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How did cosmology change during the Renaissance?

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Hint: Recall that in the middle-ages, the most prominent theory was that the Earth was at the centre of the universe, owing to deductive reasoning from naked eye-observations. However, the renaissance period saw the development of the telescope that could aid more precise observations. Think of how this would have led to a paradigm shift in the perception of celestial bodies in the sky, with the geocentric approach being replaced by a more sun-centred theory.

Complete answer:
Cosmology is one of the branches of astronomy that is concerned with the origin and the evolution of the universe. It is the scientific study that deals with the physical situation of the cosmos in the context of the structure and nature of the universe and the large scale properties of the universe as a whole.
Prior to Renaissance, the widely accepted model of the universe was the one developed by Ptolemy from the hypotheses of ancient philosophers. His model stated that the Earth lay stationery at the centre of the universe, with the Sun, moon and the known planets revolving around it in rather complicated orbits. For this reason, Ptolemy’s model was also known as the Geocentric model. The same idea was shared by Aristotle. The problem with the geocentric model was that it could not explain the retrograde motion of planets like Mars. However, in order to account for such motion, Ptolemy suggested that the planets revolved around the earth in a circular path called epicycle, the centre of which revolves around the Earth along a larger circular path.
Ptolemy’s model proved to be inconsistent and lacking following Galileo’s observation of Venus. If the geocentric model was true, then one would be able to observe only the crescent phases of Venus since it would always be between the Earth and the Sun. However, Galileo was able to observe the full, half, and crescent phases of Venus, which meant that Venus revolved around the Sun.
This led Copernicus to propose a profound idea that stated that the Sun was the centre of the solar system, with all the planets revolving around it. For this reason, it was called the Heliocentric model. However, Copernicus retained the idea that the orbits of planets around the Sun were perfectly circular.
Galileo was also able to observe the consistency of the heliocentric model with the development of the telescope. He was able to observe the phases of Venus, the moons of Jupiter, and the carters on the moon.
Two other astronomers who further developed the Heliocentric paradigm during the Renaissance were Tycho Brahe and Johannes Kepler. Brahe made important contributions by devising precise naked-eye instruments that measured and fixed positions of celestial bodies in the sky. He is known to have combined the Ptolemaic and Copernicus models to corroborate his observations, and called it the Tychonic system, which recognized that the Moon orbited the Earth and the planets orbited the Sun.
Johannes Kepler who worked as Tycho’s assistant, developed the three laws of planetary motion, which stated that the planets orbit the Sun in elliptical paths, an imaginary line drawn from the Sun to a planet would sweep out equal areas in equal intervals of time, and that the ratio of the square of the time periods of any two planets is equal to the ratio of the cubes of their average distances from the Sun. ( $T^2\propto R^3$)
Thus, the period of Renaissance saw the fall of the geocentric model which was now replaced by a much viable and observationally consistent heliocentric model governed by Kepler’s laws that we still follow today owing to its accuracy in predictive modelling.

Note:
Though Copernicus’ model seemed to be a fitting description for stellar and planetary observations, it also had a few problems because of which it took quite some time for it to be tweaked and accepted. The heliocentric model required a moving Earth, which contradicted Aristotelian physics and it was governed by no new laws of motion to describe such a requirement. By removing the Earth from the centre, to become philosophically and theologically unacceptable to many scholars. It was no more accurate in predicting planetary positions than Ptolemy’s model. Copernicus’ model was more complicated than Ptolemy’s model since he wanted to avoid the use of epicycles but retain uniform circular motion for which he had to introduce more devices and rules to fit his observations. But all these drawbacks were eventually corrected by Kepler.