Not just 1600 - it was fairly common knowledge since antiquity. In 300 BCE, we knew not only that the Earth is round, but also roughly its radius. Moon's distance and radius was estimated about 100 years later. Sun-Earth distance was also (incorrectly) estimated about the same time, but with enough precision to know it's much further and bigger than the Moon.

Columbus was being dissuaded from his voyage because people correctly calculated his supplies will run out way before he reaches Indies west-wards