The Aristotelian system was the broad term used to refer to the traditional view of the world expressed during the age of Aristotle by the ancients, and maintained and modified by the Church to fit with religious doctrine throughout the Middle Ages. The Aristotelian system included accepted truths about biology, physics, and most notably, astronomy. Many of these "truths" were proven wrong during the Scientific Revolution.
The doctrine of uniformity was an enormous step in the quest to integrate physics and astronomy. Developed by Galileo in his Dialogue on the Two Chief Systems of the World, the doctrine of uniformity states that corresponding causes produce corresponding affects throughout the universe. Thus, terrestrial physics may be used to explain the motion of heavenly bodies.
The term geocentric describes the theory on the organization of the universe presented by Ptolemy of ancient Greece, and incorporated into the Aristotelian system, which claims that the earth is the center of the solar system and that the sun and other planets orbit around it.
The term heliocentric describes the correct theory, first posed by Nicolas Copernicus, that the Earth is simply one of several planets which orbit the sun.
The Inquisition was the section of the Catholic Church devoted to the maintenance of Church doctrine by the discovery and punishment of heretics. It was the Inquisition which warned Galileo to abandon his theories after the publication of Messenger of the Heavens, and the Inquisition which committed him to house arrest after his publication of Dialogue on the Two Chief Systems of the World. Read the SparkNote on Galileo.
Though Johannes Kepler was unable to conceive a working model of the universe, he did contribute the three laws of planetary motion, all of which were at least somewhat accurate, and all of which were used extensively by Isaac Newton in his work. They are: 1. The planets move around the sun not in circles, but ellipses. 2. Planets do not move uniformly, but in such a manner that a line drawn from a planet to the sun sweeps out an equal area of the ellipse of its orbit in equal time, even if the ellipse is not perfectly centered on the sun. 3. The squares of the periods of the planets' orbits are proportional to the cubes of their distances from the sun. The physics of Kepler's rules and of orbits in general are covered in the SparkNote on Kepler.
The Royal Society of London brought together the greatest minds of the region in efforts to advance science through cooperation. The Royal Society of London, and other scientific societies that grew up in Europe during the later seventeenth century, contributed greatly to the scientific progress made during that period.
The cornerstone of Newton's explanation of the organization of the universe, the law of universal gravitation states that every particle of matter attracts every other particle with a force proportional to the product of the two masses and inversely proportional to the square of the distance between them. Read the SparkNote on the physics of Newton's work. and on Newton's life.