How Celestial Navigation Works

Finding yourself from the sky

At any instant, every celestial body is directly overhead at exactly one point on Earth, its geographic position. For the Sun that point is wherever it is local noon; for a star it is the spot from which the star would sit at the zenith. The almanac tells you where that point is for any second, as a Greenwich Hour Angle and declination. The other half of the puzzle is how far you are from it, and that is what the sextant measures.

Hold a sextant up and bring a body down to the horizon, and you read its altitude, its angle above the horizon. A body straight overhead reads 90°; one on the horizon reads 0°. The gap between your reading and 90°, the zenith distance, is exactly your angular distance from the geographic position, and one degree of it is sixty nautical miles. Measure the Sun at 50° and you are forty degrees, 2,400 miles, from the point beneath it.

One sight: a circle of position

That single measurement is not enough to say where you are, because every place at the same distance from the geographic position is just as valid. Those places form a huge circle of equal altitude drawn on the globe, centered on the point below the body. You are somewhere on that circle. A higher altitude means a smaller circle, drawn tighter around the body; a lower one means a wider circle. Slide the sextant reading above and watch the circle breathe in and out.

Two sights: a fix

Take a sight of a second body and you draw a second circle. Two circles on a sphere cross at two points, and those are the only two places that fit both measurements. A rough idea of where you are, your dead-reckoning position, is more than enough to tell the two apart, because they usually lie hundreds of miles from each other. The point that survives is your fix: your latitude and longitude, pinned down by two angles to the sky. Sailors often take three or more sights so the lines confirm one another.

The intercept method

Drawing circles thousands of miles across on a chart is impractical, so navigators use a clever shortcut worked out by the French officer Marcq Saint-Hilaire in 1875. You start from an assumed position close to where you think you are, and from the almanac you compute the altitude a body should have there, its calculated altitude. Compare that with the altitude you actually observed. If you measured higher, you are nearer the body than your assumption; if lower, farther. The difference in minutes of arc is a distance in nautical miles, the intercept. You step that many miles from the assumed position, toward the body or away from it, and draw a short straight line of position at right angles to the body’s bearing. That little line is a piece of the giant circle, straight enough to plot. Two lines cross at the fix, as the right-hand view shows. You can work a real sight this way, with live almanac data, on our Nautical Almanac and sight-reduction page.

What it takes, and why it still matters

The whole method rests on three things: a clear view of the horizon and a body, an accurate clock set to Universal Time, and the almanac that says where each body was. Time matters enormously, because the sky turns fifteen degrees an hour and a four-second error moves your line a whole mile. For most of history the hard part was the clock; the marine chronometer, perfected by John Harrison in the 1700s, is what finally made longitude findable at sea. Today satellite navigation does all of this in an instant, but it can fail or be jammed, so the sextant and the tables endure as a backup that needs no power and no signal, and as one of the most elegant pieces of practical astronomy ever devised.