He proved that comets are not objects in the atmosphere. He showed irregularities in the moon s orbit. His wall quadrant and other instruments became widely copied and lead to improved stellar instruments. Kepler used Tycho Brahe's observations when he constructed his famous laws of planetary movement. Brahe used prosthaphaeresis 3.
Assumed planets revolve the sun, but the sun revolves the earth.
From an observational point of view, this is the same as the heliocentric hypothesis of Copernicus. He also showed that a line joining the planet to the Sun sweeps out equal areas in equal times as the planet describes its orbit. Geometry existed before the creation, is coeternal with the mind of God, is God himself. I undertake to prove that God, in creating the universe and regulating the order of the cosmos, had in view the five regular bodies of geometry as know since the days of Pythagoras and Plato, and that he has fixed according to those dimensions, the number of the heavens, their proportions, and the relations of their movements. If there is anything that can bind the heavenly mind of man to this dreary exile of our earthly home and can reconcile us with our fate so that one can enjoy living then it is verily the enjoyment of mathematical sciences and astronomy.