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.
Ptolemy:
Ptolemy 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 accepted the following order for celestial objects in the solar system: Earth (center), Moon, Mercury, Venus, Sun, Mars, Jupiter, and Saturn. The Sun appears to describe a yearly circular path called the ecliptic. 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.
Copernicus:
After the destruction of the Library of Alexandria, the Roman Catholic Church absorbed Ptolemy's Solar System model into its own doctrine. Unfortunately, the geocentric model was accepted as doctrine and, therefore, was not subjected to the scientific method for hundreds of years.
Tycho Brahe:
Tycho Brahe (1580's) was astronomy's 1st true observer. He built the Danish Observatory (using sextants 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 Brahe argued that, if an object is near the Earth, its position relative to the background stars should change over night (see definition of parallax). Since he failed to measure the parallax for a supernova in 1572 and a comet in 1577, he concluded that these objects are far from the Earth. Tycho's measurements were used to show that there was ``change'' in the celestial sphere, in contradiction with the assumption of a perfect, immutable Heaven which was one of the pillars of the Greek cosmological model.
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.
Kepler developed, using Tycho Brahe's observations, the first kinematic description of orbits formulated in his three laws of planetary motion. Newton will later develop a dynamic description that involves the underlying influence (gravity)
Ellipses that are highly flattened have high eccentricity. Ellipses that are close to a circle have low eccentricity.
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
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.
Newton:
Newton (1700's) expanded on the work of Galileo to better define the relationship between energy and motion. He expanded the Galileo's work on the motion of objects introducing the concept of accleration:
and developed the following laws of motion:
Newton's Law of Universal Gravitation:
Galileo was the first to notice that objects are ``pulled'' towards the center of the Earth, but Newton showed that this same force (gravity) was responsible for the orbits of the planets in the Solar System. Objects in the Universe attract each other with a force that varies directly as the product of their masses and inversely as the square of their distances
To play a java applet and see the effects of an attractive force varying as 1/r^{2} click here.
Escape Velocity:
A perfect circular orbit occurs if the centrifugal force exactly balances the gravitational force. At the Earth's surface, this value is 7.86 km/s.
A circular orbit for object A occurs when its burnout velocity is v_{c}. When the velocity is v=1.44v_{c}, then a parabolic orbit is achieved and we say the object has reached escape velocity. For a greater velocity, the orbit is hyperbolic.
With vector calculus, Newton was able to develop a cosmology which included the underlying cause of planetary motion, gravity, explained Kepler's laws, and completed the solar system model begun by the Babylonians and early Greeks. The mathematical formulation of Newton's dynamic model of the solar system became the science of celestial mechanics, the greatest of the deterministic sciences.
Scientific Method:
Science is any system of knowledge that is concerned with the physical world and its phenomena and entails unbiased observations and/or systematic experimentation. In general, a science involves a pursuit of knowledge about the operations of fundamental laws of nature.
Science can be separated from pseudo-science by the principle of falsifiability, that is, ideas must be capable of being proven false in order to be scientifically valid. In this regard, science is also separated from religion. Example of pseudo-science are some theories behind crop circles and astrology.
The keystone to science is proof or evidence/data, which is not to be confused with certainty. Except in pure mathematics, nothing is known for certain (although much is certainly false). Central to the scientific method is a system of logic. The scientific method has four steps:
Note that there is an emphasis on falsification, not verification. If a theory passes any test then our confidence in the theory is reinforced, but it is never proven correct in a mathematically sense. Thus, a powerful hypothesis is one that is highly vulnerable to falsification and that can be tested in many ways.
The goal of the scientific method is the construction of models and theories, all with the final goal of understanding.