How did Galileo's observation provide evidence against the previous hypothesis?

Answer 1

Galieo was the first scientist to study the night sky systematically with a telescope. One of the things he discovered was the phases of Venus, which had not been seen before.

In a telescope Venus looks like a crescent when it passes between the Earth and Sun, for a few weeks either side of its closest approach to Earth, called inferior conjunction, when it is invisible (in line with the Sun approximately). That was consistent with the old geocentric theory that placed the Earth at the centre of everything.

Galileo also discovered that when Venus is near its furthest point, superior conjunction, it shows a gibbous phase (like the Moon between half-moon and full moon). That is not explained by the geocentric theory called the Ptolemaic system, that had lasted for 1500 years, because it shows that Venus in this part of its orbit is further away from us than the Sun, which is impossible in the Ptolemaic system.

Galileo used this as a proof of Copernicus's heliocentric theory, but he was mistaken in this because Tycho Brahe had produced a geocentric theory that still had the Earth at the centre, but allowed Venus to pass behind the Sun (as seen from Earth).

It needed many further discoveries after the time of Galileo to make people realise that the heliocentric concept is the correct one. The modern system uses Kepler's model. Kepler used the Copernican idea of having the Sun at the centre, but threw out the circles and epicycles of the Copernican theory. In the modern theory based on Kepler's laws, each planet is in an elliptical orbit with the Sun occupying one focus.