Minute to Sextant

One arcminute of latitude was a convenient natural standard for sailors because it could be derived directly from celestial observations with a sextant. Measuring the Sun's altitude to the nearest arcminute and looking up the result in a table gave you your latitude to within one nautical mile — no sophisticated instruments needed. The modern nautical mile (1,852 m) is a standardized approximation of this relationship, and it still underpins all maritime and aviation distance calculations worldwide.

MOA stands for Minute of Angle. One MOA subtends about 29.1 mm (roughly 1.047 inches) at 100 meters, which conveniently rounds to "one inch at a hundred yards" for American shooters. Rifle scope turrets are typically calibrated in ¼ MOA clicks, so four clicks shift the point of impact about one inch at 100 yards. Competitive shooters obsess over MOA because a rifle that groups within 1 MOA is considered accurate enough for serious target work.

Divide arcminutes by 60 to get decimal degrees. So 30 arcminutes is 0.5°, and 7.5 arcminutes is 0.125°. Going the other way, multiply decimal degrees by 60. A GPS coordinate of 51.5074° means 51° plus 0.5074 × 60 = 30.444 arcminutes, or 51°30′26.6″. Most mapping software handles this conversion internally, but knowing it matters when reading older nautical charts or surveying records that use degrees-minutes-seconds notation.

The full Moon spans about 31 arcminutes (roughly half a degree). That means one arcminute on the lunar face corresponds to about 56 km of actual surface. The largest crater visible to the naked eye, Tycho, spans approximately 1.5 arcminutes. This is right at the edge of human visual resolution, which is why you can just barely make out the major dark maria (the "seas") but not individual craters without binoculars.

It really is a coincidence. The Sun is about 400 times the diameter of the Moon, but it also happens to be roughly 400 times farther away — so both subtend almost exactly 30 arcminutes (half a degree) as seen from Earth. This near-perfect match is what makes total solar eclipses possible, with the Moon barely covering the solar disc while leaving the spectacular corona visible. It won't last: the Moon recedes about 3.8 cm per year, so in roughly 600 million years total eclipses will no longer occur.

A sextant uses two mirrors to superimpose the image of a celestial body onto the horizon. The navigator looks through the eyepiece and sees the horizon directly through a half-silvered mirror, while a second mirror on a movable arm reflects the Sun or star down into the same field of view. You swing the arm until the star appears to sit exactly on the horizon, then read the angle off the graduated arc. The double-reflection design means the arc only needs to span 60° (one sextant) to measure angles up to 120°.

The name refers to the arc of the instrument, not its measurement range. A sextant's arc is one-sixth of a circle (60°), but thanks to the double-reflection principle — where the angle of reflection doubles the arc angle — it can actually measure angles up to 120°. Similarly, an octant (one-eighth of a circle, 45° arc) measures up to 90°. The naming convention describes the physical shape of the tool, not its capability.

Yes, and navies worldwide still require it. The US Naval Academy reintroduced mandatory celestial navigation in 2015 after a decade-long hiatus, citing concerns about GPS vulnerability to jamming, spoofing, and satellite failure. A skilled celestial navigator with a sextant, an accurate clock, and a nautical almanac can determine position to within about 1–2 nautical miles — good enough to make port safely. Several solo round-the-world sailors carry sextants as backup specifically because they have no electronics to fail.

The sextant itself couldn't solve longitude — that required an accurate clock (John Harrison's marine chronometer, completed in 1761). But the sextant was the other half of the solution. A navigator used it to measure the Sun's altitude at local noon to find the exact time of solar noon at their position. Comparing this to Greenwich time on the chronometer gave the time difference, and since Earth rotates 15° per hour, that time difference directly yielded longitude. Sextant + chronometer = position anywhere on Earth.

Sixty degrees is the interior angle of an equilateral triangle — the simplest regular polygon after the square. Honeycomb cells are hexagons (six 120° angles, each the supplement of 60°) because hexagonal packing is the most efficient way to tile a plane. Carbon atoms in graphene and diamond form 60° and 109.5° angles respectively. The 60° angle appears everywhere in nature because it's the geometric consequence of close-packing equal-sized spheres or circles.