Minute and second of arc

We use small parts to measure angles.

A big turn is made of degrees. We can split one degree into sixty parts. These parts are called minutes.

We can split a minute into sixty even smaller parts. These are called seconds. People use them to look at stars. They also help with maps and ships. Even marksmen use them to aim. These tiny bits help us see the world clearly.

When we look at the sky, things can seem very far away. We use degrees to measure the angles of turns. But sometimes, we need to measure very tiny angles.

To do this, we split one degree into sixty parts. We call these parts arcminutes. We can split one arcminute into sixty even smaller parts. These are called arcseconds.

These ideas came from the ancient Babylonians. They used a system based on the number sixty. Today, people use these tiny units for many jobs. Astronomers use them to study the stars. For example, the full Moon looks about 31 arcminutes wide.

People who make maps also use them. Sailors use these units to find their place on Earth. Even people who use rifles use them to aim. In that job, they often call an arcminute a "minute of angle."

These small units help us measure the world with great care.

Sometimes we need to measure very tiny turns. We usually use degrees to talk about angles. But a degree is still quite large for some jobs. To be more precise, we can split one degree into sixty equal parts. Each of these tiny parts is called an arcminute. We can even split one arcminute into sixty smaller pieces. These tiny pieces are called arcseconds.

These units help us describe things that look very small from far away.

Think about how these units work in the real world. An arcminute is about the size of two lines that a person with perfect vision can see. The full Moon in the sky looks about 31 arcminutes wide.

An arcsecond is much smaller. For example, an arcsecond is the angle of a U.S. dime seen from 100 meters away. Scientists can even use milliarcseconds or microarcseconds for even tinier measurements. A microarcsecond is like seeing a tiny dot from a manual on the Moon while you are on Earth.

These ideas are very old. They come from ancient Babylonian astronomy. The Babylonians used a system based on the number sixty. They divided the Sun's path across the sky into 360 degrees. They then split each degree into 60 minutes and each minute into 60 seconds.

This way of counting is called sexagesimal. It has helped people measure both angles and time for a very long time.

Many different people use these measurements today. Astronomers use them to find where stars are in the sky. They use them to measure how much a planet like Venus looks like a crescent.

Map makers also use them to show where places are on Earth. Sailors use degrees, minutes, and seconds to find their latitude and longitude. Even people who use rifles use these units. In that job, they often call an arcminute a "minute of angle."

One minute of angle is about one inch wide at 100 yards.

These tiny units link math to the world around us. They connect the movement of the Earth to the stars we see. For example, the Earth rotates at a rate of 15 arcminutes every minute of time. This helps us know when to look through a telescope.

Whether we are looking at a coin or a distant galaxy, these units help us be exact. They turn the huge sky into something we can measure and understand.

When we measure a turn or an angle, we often use degrees. However, degrees are sometimes too large for precise work. To solve this, mathematicians use smaller subdivisions called arcminutes and arcseconds. An arcminute, or minute of arc, is exactly 1/60 of a degree. An arcsecond, or second of arc, is 1/60 of an arcminute. This means an arcsecond is 1/3,600 of a degree. These units allow us to describe incredibly tiny angles with great accuracy.

The mechanism for these units relies on a sexagesimal system. This is a base-60 counting system. In this system, you divide a whole into sixty parts, and then divide those parts into sixty more. An arcminute is also 1/60 of a radian. An arcsecond is approximately 1/206,265 of a radian. To represent these in writing, we use special symbols. A single prime symbol (′) represents an arcminute. A double prime symbol (″) represents an arcsecond.

These units originated in ancient Babylonian astronomy. The Babylonians were influenced by the Sumerians. They used the sexagesimal system to track the Sun's motion. They divided the Sun's path across the sky into 360 degrees. Each degree was split into 60 minutes, and each minute into 60 seconds. While these units are used for angles, they are different from units of time. For example, the Earth's rotation rate is 15 arcminutes per minute of time. This is not a 1:1 match with how we measure minutes on a clock.

In astronomy, these measurements are vital for seeing the universe. Astronomers use arcminutes and arcseconds to measure the angular diameter of celestial bodies. The full Moon has an average apparent diameter of about 31 arcminutes. The planet Venus can measure between 60 and 66 arcseconds during its crescent phase. For even smaller scales, scientists use milliarcseconds (mas) and microarcseconds (μas). One milliarcsecond is 1/1,000 of an arcsecond. One microarcsecond is 1/1,000 of a milliarcsecond.

To understand how small these are, consider some specific examples. An arcsecond is the angle of a U.S. dime seen from 100 meters away. An arcminute is roughly the distance two lines can be separated and still be seen by someone with 20/20 vision. A milliarcsecond is about the size of a half-dollar coin seen from the distance between the Washington Monument and the Eiffel Tower. A microarcsecond is like seeing a period at the end of a sentence in an Apollo mission manual on the Moon while standing on Earth.

Navigation and cartography also rely heavily on these tiny units. In the past, a nautical mile was defined as the arc length of one minute of latitude on a spherical Earth. This makes the Earth's circumference approximately 21,600 nautical miles. Sailors use degrees, minutes, and seconds to determine latitude and longitude. This helps them find their exact position on the Earth's surface. Modern GPS receivers often use decimal minutes instead of seconds to show these locations.

Other fields use these units for extreme precision. In the firearms industry, an arcminute is often called a "minute of angle" or MOA. One MOA subtends a circle about 1.047 inches in diameter at a distance of 100 yards. This helps shooters adjust their telescopic sights for accuracy. Even land surveyors use these fractions of a degree to define property boundaries. By using arcminutes and arcseconds, humans can map everything from a small backyard to the furthest stars in the galaxy.