1502 in science
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- January 1 – Portuguese explorers, led by Pedro Álvares Cabral, sail into Guanabara Bay, Brazil, mistaking it for the mouth of a river, which they name Rio de Janeiro.
- May 11 – Christopher Columbus leaves Cadiz, Spain for his fourth and final voyage to the New World.
- May 21 – Portuguese navigator João da Nova discovers the uninhabited island of Saint Helena.
- August 14 – Columbus lands at Trujillo and names the country 'Honduras'.
- September 18 – Columbus lands in Costa Rica.
- Amerigo Vespucci, on his return to Lisbon from a voyage to the New World, writes a letter, Mundus Novus, to Lorenzo de' Medici indicating that South America must be an independent continent.
- The Cantino planisphere is the first known world map showing Portuguese discoveries.
- In Germany, Peter Henlein of Nuremberg uses iron parts and coiled springs to build a portable timepiece, the first "Nuremberg Egg".
- Pedro Nunes, Portuguese mathematician (died 1578)
- approx. date – Jorge Reinel, Portuguese cartographer (d. after 1572)
- Grun, Bernard (1991). The Timetables of History (3rd ed.). New York: Simon & Schuster. p. 223.