An ancient Greek hand-powered geared device from the 2nd century BC that modelled the Sun, Moon and calendars and predicted eclipses. It is often called the oldest known analogue computer.
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Nobody knows. Ancient Greeks assumed a single poet, but most scholars now see the epics as products of a long oral tradition, and whether a 'Homer' shaped them remains debated.
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The distance comes from the 1908 London Olympic course, adopted as standard in 1921. Why that course was that length is disputed, and the royal-nursery story is contested.
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Troy was a real city that was attacked and destroyed more than once. Whether any of this was Homer's ten-year war is unproven, though many specialists see a historical kernel.
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Around 240 BC, Eratosthenes compared the Sun's shadow angle at Alexandria with the overhead Sun at Syene, then scaled up the distance between them to get Earth's circumference.
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