Degree, Arc Minutes, Arc Seconds: The Ultimate Astronomical Guide

Describing the positions and movements of celestial objects against the vast backdrop of the sky demands precision. In the past, tools like sextants, quadrants, and astrolabes were used to make fairly precise measurements in the sky, to within fractions of an arc minute. Subsequent introductions of the telescope and precise tools like meridian circles or crosshair eyepieces allowed astronomers to map the stars with hundreds of times greater accuracy, but today digital tools are used in conjunction with high-resolution cameras and purpose-built telescopes to measure the position, angular sizes, and apparent distances between objects in the sky.

In geography, the Earth is often divided into longitudinal and latitudinal lines to determine position. These lines are measured in degrees, minutes, and seconds. Similarly, in the realm of astronomy, the celestial sphere—a conceptual tool that imagines the universe as a vast sphere with the Earth at its center—uses a similar coordinate system to pinpoint the position of celestial objects. The units of measure are analogous: degrees, arc minutes, and arc seconds, though the application is slightly different.

Degree to arc minutes and arc seconds
Credit: US Digital

What’s a Degree?

A degree (°) is the primary unit used to measure angles in the celestial sphere, reminiscent of the measurement of angles on a plane or degrees of latitude/longitude on the globe. With 360 degrees completing a full circle, it gives observers a broad sense of positioning. For instance, the distance from the horizon straight up to the zenith point overhead measures 90°. Degrees are commonly used both to reference the size of an object and its height above the horizon as well as positional coordinates.

The Orion Nebula (M42) spans about 1 degree across the sky, and typical backyard telescopes can have a maximum low-power field somewhere between 0.5° and 5°, though the majority of typical amateur instruments provide a maximum field of 1-3°.

What’s an Arc Minute?

Delving deeper into precision, an arc minute (‘) or arcmin is 1/60th of a degree. This granularity is useful for more precise positioning and describing the angular size of objects that span less than a degree in the sky. It is also, coincidentally, about the limit of the resolving power of the human eye.

The Moon, and Sun, both with an angular diameter hovering around 0.5°, equate to approximately 30 arc minutes, though we usually express it as being half a degree. The planets Venus and Jupiter both subtend just under one arc minute in the sky when they are closest to us.

What’s an Arc Second?

Yet finer detail is captured with an arc second (“), or arcsec for short, which is 1/60th of an arc minute or 1/3600th of a degree. This meticulousness is indispensable for the study of celestial objects like the distance between close double stars or the angular size of planets. A typical amateur telescope has a resolving power of between 0.5-2 arcsec, depending on aperture, though the Earth’s atmosphere often blurs things closer to the latter measurement.

The planet Neptune spans an angle of 2–2.5 arc seconds, while Jupiter’s Galilean moons range from 1-2 arc seconds. Saturn’s moon Titan, the dwarf planet Ceres, and the asteroid Vesta all appear a little under an arc second in apparent size.

For observations demanding even greater precision, SI unit prefixes are used to imply smaller distances in relation to an arc second. Most commonly, the milliarcsecond (mas) comes into play, representing 1/1000th of an arc second. Techniques like radio interferometry or the parallax method, used to gauge distances to proximate stars, often employ milliarcseconds. To put it in perspective, a star exhibiting a parallax of 1 milliarcsecond lies 1 kiloparsec away, equivalent to about 3,262 light-years (though the nearest star to us is another light-year further than that). The star Betelgeuse spans an angular size of about 50 mas in the sky, making it one of the largest as seen from Earth.

Beyond the milliarcsecond, there’s the microarcsecond—a unit 1/1000th of a milliarcsecond. This ultra-fine measure has become increasingly significant with the advent of techniques capable of such resolution, especially in projects aiming to measure the tiny apparent motions of stars.

Marking Coordinates in the Sky

In astronomy, positioning celestial objects is crucial, and there are two main coordinate systems employed for this purpose: the Horizontal (or Altitude-Azimuth) system and the Equatorial system. Each system is suited to specific applications and is defined by a distinct set of coordinates.

The horizontal, or altitude-azimuth system is based on your local horizon. It’s highly intuitive and changes depending on your location and the time. Altitude, or elevation, is the angle between the object and the observer’s local horizon. It measures how high the object is in the sky. An object right at the horizon has an altitude of 0°, while one directly overhead (zenith) has an altitude of 90°. Azimuth is the angle measured clockwise from the north direction to the object’s vertical circle (a circle drawn through the object and the zenith). An object due north has an azimuth of 0°, due east has 90°, due south has 180°, and due west has 270°.

Altitude-azimuth coordinates are only used for finding out the current position of an object you are trying to aim your telescope at; analog or digital setting circles are often employed for this task. These coordinates are also useful if you are waiting for an object to clear an obstruction, such as a building or trees, in which case you can measure the altitude and azimuth ranges that are obstructed and plan observations accordingly.

The equatorial system is based on the celestial equator and the vernal equinox. It remains consistent regardless of the observer’s location, making it ideal for indicating the location of objects in the sky over time, like points on a map. It is the coordinate system used for most astronomy, regardless of whether your telescope uses an alt-azimuth or equatorial mounting.

Analogous to longitude on Earth, Right Ascension (RA) measures the eastward angle from the vernal equinox (a specific point in the sky defined by where the Sun crosses the celestial equator during the March equinox). Unlike longitude, RA is often expressed in hours, minutes, and seconds, given the Earth’s rotation: 24 hours equate to the 360° of the celestial sphere. An object with an RA of 3 hours, for instance, is 45° from the vernal equinox. Analogous to latitude on Earth, declination (Dec) measures how far north or south a celestial object is from the celestial equator. It’s expressed in degrees, where the celestial equator is 0°, the North Celestial Pole is +90°, and the South Celestial Pole is -90°.

Latitude and longitude coordinates are traditionally described using degrees, minutes, and seconds. However, especially in the digital age with GPS technology, it’s become common to use decimal degrees. For instance, instead of saying 40° 45′ 30″ N, one might see it as 40.7583° N. The same goes for positions in the sky. For expressing equatorial coordinates, you might say the star Vega is located at RA 18h 36m 56s and Dec +38° 47′ 1′′, for instance, but you could also write it as RA 18.6156 and Dec 38.7836, though this is less popular. In contrast, altitude and azimuth coordinates are usually expressed in decimal format rather than in minutes/seconds.

An amateur astronomer and telescope maker from Connecticut who has been featured on TIME Magazine, National Geographic, Sky & Telescope, La Vanguardia, and The Guardian. Zane has owned over 425 telescopes, of which around 400 he has actually gotten to take out under the stars.

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