Modern science began with the problem of planetary motion. Cosmologies that start with an earth-centric universe may be comforting to people and their religions, but they have a hard time explaining the motions of the planets, especially retrograde motion wherein a planet appears to move backwards in its orbit for a few weeks.
In 1530 the Polish astronomer Copernicus published a new theory in which he posited that the Earth is a planet, and that all the planets orbit the Sun. This had two immediate benefits, it explained retrograde motion, and offered a much simplified way to calculate the orbits of the planets. At the time the vast majority of people were illiterate, so the new theory initially meant little to the masses. Amongst the European intelligensia the new theory slowly gained adherents in spite of the fact that it still did not precisely predict planetary motion. The new theory continued to suffer from one of the flaws of the old theory, the demand that all planets move in circular orbits. This problem was finally solved by Kepler between 1610 and 1619 using the precise measurements of the motion of Mars made by Tycho Brahe.
Kepler’s three laws of planetary motion for the first time allowed the motions of the planets to be calculated with extreme precision. The first of these laws states that planets move in elliptical orbits, rather than the more constrained circular orbits. Amongst the mathematically sophisticated, Kepler’s work cinched the issue, the Earth was clearly a planet, and planets clearly move in elliptical orbits.
Both of these ideas were seen as a major blow to established power structures of the day. The Catholic Church condemned the new theory as heresy. Early adopters of the new theory faced harsh punishment, including the house arrest and the threat of torture (Galileo), and begin burned at the stake (Bruno). Kepler himself was interrupted in his work because his mother was charged with being a witch. Kepler and Tycho jointly deserve credit for inventing modern science. Tycho was convinced that the solution to the problem would require the most precise measurements possible, including an accurate estimate of measurement uncertainty.
Kepler understood the importance of Tycho’s measurements of Mars, and was driven to come up with a mathematical description that fit the data within the measurement uncertainty.
This is the basis of modern science, precise measurement, careful estimation of measurement uncertainty, and mathematical models that fit the data within the measurement uncertainty.