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Old strings: the height of stars

Sailors found their way by drawing circles from the height of stars

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Old strings: the height of stars

Long before satellites, sailors at sea found their way the same way. Their strings weren’t distances to satellites but the height of stars. If Polaris looks 35° above the horizon, you’re somewhere on the yellow circle that joins every place where Polaris looks exactly that high. Draw a second, purple circle with Vega, and where the two circles cross is where you are. But this method needed a very accurate clock.

Why?There is one spot on the ground where a star sits straight overhead. The farther you go from there, the lower the star looks. So if you join every place where the star looks equally high, you get a circle around that spot. It’s the same idea as joining every place at the same distance from a satellite to make a sphere.

Learn moreBecause Earth spins, stars move across the sky by 15° every hour. So you have to know the exact time to draw the circle in the right place. If your clock is 4 minutes off, at this latitude your position slips about 90 km east or west. Only after clocks that kept good time on a rocking ship appeared in the late 1700s could sailors know where they were far out at sea. This is called “celestial navigation.” The other point where the two circles cross is in the middle of the Pacific, so it’s easy to throw out. The constellation lines and the sky grid are drawings, but the stars are placed at their real sky coordinates.

How high Polaris looks
35°

textbook formulas

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Wikipedia: Celestial navigation · Wikipedia: Marine chronometer

More in the series

Orbits, distances and clock differences are calculated with textbook formulas (Kepler’s laws and simple forms of special and general relativity). The 30 satellites follow the real GPS layout but are not the real satellites or positions. In the 3D view, the satellite models are drawn huge and radio waves move far slower than in real life.