How big is an arc minute anyway?

Sizes on the sky are angles. A circle is 360 degrees, a degree is 60 arcminutes (1′), and an arcminute is 60 arcseconds (1″).

The ladder

• A fist at arm's length: about 10 degrees.
• Orion's belt, end to end: 2.7 degrees.
• Saturn moved about 1.8 degrees a month this autumn, three and a half Moons, going backwards (westwards) through the stars. This is retrograde motion: near opposition we orbit much faster, so as Earth catches it up and overtakes, it seems to slip back.
• Orion's sword, from c Ori down to iota Ori at its tip: about 1 degree, two Moons, with the Orion Nebula in the middle.
• Neptune moved about 44 arcminutes a month, a Moon and a half, also retrograde.
• Polaris to the true pole: 38 arcminutes this year, a little more than a Moon.
• The Moon, and the Sun: each about half a degree, which is 30 arcminutes.
• 15 arcminutes: how far the sky turns in one minute, on the celestial equator. Half a Moon.
• 11 by 7 arcminutes: the Whirlpool Galaxy, M51, about a third of the Moon across, though only its bright core shows in a small telescope.
• 8.2 arcminutes: iota Ori and Struve 747, the closest pair eclipticam v3w has split, a quarter of the Moon.
• 5 arcminutes: a small ant's head at arm's length.
• 1.8 arcminutes: one eclipticam v3w photosite at the centre of the frame, about 1 near the edges.
• One arcminute: one astrocam v3 photosite. A fifth of a millimetre at arm's length, two or three hairs side by side. About the finest detail a sharp eye can see.
• 45 arcseconds: Saturn's rings, end to end, this autumn.
• 15 arcseconds: how far the sky turns in one second.
• 2 arcseconds: about the finest detail the FirstScope's 76 mm mirror can show, and about what London's air allows on a good night. Neptune's whole disc is 2.4 arcseconds.
• One arcsecond: a sixtieth of an arcminute, 3 thousandths of a millimetre at arm's length.

Hours of right ascension

Astronomers give a star's east-west position, its right ascension, in hours, because the sky turns once a day: 24 hours make the full circle.

• 1 hour of right ascension = 15 degrees.
• 1 minute of right ascension = 15 arcminutes.
• 1 second of right ascension = 15 arcseconds.

Confusingly, but funnily, a minute of right ascension is not an arcminute: it is a minute of time, the turn of the sky in one minute by the clock, and it is 15 arcminutes wide. There is no such thing as an arc hour.

That holds on the celestial equator. Away from it the circles of right ascension crowd together towards the pole, like lines of longitude: at declination 60 degrees an hour is only 7.5 degrees wide (15 times the cosine of the declination).

It is also why a camera that does not move sees every star drift: 15 arcseconds every second, 15 arcminutes in a one-minute exposure.

Eclipticam v3w in these units

• The whole frame is about 104 x 68 degrees.
• The sensor is a grid of photosites, each behind a red, green or blue filter, laid out in repeating 2 x 2 sets: one red, two green, one blue (RGBG). Most of our work bins each set into one colour pixel, so a binned pixel is 2 x 2 photosites.
• Wide angle means low resolving. A photosite covers about 1.8 arcminutes at the centre of the frame, shrinking to about 1 near the edges, because the lens squeezes the edge of its view. A binned pixel is twice that: 3.5 arcminutes at the centre and about 2 at the edges.
• A one-minute exposure smears a star near the equator into a dash 15 arcminutes long: about 8 photosites, or 4 binned pixels, at the centre.
• The Moon is about 17 photosites (8 binned pixels) across at the centre of the frame, and the whole of Orion fits in about 400 by 550 binned pixels.