Small Circles And Great Circles: Longitude & Latitude Concepts

Great circles and small circles are important concepts that help summarize latitude and longitude (Figure below). A great circle is any circle of Earth’s circumference whose center coincides with the center of Earth. An infinite number of great circles can be drawn on Earth. Every meridian is one-half of a great circle that passes through the poles. On flat maps, airline and shipping routes appear to arch their way across oceans and landmasses. These are great circle routes, the shortest distance between two points on Earth.

Circles a: Examples of great circles and small circles on Earth.

Circles b: Any plane that divides Earth into equal halves intersects the globe along a great circle; this great circle is a full circumference of the globe and is the shortest distance between any two surface points.

Circles c: Any plane surface that splits the globe into unequal portions intersects the globe along a small circle.

In contrast to meridians, only one parallel is a great circle the equatorial parallel. All other parallels diminish in length toward the poles and, along with any other nongreat circles that one might draw, constitute small circles. These circles have centers that do not coincide with Earth’s center.

This figure below combines latitude and parallels with longitude and meridians to illustrate Earth’s complete coordinate grid system. Note the dot that marks our measurement of 49° N and 60° E, a location in western Kazakstan. Next time you look at a world globe, follow the parallel and meridian that converge on your location.

Earth’s coordinate grid system. Latitude and latitude parallels, as well as longit-ude and meridians, allow us to locate all places on Earth precisely. The red dot circles is at 49°N latitude and 60° E longitude.

The Timely Search for Longitude

Unlike latitude, longitude cannot be determined readily from fixed celestial bodies. Determining longitude is particularly critical at sea, where no landmarks are visible. The problem is Earth’s rotation, which constantly changes the apparent position of the Sun and stars.

In the early 1600s, Galileo explained that longitude could be measured by using two clocks. Any point on Earth takes 24 hours to travel around the full 360° of one rotation (1 day). If you divide 360° by 24 hours, you find that any point on Earth travels through 15° of longitude every hour. Thus, if time could be accurately measured at sea, a comparison of two clocks could give a value for longitude.

One clock would indicate the time back at homeport (Figure below). The other clock would be reset at local noon each day, as determined by the highest Sun position in the sky (solar zenith). The time difference between the ship and homeport would indicate the longitudinal difference traveled: 1 hour for each 15° of longitude. The principle was sound; all that was needed was accurate clocks. Unfortunately, the pendulum clock invented by Christian Huygens in 1656, and accurate on land, did not work on the rolling deck of a ship at sea!

Clock time determines longitude, If the shipboard clock reads local noon and the clock set for home port reads 3:00 P.M., ship time is 3 hours earlier than home time. Therefore, calculating 3 hours at 15° per hour puts the ship at 45° W longit from home port.

In 1707, the British lost four ships and 2000 men in a sea tragedy that was blamed specifically on the longitude problem. In response, Parliament passed an act in 1714—“Publik Reward . . . to Discover the Longitude at Sea”—and authorized a prize worth more than $2 million in today’s dollars to the first successful inventor of an accurate sea-faring clock. The Board of Longitude was established to judge any devices submitted.

John Harrison, a self-taught country clockmaker, began work on the problem in 1728 and finally produced his brilliant marine chronometer, known as Number 4, in 1760. The clock was tested on a voyage to Jamaica in 1761. When taken ashore and compared to land-based longitude, Harrison’s ingenious Number 4 was only 5 seconds slow, an error that translates to only 1.259′ or 2.3 km (1.4mi) or well within Parliament’s standard. After many delays, Harrison finally received most of the prize money in his last years of life.

With his marine clocks, John Harrison tested the waters of space–time. He succeeded, against all odds, in using the fourth temporal dimension to link points on the three dimensional globe. He wrested the world’s whereabouts from the stars, and locked the secret in a pocket watch. (From Dava Sobel, Latitude: The Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time (New York: Walker and Co., 1995), p. 175.)

From that time, it was possible to determine longitude accurately on land and sea, as long as everyone agreed upon a meridian to use as a reference for time comparisons, which became the Royal Observatory in Greenwich, England. In this modern era of atomic clocks and GPS satellites in mathematically precise orbits, we have far greater accuracy available for the determination of longitude on Earth.