The Sextant: Double Reflection, Swinging the Arc, and Aldrin's Backup Math

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Artemis II astronauts carry an emergency backup built on a design about 300 years old: the sextant. Isaac Newton sketched the theory in unpublished writings, and around 1731 John Hadley in England and Thomas Godfrey in America independently built instruments using double reflection. Older tools like the mariner's astrolabe and cross staff depended on a steady plumb line, useless on a pitching deck, but two mirrors let a navigator lay the sun or a star directly on the horizon so both images move together. Rotating the index mirror doubles the reflected angle, so a 60 degree arc reads 120 degrees. The episode walks through a noon sun sight: holding the handle, not the arc, lowering the sun to the horizon, and swinging the sextant to find the bottom of the arc.

A sight also needs exact time and the height of eye to correct for dip. Brass and aluminum trade stability against fatigue, heat warps both, and a pool of mercury or a bubble can stand in for a hidden horizon. Carlos Viegas Gago Coutinho adapted the instrument for aircraft around 1922, and later bubble sextants used clockwork averagers to cancel turbulence. Neil Armstrong pushed for a sextant built into the Apollo capsules.

• A skilled navigator can fix a position to within a tenth to a quarter of a nautical mile.
• Star sights must be taken in nautical twilight, while stars show but the horizon is still visible.
• The four adjustable errors, perpendicularity, side, collimation, and index, must be corrected in that order.
• When Gemini 12's rendezvous radar failed, Buzz Aldrin worked out the rendezvous with a handheld sextant, star charts, and a slide rule.
• Experiments on the International Space Station in 2018 showed a handheld sextant could guide an emergency return.