Meridian arc

A meridian arc is an important idea used in geodesy and navigation. It describes the curve between two points on Earth that share the same longitude.

People have studied meridian arcs for many years. They use special tools to measure these curves and also use math to calculate their lengths. This helps us understand the shape and size of our planet better. This knowledge is useful for maps, GPS, and many other tools we use every day.

The study of meridian arcs has helped scientists learn more about Earth. By measuring these curves, they can figure out distances between places and how the ground is shaped. This information is important for many jobs, like making maps and planning journeys across the world.

Measurement

Measuring meridian arcs helps us learn about the shape of the Earth. By measuring these curves, scientists can find the best shape to represent our planet, called a reference ellipsoid. These measurements, taken in many places around the world, help make a model that shows the whole Earth.

Long ago, people used simple tools to measure these arcs. Today, we use advanced tools like satellites to get more accurate results. These measurements are important for things like mapping and navigation.

19th century

After the French Revolution in 1789, people worked hard to create new ways to measure things. Scientists wanted to measure a special curve of Earth called the meridian that passed through Paris. This would help them decide the length of a metre. The French Academy of Sciences led this work.

Groups of scientists traveled far to measure this distance from north to south. They had many problems, like hard travel and political trouble after the Revolution. They measured parts of the meridian in France, from Dunkirk to Barcelona. These measurements helped create the metric system. This careful work helped scientists learn more about the shape of our Earth.

The nautical mile

Long ago, a nautical mile was thought to be the distance of one small part of Earth's curve. Today, it is exactly 1,852 metres. For most everyday uses, people still measure distances using the latitude scale on maps. On these maps, one small part of latitude is treated as one nautical mile.

Calculation

See also: Latitude § Meridian arc

On a round Earth, the length of a meridian arc is just how far you go along a circle. For very long arcs, we find the length by subtracting the distance from the equator to two points at different latitudes.

This idea is important for making maps, especially for a type of map called the transverse Mercator projection.

The exact formulas use special math, but they help scientists and mapmakers measure distances very well on Earth.

Quarter meridian

The distance from the equator to the pole is called the quarter meridian. It was used to help define the metre and the nautical mile.

The quarter meridian can be calculated using special math formulas. For Earth, it is about 10,001,965.729 metres long.

The inverse meridian problem for the ellipsoid

Sometimes we need to solve the opposite problem: if we know the distance between two points, how can we find their latitude? One way to do this is by using a step-by-step method called Newton's method. This method keeps improving its guess until it gets very close to the right answer.

There is also another way using special math patterns called series. These patterns help us calculate the latitude when we know the distance between points. A famous mathematician named Adrien-Marie Legendre showed that measuring distances on Earth is related to shapes called ellipses. This idea helps solve problems about measuring distances on our planet.