How did Polynesian navigators cross thousands of kilometres of open ocean by the stars?

They used the stars as a compass, and a lifetime of memorised knowledge as a map. Polynesian wayfinding was used for thousands of years for long voyages across thousands of kilometres of the open Pacific Ocean. Navigators used the stars, and also birds, ocean swells and wind patterns, relying on a large body of knowledge from oral tradition, passed from master to apprentice, often in the form of song.

The stars work as a compass because they keep fixed positions year-round, changing only their rising time with the seasons, so each star gives a bearing as it rises or sets. Voyagers would set a heading by a star near the horizon, and switch to a new one once the first rose too high. A specific sequence of stars would be memorised for each route. Some star compass systems specify as many as 150 stars with known bearings, though most have only a few dozen.

The stars also give latitude. The Polynesians took measurements of stellar elevation to determine their latitude, and because the latitudes of specific islands were known, they used the technique of sailing down the latitude. When clouds or daylight hid the stars, a navigator would use the winds and swells as guides.

The knowledge nearly vanished. It was widely lost after contact with and colonisation by Europeans. In 1976 the Micronesian navigator Mau Piailug guided the canoe Hokule'a from Hawaii to Tahiti without instruments, proving the efficacy of his navigational system to the world, and modern re-creations of Polynesian voyaging have largely used his teachings.