Galileo
The telescope
By looking into space with the telescope.
Galileo's observations with his telescope supported the concept of heliocentricism. He noted that the satellites of Jupiter and Venus, based on their range of phases, did not match geocentricism supported by Ptolemy. He noted that based on these findings, that the Heliocentric theory was correct.
Galileo Galilei . He only helped support the theory through his observations , he didn't invent the model, Copernicus did.
telescope, he used this to observe different heavenly bodies
Galileo Galilei made the telescope by putting two lenses in to a wooden tube. the lenses focused the light coming through the tube, making the distant ojects seem closer.
Jamestown colonists founded the first plantations in a bid to make the colony more financially viable. Pocahantas (the real one) was also kidnapped by the English.
None of it but Galileo's discoveries with the telescope were very important in raising questions about the old Ptolemaic theory, which was geocentric. However Galileo's discovery of Venus's phases was not a proof of the heliocentric principle because Tycho produced a geocentric model that explained Venus's phases.
Galileo's discoveries showed faults with the old Ptolemaic theory, which had the Sun at the centre. So he was right to publicise these but not to proclaim that the heliocentric theory of Copernicus was correct. Tycho produced a geocentric theory that explained the phenomena discovered by Galileo, which were (mainly) the full range of phases dislplayed by Venus. Eventually Johannes Kepler brought out a new heliocentric theory with novel elliptical orbits for the planets. It was later backed up by Newton's theoretical discoveries and by later measurements, and it is the model used and accepted today.
If you have the money and the diplomatic support, you should by the Hubble Space Telescope.
You need to say which theories you are asking about.
The Jovian moons. Galileo had little evidence for the heliocentric theory, which was later (in the 18th century) generally accepted as correct after the laws of motion and the law of gravity showed that the Sun is by far the most massive object in the solar system and therefore must be at the centre. Galileo did not have the other major piece of evidence supporting the heliocentric theory, which is the parallax shown by relatively close stars as the Earth moves round its orbit. Parallax is extremely small and was impossible to observe in Galileo's time, and this was used to support the idea that the Earth is at the centre. Bessel made the first measurements of parallax in the 19th century.