Who (and when) discovered that the earth's axis is on a 23 degree tilt?
Astronomers define a coordinate system on the sky that lets them identify the relative positions of stars, planets, the Sun and other celestial phenomena (the coordinates are called "right ascension" and "declination", but we don't need to worry about that here). Because of their great distance from the Earth, the positions of most stars are fixed on the grid. The positions of the planets and the Sun, however, are seen to "travel" through the coordinate grid in systematic (though sometimes complicated) patterns. The paths of the planets was carefully observed by Tycho Brahe in the late 1500s. Following Brahe's death in 1601, Johannes Kepler used the data to develop a set of laws that govern the way the planets move around the Sun (he proposed them in 1609). These laws, (creatively) called Kepler's Laws, still hold today.
With Kepler's laws in hand, one can easily interpret the motion of the Sun through the coordinate grid described above as the result of the tilt of the Earth by 23.5 degrees with respect to the plane in which the Earth orbits the Sun. Since Kepler was the one to correctly interpret the motion of the planets and the Sun through the sky, he is the one that I would attribute the title "Discoverer of the 23.5 degree tilt", in the early 1600s.
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