Minute and second of arc

A minute of arc, also called an arcminute, is a way to measure very small angles. It is equal to 1/60 of a degree. Since a full circle is 360 degrees, one arcminute is a tiny part of that circle. Long ago, sailors used arcminutes to help measure distances on Earth using the stars.

A second of arc, or arcsecond, is even smaller. It is 1/60 of an arcminute, or 1/3600 of a degree. This tiny measurement is important in subjects like astronomy, where scientists study stars and planets. It is also used in eye exams, navigation, and in shooting sports.

These units come from ancient Babylonian ideas about numbers, using a system based on the number 60. Today, scientists sometimes use even smaller units, like milliarcseconds and microarcseconds, to study very tiny changes in angles. These measurements help us understand the universe and navigate the Earth with great accuracy.

Symbols and abbreviations

The symbol ′ is used to show an arcminute, a way to measure very small angles. People often use a single quote ' instead when they can only use simple characters. We write one arcminute as 1′. It can also be called arcmin or amin.

Another symbol, ″, is used for an arcsecond, an even smaller angle. Sometimes a double quote " is used instead when only simple characters are allowed. We write one arcsecond as 1″. It can also be called arcsec or asec.

In sea navigation and in some GPS devices, people usually work with degrees and minutes, sometimes adding decimals, like 42° 25.32′. But using degrees, minutes, and seconds (DMS notation) is also common.

Common examples

An arcminute is about how far apart two lines can be and still look separate to someone with good eyesight. The Moon looks about 31 arcminutes wide in the sky.

An arcsecond is a very small angle. It is the size of:

• a small coin seen from several kilometers away
• something very small seen from far away
• the movement of stars in the sky over a short time

Some examples in arcseconds include:

• the sharp view of the Hubble Space Telescope
• the planet Venus when it is a thin crescent

Smaller angles, like milliarcseconds and microarcseconds, can describe things that are extremely tiny when seen from far away.

History

The ideas of degrees, minutes, and seconds for measuring angles and time started with ancient Babylonian astronomers. The Babylonians, influenced by the Sumerians, split the Sun's path across the sky over one full day into 360 degrees. They then divided each degree into 60 minutes, and each minute into 60 seconds.

Uses

Astronomy

Astronomers have used the arcminute and arcsecond for a long time. These units help measure the positions of stars and planets. For example, they use these units to measure altitude and azimuth in the horizon system, and declination in the equatorial coordinate system.

The arcsecond is also used to describe very small angles in space, like the width of planets or the movement of stars over time. The unit parsec, used for measuring distances to stars, is based on the arcsecond.

Cartography

Minutes and seconds of arc are important in maps and navigation. At sea level, one minute of arc along the equator equals about one nautical mile. This helps sailors and mapmakers pinpoint locations using degrees, minutes, and seconds for latitude and longitude.

Property cadastral surveying

Surveyors use fractions of a degree to describe property lines. They start from a reference point and describe directions and distances using angles.

Firearms

In firearms, the arcminute is often called minute of angle (MOA). It helps shooters adjust their sights for better accuracy. For example, at 100 yards, 1 MOA equals about 1 inch.

Human vision

Humans with good vision can see details that are about one minute of arc apart. This is why the term "20/20 vision" is used — it means someone can see objects clearly from 20 feet away.

Materials

In optical engineering, scientists use arcminutes and arcseconds to measure very small angles between surfaces. These units are also used in special measurements of thin films.

Manufacturing

Some tools can measure very small angles using arcminutes and arcseconds. This is helpful when measuring very small objects.