B. The moderns: the beginning and growth of science JOHANNES KEPLER (1571-1630)

Originally, Kepler wanted to be a theologian. Lacking money, he made a living as a mathematics teacher in a small Austrian town where he supplemented his income with astrological calendars. There, at age 25 while teaching, he realized that the orbits of the then known 5 planets could be circumscribed within the 5 known regular solids. Eventually, Kepler became Tycho Brahe's assistant at the imperial court in Prague. Brahe died shortly after Kepler's arrival and Kepler took over as court mathematician and astronomer.

At Brahe’s request that he be able to prove that his model was correct and armed with Brahe's extensive data, Kepler discovered that he could indeed arrive at a mathematical fit for the observed paths of the planets and eventually described the three laws of planetary motion. They were to prove not only the Ptolemaic system wrong but also, despite his hopes, the Tychonic (Brahe's) system as well.

Kepler's Laws:

First, calculations and observations match if the planetary paths are made to follow an ellipse instead of a circle and by placing the sun at one of the foci of these ellipses.
Second, it is the sun that is the moving force, and because the force of the sun decreases with distance, a planet travels faster when it is nearer the sun (equal areas in equal times).
Third, for the same reason, the orbital velocity of the planets decreases outward, in other words there is a relationship between the period of a planet and its distance from the sun (p2= d3).

Kepler ushered in modern astronomical science, combining careful observation largely inherited from Brahe, with mathematical reasoning, (still the trademark of modern science) to arrive at a description of the universe. For the first time, the explanations are driven by data, not the explanation made to fit a preconceived model.
More on Kepler's life GALILEO GALILEI (1564-1642)

Originally, Galileo studied medicine at the University of Pisa. In 1583, while attending a service at the cathedral of Pisa, he noticed that the swing of the lamps always took the same length of time no matter how wide the swing. This discovery led him away from the study of medicine to that of mathematics and physics. By 1589 he becomes professor of mathematics at the university of Pisa. In 1597, while teaching in Padua, he is still supporting the ptolemaic system in his lectures. It is his involvement with the telescope that was to change his, and others', view of the universe forever.

The first telescope was most likely the invention of a Dutch spectacle maker, Lippershey around 1600. By 1609, it was known all over Europe. Galileo, then professor of mathematics at the University of Padua, also ran an instrument making shop to supplement his income. Having learned how telescopes were made, he produced a nine power telescope for Venice in 1609, which he quickly (within four months) improved to a 30 power instrument. Using this refracting telescope as an astronomical tool in January 1610, he noticed all sorts of new features in the sky which so impressed him that he published them in a 24 page pamphlet entitled Sidereus Nuncius (the Starry Messenger) in March of the same year.

Among them:

there were many more stars than could be seen with the naked eye;
the rough surface of the moon, where he saw mountains and valleys, craters and seas;
the starry nature of the Milky Way;
he saw the four large satellites of Jupiter which we still call the Galilean moons, as well as that planet's giant red spot. It is these moons that convinced him that Copernicus and Kepler were right and further shattered the notion of crystalline spheres of the ancients.

After moving to Florence (even though his official appointment was to Pisa) in 1610, he continued his observations and saw:

an oval appearance to Saturn;
the phases of Venus, whose sequence could only be possible if Venus revolved around the sun;
sunspots indicating that not even the sun was the perfect celestial sphere of the ancients.

As a result of these discoveries he was invited to Rome and there had an audience with Pope Paul V who received him with great honor, and later, the Academy of the Lynxes, an early scientific society, held a lavish banquet in his honor. While his observations convinced him of the correctness of the Copernican model and the telescope allowed all to see what he himself saw, nevertheless, many failed to be convinced. Some church members even felt that he was heretical.

In 1616, he went to Rome to defend himself against that charge (heresy), and had an audience which included no less than the same Pope Paul V. Unable to convince the church of the validity of the Copernican model (neither with his evidence nor his theological arguments) the notion of a moving earth was specifically condemned as the result of this meeting. However, he himself was neither condemned nor were his books forbidden.

In 1624, Galileo returned to Rome to ask for the right to publish a comparison between the Copernican and Ptolemaic systems. He is refused. Nevertheless, in 1632, he published the Dialogue on the Two Principal Systems of the World, in which he defended the Copernican point of view and showed the limitations of the geocentric model. Caught within the catholic church's counter-reformational need to reaffirm ancient christian dogma, the church forced the extremely ill 70 year old Galileo to come to Rome where he was tried in 1633. His books were forbidden, Galileo had to abjure that the earth was moving, and he was imprisoned and died under house arrest nine years later (1642), but not before publishing a book on mechanics upon which Newton built his laws of motion and another on the strength of materials.

In 1638 he published the Dialogue of Two New Sciences, which included uniform motion, acceleration of falling bodies which included the notion that objects fall at the same rate regardless of their size, density or weight and the parabolic trajectory of projectiles. He also discovered that the period of a pendulum is a function of its length.