Planets and the Celestial Sphere:

The primary reason for developing the equatorial coordinate system for the celestial sphere was to follow the position of the Sun, Moon and planets in the sky. The Sun and the Moon were important for determination of the calendar and navigation. The planets (Greek for `wanderers') were important to the new science of astrology, the belief that the position of the planets in the sky foretold important events.

There were only seven objects visible to the ancients, the Sun and the Moon, plus the five planets, Mercury, Venus, Mars, Jupiter and Saturn. It was obvious that the planets were not on the celestial sphere since the Moon clearly passes in front of the Sun and planets, plus Mercury and Venus can be seen to transit the Sun. Plato first proposed that the planets followed perfect circular orbits around the Earth. Later, Heraclides (330 B.C.) developed the first Solar System model, placing the planets in order from the Earth it was is now called the geocentric solar system model.

Note that orbits are perfect circles (for philosophical reasons = all things in the Heavens are "perfect"). Heraclides model became our first cosmology of things outside the Earth's atmosphere.

Slightly later, Aristarchus (270 B.C.) proposed an alternative model of the Solar System placing the Sun at the center with the Earth and the planets in circular orbit around it. The Moon orbits around the Earth. This model became known as the heliocentric theory

Problems for Heliocentric Theory:

While today we know that the Sun is at the center of the solar system, this was not obvious for the technology of the times per-1500's. In particular, Aristarchus' model was ruled out by the philosophers at the time for three reasons:

  1. Earth in orbit around Sun means that the Earth is in motion. Before the discovery of Newton's law of motion, it was impossible to imagine motion without being able to `feel' it. Clearly, no motion is detected. For example, the wind does blow in a constant direction.
  2. If the Earth undergoes a circular orbit, then nearby stars would have a parallax. A parallax is an apparent shift in the position of nearby stars relative to distant stars.

    Of course, if all the stars are implanted on the crystal celestial sphere, then there is no parallax.

  3. Lastly, geocentric ideas seem more `natural' to a philosopher. Earth at the center of the Universe is a very ego-centric idea, and has an aesthetic appeal.

Ptolemy:

Ptolemy (200 A.D.) was an ancient astronomer, geographer, and mathematician who took the geocentric theory of the solar system and gave it a mathematical foundation (called the "Ptolemaic system").

Ptolemy wrote a great treatise on the celestial sphere and the motion of the planets call the Almagest. The Almagest is divided into 13 books, each of which deals with certain astronomical concepts pertaining to stars and to objects in the solar system. It was, no doubt, the encyclopedic nature of the work that made the Almagest so useful to later astronomers and that gave the views contained in it so profound an influence. In essence, it is a synthesis of the results obtained by Greek astronomy; it is also the major source of knowledge about the work of Hipparchus.

The Christian Aristotelian cosmos, engraving from Peter Apian's Cosmographia, 1524

In the first book of the Almagest, Ptolemy describes his geocentric system and gives various arguments to prove that, in its position at the center of the universe, the Earth must be immovable. Not least, he showed that if the Earth moved, as some earlier philosophers had suggested, then certain phenomena should in consequence be observed. In particular, Ptolemy argued that since all bodies fall to the center of the universe, the Earth must be fixed there at the center, otherwise falling objects would not be seen to drop toward the center of the Earth. Again, if the Earth rotated once every 24 hours, a body thrown vertically upward should not fall back to the same place, as it was seen to do. Ptolemy was able to demonstrate, however, that no contrary observations had ever been obtained.

Ptolemy accepted the following order for celestial objects in the solar system: Earth (center), Moon, Mercury, Venus, Sun, Mars, Jupiter, and Saturn. However, when the detailed observations of the planets in the skies is examined, the planets undergo motion which is impossible to explain in the geocentric model, a backward track for the outer planets. This behavior is called retrograde motion.

He realized, as had Hipparchus, that the inequalities in the motions of these heavenly bodies necessitated either a system of deferents and epicycles or one of movable eccentrics (both systems devised by Apollonius of Perga, the Greek geometer of the 3rd century BC) in order to account for their movements in terms of uniform circular motion.

In the Ptolemaic system, deferents were large circles centered on the Earth, and epicycles were small circles whose centers moved around the circumferences of the deferents. The Sun, Moon, and planets moved around the circumference of their own epicycles. In the movable eccentric, there was one circle; this was centered on a point displaced from the Earth, with the planet moving around the circumference. These were mathematically equivalent schemes.

Even with these, all observed planetary phenomena still could not be fully taken into account. Ptolemy therefore exhibited brilliant ingenuity by introducing still another concept. He supposed that the Earth was located a short distance from the center of the deferent for each planet and that the center of the planet's deferent and the epicycle described uniform circular motion around what he called the equant, which was an imaginary point that he placed on the diameter of the deferent but at a position opposite to that of the Earth from the center of the deferent (i.e., the center of the deferent was between the Earth and the equant). He further supposed that the distance from the Earth to the center of the deferent was equal to the distance from the center of the deferent to the equant. With this hypothesis, Ptolemy could better account for many observed planetary phenomena.

