has 60 minutes (′), and each minute has 60 seconds (″). One second of latitude covers about 30.7 m on the ground [2].
• Parallels never meet. They stay the same distance apart from the equator to the poles [2].

Range and number of parallels

• Equator = 0°. North Pole = 90°N. South Pole = 90°S.
• If you draw a parallel at every 1°:
• there are 89 parallels in each hemisphere (1° to 89°), and
• 179 parallels in all, counting the equator.

• The poles (90°) are points, not circles, so they are not counted.

• Important named parallels (approximate values) [2]:

Parallel	Approx. latitude
Arctic Circle	66½°N
Tropic of Cancer	23½°N
Equator	0°
Tropic of Capricorn	23½°S
Antarctic Circle	66½°S

How latitude is found

• The sun's altitude: altitude means how high the sun stands above the horizon at noon. With the date, it gives the latitude.
• The Pole Star (Polaris): in the northern hemisphere, the Pole Star's height above the horizon is roughly equal to the place's latitude.
• At the equator (0°), the Pole Star sits on the horizon.
• At the North Pole (90°N), it is almost straight overhead.

• It cannot be seen from the southern hemisphere.

• Latitude and longitude have been used in astronomy and navigation since ancient times. NOAA's National Ocean Service has kept watch on latitude since 1899 from observatories at Gaithersburg (Maryland) and Ukiah (California), USA [2].

• Drawing a parallel: NCERT (Class 11, Fig. 3.2) draws parallels with a protractor. You mark the angle from the earth's centre, measured from the equator, then draw a line parallel to the equator through that point.

The equator

• The equator is the 0° parallel and the longest parallel.
• It divides the earth into the Northern Hemisphere and the Southern Hemisphere [2][3].
• Its circumference (the distance once around it) is about 40,075 km [3].
• Great circles that pass through the poles measure about 40,000 km.
• The equator is longer because the earth bulges at the equator (the equatorial bulge) [3].

Great circle and small circle

Feature	Great circle	Small circle
Definition	A circle whose plane passes through the earth's centre	A circle whose plane does not pass through the centre
Effect on the globe	Cuts the earth into two equal halves	Does not cut the earth into equal halves
Size	The largest circle you can draw on a sphere [3]	Smaller. Parallels shrink towards the poles
Examples	The equator; every meridian together with its opposite meridian (for example 0° + 180°)	Every parallel except the equator, such as the Tropic of Cancer and the Arctic Circle

• The equator is the only parallel that is a great circle. It is the earth's only east–west great circle [3].
• Meridians (north–south lines of longitude) all meet at the poles. Each meridian joined with its opposite meridian forms a great circle [3].

Great-circle route: why it is the shortest

• Cause: the earth is a sphere, so a straight line on a flat map is not the shortest path on the globe.
• Process: the shortest path between two points on a sphere always lies 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. Pilots still adjust these routes for weather and winds [3].
• Example (NCERT Class 12): the sea route from Vancouver (Canada) to Yokohama (Japan) across the North Pacific follows a great-circle arc.

• Example: flights between Atlanta (USA) and Athens (Greece) are planned along a great circle [3].

• On many flat map projections, a great-circle route looks curved and bends towards the pole. This is why the angle at which a map is projected matters when showing routes (see map projections).

Length of a degree

Length of 1°	Equator	45°	Poles
1° of latitude	110.6 km	≈111 km	111.7 km
1° of longitude	111.3 km	≈79 km	0 km

• Degree of latitude: almost the same everywhere (about 111 km) [2].
• More exact values are 110.567 km at the equator and 111.699 km at the poles [4] (NCERT: 110.6 km and 111.7 km).

• Why it is longer at the poles:

  • the earth is flattened at the poles (it is an oblate spheroid: a slightly squashed ball);
  • so the surface curves less there;
  • a flatter curve means you must travel slightly farther along the ground to change your angle by 1°;
  • so 1° of latitude is longer at the poles [4].

• Degree of longitude: shrinks towards the poles.

• Meridians are widest apart at the equator and meet at the poles.

• Length of 1° of longitude ≈ 111.3 km × cos(latitude):

  • at 0°: 111.3 km;
  • at 45°: 111.3 × 0.707 ≈ 79 km;
  • at 60°: about 55.7 km, roughly half of the equator figure;
  • at 90°: 0 km.

• Trap: a degree of latitude is slightly longer at the poles than at the equator. A degree of longitude is the opposite: longest at the equator and zero at the poles.

Prelims Hooks

• At 1° spacing there are 179 parallels in all: 89 in each hemisphere plus the equator.
• The equator is the only parallel that is a great circle. All other parallels are small circles.
• Every meridian taken with its opposite meridian (for example 0° and 180°) forms a great circle.
• The equator's circumference is about 40,075 km, a little more than the roughly 40,000 km of the meridian great circles, because of the equatorial bulge [3].
• 1° of latitude is 110.6 km at the equator and 111.7 km at the poles, so it is longer at the poles because of polar flattening [4].
• 1° of longitude: 111.3 km at the equator → about 79 km at 45° → 0 km at the poles.
• In the northern hemisphere, the Pole Star's altitude ≈ the latitude of the place.
• The shortest route between two points on the globe is a great-circle arc. Example: the Vancouver–Yokohama route across the North Pacific.
• One second of latitude ≈ 30.7 m [2].

Mains Points

• Great-circle navigation and transport (GS-I/GS-III): air and shipping routes follow great-circle arcs to cut distance, fuel use and emissions.
• This is why many flights between Asia and North America pass over the Arctic.
• It is also why North Pacific shipping lanes curve northwards.

• Routes still change with weather, jet streams and airspace limits [3].

• Earth's shape and measurement: the earth is an oblate spheroid (bulging at the equator, flattened at the poles).

• This explains the 40,075 km equatorial circumference [3].
• It also explains why a degree of latitude is longer near the poles [4].

• Accurate geodesy (the science of measuring the earth's shape and size) underlies mapping by the Survey of India and satellite positioning.

• Latitude as a control on climate: parallels such as the Tropics and the Arctic Circle mark the limits of the overhead sun and of the midnight sun.

• Latitude therefore shapes how much sunlight a place gets (insolation), its temperature belt and its vegetation.

• In India, the Tropic of Cancer splits the country into a tropical south and a sub-tropical or temperate north.

• Convergence of meridians: east–west distances shrink with latitude, so the same number of degrees covers a smaller ground area at high latitudes.

• This matters for map projections, for gridded data such as satellite imagery, and for reading area correctly on world maps.