How Does a Sextant Work? Measuring an Angle From a Moving Deck
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Finding your position at sea means measuring how high a known star or the sun sits above the horizon, to about a minute of arc, while standing on a deck that will not hold still. The instrument that solved that problem uses a trick that makes the measurement immune to the motion: it brings two images together in the same field of view, so the angle between them stays correct however the observer is thrown about.
The double reflection
A sextant has a frame carrying an arc marked in degrees, a movable arm called the index arm pivoting at the centre of that arc, a mirror fixed to the top of the index arm called the index mirror, a half-silvered horizon mirror fixed to the frame, and a small telescope aimed through the horizon mirror. Light from the sun strikes the index mirror, reflects down to the horizon mirror and reflects again into the telescope, while light from the horizon passes straight through the clear half of the same horizon mirror. The observer therefore sees both at once and moves the index arm until the reflected sun appears to sit exactly on the horizon line. The essential geometry is that when a ray is reflected by two mirrors in succession, the angle it is turned through is twice the angle between the mirrors, which is why the arc of a sextant spans only sixty degrees, a sixth of a circle and the source of its name, while measuring angles up to one hundred and twenty.
Why it works on a moving ship
The reason the instrument beat everything before it is that it measures the angle between two objects rather than the angle of one object from something fixed to the earth. An astrolabe or a quadrant hangs from a plumb line or sights against a frame, so any roll of the ship corrupts the reading directly. In a sextant both images move together when the observer moves, since both arrive through the same optical path, and the separation between them is unchanged. The practical technique exploits this: the navigator swings the instrument gently through an arc so the reflected body appears to sweep a curve, and takes the reading at the lowest point of that swing, which guarantees the sextant was vertical at that instant. A trained observer can hold about one minute of arc, which corresponds to one nautical mile of position error, from a small boat in a seaway.
From an angle to a position
The reading alone is useless without a precise time, and this is the part that took longest to solve historically. The procedure runs in stages:
- •Measure the altitude of the body above the visible horizon and note the time to the second, which is why a marine chronometer accurate over months mattered so much and why Harrison's clocks were worth a national prize
- •Correct the reading for index error, for the height of the observer's eye above the sea, which lowers the apparent horizon, for atmospheric refraction, which lifts the apparent body, and for the semidiameter of the sun since the limb rather than the centre is observed
- •Look up the body's position on the celestial sphere for that exact moment in a nautical almanac
- •Compute the altitude the body would have had from an assumed position, and compare it with the measured altitude
- •The difference, called the intercept, places the observer on a line of position at a known distance towards or away from the body
- •Repeat with a second and third body, or with the same body hours later, and the crossing lines fix the position
What replaced it and why it survives
Satellite navigation made celestial navigation redundant for routine use, giving a position in seconds to a few metres with no skill required, and most merchant fleets stopped teaching it. It has not disappeared. Several navies reinstated celestial navigation training after concluding that satellite signals are jammable, spoofable and dependent on infrastructure that an adversary can attack, and the United States Naval Academy resumed teaching it in 2015 having dropped it a decade earlier. It requires no power, no signal and no electronics, which makes it the only fully independent backup, and it is still a legal requirement in some certification regimes. It also remains the standard by which a navigator understands what a position actually is, since a satellite receiver hands over an answer while a sextant forces the user to know what was measured, what was corrected for and how large the error might be.
The takeaway
A sextant reflects a celestial body off two mirrors into the same view as the horizon, so the observer aligns the two images and reads the angle between them. Because both images travel the same optical path, the reading survives the motion of a ship, which fixed instruments could not. Two successive reflections turn a ray by twice the angle between the mirrors, so a sixty degree arc measures one hundred and twenty. The angle becomes a position only with a precise time, corrections for refraction and eye height, and an almanac.