Although Ptolemy realized that the planets were much closer to the Earth than the "fixed" stars, he seems to have believed in the physical existence of crystalline spheres, to which the heavenly bodies were said to be attached. Outside the sphere of the fixed stars, Ptolemy proposed other spheres, ending with the primum mobile ("prime mover"), which provided the motive power for the remaining spheres that constituted his conception of the universe. His resulting solar system model looked like the following, although the planets had as many as 28 epicycles to account for all the details of their motion.

This model, while complicated, was a complete description of the Solar System that explained, and predicted, the apparent motions of all the planets. The Ptolemic system began the 1st mathematical paradigm or framework for our understanding of Nature.

Copernicus:

As we know from history, the great library at Alexandria burns in 272 AD, destroying a great deal of the astronomical data for the time. Roman culture collapses and we enter the Dark Ages. But, the Roman Catholic Church absorbs Aristotle's scientific methods and Ptolemy's model into its own doctrine. Thus, preserving the scientific method and Ptolemy's Solar System. Unfortunately, the geocentric model was accepted as doctrine and, therefore, was not subjected to the scientific method for hundreds of years.

Copernicus (1500's) reinvented the heliocentric theory and challenged Church doctrine. The heliocentric model had a greater impact than simply an improvement to solve retrograde motion. By placing the Sun at the center of the Solar System, Copernicus forced a change in our worldview = paradigm shift or science revolution.

However, Copernicus, like Ptolemy, also used circular orbits and had to resort to epicycles and deferents to explain retrograde motions. In fact, Copernicus was forced to use more epicycles than Ptolemy, i.e. a more complicated system of circles on circles. Thus, Copernicus' model would have failed our modern criteria that a scientific model be as simple as possible (Occam's Razor).

Planetary Configurations:

The planets outside of the Earth's orbit (Mars, Jupiter, Saturn, Uranus, Neptune, Pluto) are called superior planets

Likewise, the planets inside of the Earth's orbit (Mercury, Venus) are called inferior planets.

Other configurations are:

Tycho Brahe:

Tycho Brahe (1580's) was astronomy's 1st true observer. He built the Danish Observatory (using sextant's since telescopes had not been invented yet) from which he measured positions of planets and stars to the highest degree of accuracy for that time period (1st modern database). He showed that the Sun was much farther than the Moon from the Earth, using simple trigonometry of the angle between the Moon and the Sun at 1st Quarter.

Tycho's measurements were used to show that there was no detectable parallax with the naked eye, in support of the geocentric theory. So, even though his observations were the best for his time, his result was wrong, a lesson in how science is done.

Kepler:

Kepler (1600's) a student of Tycho who used Brahe's database to formulate the Laws of Planetary Motion which corrects the problems of epicycles in the heliocentric theory by using ellipses instead of circles for orbits of the planets.

This is a key mathematical formulation because the reason Copernicus' heliocentric model has to use epicycles is due to the fact that he assumed perfectly circular orbits. With the use of ellipses, the heliocentric model eliminates the need for epicycles and deferents. The orbital motion of a planet is completely described by six elements: the semi-major axis, the eccentricity, the inclination, the longitude of the ascending node, the argument of the perihelion and the time of the perihelion.

The formulation of a highly accurate system of determining the motions of all the planets marks the beginning of the clockwork Universe concept, and another paradigm shift in our philosophy of science.

Galileo:

Kepler's laws are a mathematical formulation of the solar system. But, is the solar system `really' composed of elliptical orbits, or is this just a computational trick and the `real' solar system is geocentric. Of course, the answer to questions of this nature is observation.

The pioneer of astronomical observation in a modern context is Galileo. Galileo (1620's) developed laws of motion (natural versus forced motion, rest versus uniform motion). Then, with a small refracting telescope (3-inches), destroyed the the idea of a "perfect", geocentric Universe with the following 5 discoveries:

spots on the Sun

mountains and "seas" (maria) on the Moon

Milky Way is made of lots of stars

These first three are more of an aesthetic nature. Plato requires a `perfect' Universe. Spots, craters and a broken Milky Way are all features of imperfection and at odds with Plato's ideas on purely philosophical grounds. However, the laws of motion are as pure as Plato's celestial sphere, but clearly are not easy to apply in the world of friction and air currents etc. So these observations, by themselves, are not fatal to the geocentric theory. The next two are fatal and can only be explained by a heliocentric model.

Venus has phases

Jupiter has moons (Galilean moons: Io, Europa, Callisto, Ganymede)

Notice that planets with phases are possible in a geocentric model. But for a planet to change in apparent size with its phases, like Venus is impossible if the planet orbits the same distance from the Earth. And, lastly, if all bodies orbit around the Earth, then the moons of Jupiter, which clearly orbit around that planet, are definitive proof that the geocentric model is wrong.

Today our Solar System looks like this.