The Renaissance

We can track the changes in Astronomy during the Renaissance through the contributions of five men: Nicholas Copernicus, Tycho Brahe, Johannes Kepler, Galileo Galilei, and Isaac Newton.

Copernicus taught Aristotelian philosophy at the University. He thinks the old model of Ptolemy is too complex to be correct. Copernicus believes the heliocentric model must be correct. The Earth is now placed as the third planet moving around the Sun. So the first change is that all of the motions we have been observing have the motion of the Earth incorporated in them. We must distinguish between the synodic and sidereal period of planets. The synodic period is the time it takes to orbit the Sun as viewed from someplace that moves, while the sidereal period is the period from someplace that doesn't move. Copernicus finds that he can measure the synodic periods of the planets and convert them into sidereal periods.

Planetary Configurations - Inferior Planets (closer to Sun than Earth)

· Inferior Conjunction (worst observing)

· Superior Conjunction (worst observing)

· Greatest Elongation (best observing)

Planetary Configurations - Superior Planets (farther from Sun than Earth)

· Conjunction

· Opposition (best observing - closest to Earth, high in sky at midnight)

· Quadrature

Comparable terms for lunar orbit

· Full moon is opposition

· New Moon is conjunction

· First Quarter is quadrature

Copernicus uses trigonometry with the planets in these configurations in order to solve for the planet-Sun distance. This gives us the first scale model of the Solar System in astronomical units. The new heliocentric model was no more accurate than the system of Ptolemy, in part because Copernicus still had circular orbits.

Tycho Brahe was a late 16^th century Danish nobleman who carried out an extensive observing program of the planets. He believed that only through observations could we discern one model from another. After being expelled from Denmark and settling in Prague, he hired Johannes Kepler to show what the orbits of the planets were.

Johannes Kepler devised the very first natural laws with his laws of planetary motion. The first law showed that planets orbit the Sun in elliptical paths, the Sun being at one focus of the orbit. The second law tells us how the planets move on their orbits - faster closer to the Sun, slower farther away. The third law relates the orbital period to the size of the orbit. The laws of planetary motion were empirical and universal, although Kepler never correctly surmised the cause of the orbits.

Galileo Galilei is given credit for being among the first to turn a telescope onto the sky. In the course of three years of observing, he convincingly overturned 1500 years of Aristotelian thought. Most of his observations circumstantially argue against the old order. These include:

· The vast number of stars in the Milky Way - people believed that Aristotle told us everything there was to know. Also even though individually too faint to see, we can observe the combined light of these faint stars.

· The Moon - Earthlike features on an object clearly in the Celestial Realm.

· The moons of Jupiter - some objects do not go around the Earth.

· Sunspots - the personification of God had flaws.

One of his observations, however, provided proof that the geocentric models were wrong. Venus went through a full range of phases just like our Moon. Galileo also gave us the Law of Inertia and the Scientific Method.

Isaac Newton closed the era by providing the three laws of general motion:

· Forces cause changes in motion.

· SF = ma

· For every action force there is an equal and opposite reaction force.

These laws completely restructure physics. No longer is it necessary to know the composition of an object in order to predict its motion. The artificial Celestial and Terrestrial Realms have disappeared.

Next Newton gives us a comprehensive theory of gravity. The force of gravity is directly proportional to the product of the masses and inversely proportional to the square of their separation. Some of the consequences of this formulation for gravity are:

· Gravity is the first of many inverse square laws.

· Gravity never becomes zero. All objects ion the universe have a gravitational attraction for all other objects.

· Mass causes gravity

· Gravity is only attractive which means there is only one kind of mass.

· The gravitational constant G is very small.

Using the laws of motion and the new formulation for gravity, Newton is able to prove Kepler's Laws. Newton generalizes the laws of Kepler, showing that possible orbits under the influence of gravity are conic sections. Kepler's Laws are now seen to be universal, applying anytime the attractive force is gravity.

He can also prove Galileo's assertion that all objects near the surface of the Earth accelerate in the same way. Combined with the new view of orbiting (falling without getting closer to the surface), we can now explain apparent weightlessness.