CHAPTER IN BRIEF:
CHAPTER IN DETAIL
It is all about our place in the universe and the Planetary motion.
KEY POINTS: Aristotle, Parallax, Ptolemy, Geocentric model, uniform circular motion, retrograde motion, epicycle, deferent, equant,Copernicus, heliocentric model, De Revolutionibus, explanation of retrograde motion, simplicity of the model over Ptolemaic model,Tycho Brahe, appearance of a new star, Tycho Brahe's model, Johannes Kepler, Kepler's 3 laws, HYPOTHESIS, THEORY AND NATURAL LAW, Rudolphine tables, Galileo Galilei, telescopic observations, moon is not perfect, it has mountains and valleys, 4 moons of Jupiter revolve around Jupiter, Phases of venus, Dialogo and the Trial, Isaac Newton and theory of gravity.
CHAPTER IN DETAILS
Early Cosmology
Greek and Roman beliefs that heavens were made of a huge Crystalline Sphere, called the universe with the earth at its center. The area close to earth is made of spheres of water, air and fire. The moon, the sun and the planets are placed in the outer shell of this sphere, beyond that distance are the areas of fixed stars, the rest places of gods and goddesses or the divine. The seven planets (Wanderers), Mercury, Venus, Mars, Jupiter, Saturn, the moon and the Sun, each move in a spherical surface.
The name of Aristotle (384-322 B.C.) the great master of the antiquity, is often quoted for putting forward this model of the Universe. He together with his teacher, the great philosopher Plato believed that the earth was imperfect and changeable whereas the heavens were perfect and immutable. The most perfect geometric figure being a sphere, the heavenly bodies must be made of spheres and the natural motion of the sphere can only be rotation. With no observable parallax in the position of the planets with respect to the distant background stars, they concluded the earth to be at rest. Actually, the parallax is too small for naked eye observation. Parallax is the change in the apparent position of an object due to the change in the location of the observer. Our brain uses parallax method all the times for determining the relative distances between two objects seen by our eyes.
Ptolemy's Almagest (Arabic, meaning the masterpiece) compiled around 140 A.D., contained descriptive motion of heavenly bodies in terms of motion of a wheel, and wheel within a wheel, what is known as retrograde motion with epicycle. The Arabs perfected this model, with apparently no mistake about predicting the location of moon and the planets. This was done by adjusting the constants of the epicycle model.
Following Aristotle, Ptolemy (140 A.C.) working out of Alexandria in Egypt, produced a mathematical model for the planetary motion of the seven planets the believed to be the sun, moon, Mercury, Venus, Mars, Jupiter and Saturn. Ptolemy's book called Mathematical Syntaxis now known as Almagest (from Arabic Al-Magisti, meaning masterpiece), contained descriptive circular motion of the heavenly bodies that compares well with the motion of a wheel, and wheel within a wheel. The model explained the retrograde motion of the planets. In this model, the planets moved on a small circle called Epicycle that was centered on a larger circle called Deferent. The earth was placed close to the center of Deferent. The center of the Epicycle moved with constant speed with respect to a point called Equant placed near the center of the Deferent opposite to earth. Such a model was able to predict the retrograde motion of the planets. Later, the Islamic scholars of the middle ages found much disagreements in this geocentric model of the universe for predicting planet's position in the sky. As a result, they had to introduce new constants and new epicycles to preserve this model for accurate prediction. We must understand that improvements to this model made by Muslim Astronomers were reasonably good at predicting the position of the planets in the sky. This geocentric model survived for a long time by reasoning that no observable parallax exists when one looks at the planets against the background of distant stars. This was the argument put forward by Aristotle.
Nicolaus Copernicus (1473 - 1543) was the first to suggest that the sun was at the center of circular motion of all planets (the heliocentric model), including the earth. He published his ideas before his death in a book called De Revolutionibus. His model could explain the retrograde motion without epicycle. But, it was not completely free of Ptolemy's ideas. He preserved the circular orbits of the planets and introduced equants and small epicycles to explain minor variations from circular orbits. This resulted in simplified calculations with far less number of constants needed to predict position of a planet in the sky. Copernicus is credited for his correct intuition and simple explanation of the planetary motion that resulted from his placing the sun at the center of the universe. The accuracy of predicting the positions of the planets in his model was no better than earlier geocentric model. Yet, he would be remembered for putting the humanity's place on earth as orbiting like any other planet around sun.
HYPOTHESIS: An assertion or conjecture (may or may not be true) with some reasoning, that must be tested for truthfulness. Example, Copernicus asserted that the sun was at the center of all planetary motion.
MODEL: A model is the description of natural phenomenon that may be right or wrong, usually constructed out of a hypothesis.
THEORY: A theory may or may not begin as a hypothesis. It is tested, may be expanded, and generalized.
So, the idea of heliocentric model was a hypothesis to explain the planetary motion in the sky. Later this model was successfully expanded and tested by Kepler and Newton.
Tycho Brahe (1546 - 1588) in his lifetime accumulated a vast amount observational data on the motion of planets. Being a strong supporter of the church, he defended the church's belief that the earth is at rest around which the sun moves in a circle, while other planets move around the sun. This model did not gain much popularity at his death.
Johannes Kepler (1571 - 1630) had the advantage of analyzing the vast amount of Tycho Brahe's data. He was able to show that, all planets move around the sun in elliptic orbits instead of circular orbits. This is known as Kepler's first law of planetary motion.
LAWS OF KEPLER: The following are the three laws of Kepler.
Actually, the orbits of all the planets are nearly circular. Kepler certainly deserves full credit for his famous three empirical laws, describing the planetary motion in the solar system. Later, in Newton's hands, these became natural laws of physics.
His third law may be written as:
P^{2} (in years) = a^{3} (in AU)
Kepler's published work called Rudolphine's Table is a masterpiece. This table was able to predict the position of a planet with very high accuracy.
Later, Galileo Galilei (1564 - 1642 A.C.) supported the heliocentric model of Copernicus and modified by Kepler. By use of the newly invented telescope, Galileo was the first to observe,
1. The 4 moons of the Jupiter circling around the Jupiter as center. So, the notion that moon will be left behind if the earth moved is invalid. Because, Jupiter moved and kept its 4 moons orbiting around it. Also, a direct proof that heavenly bodies also orbit around other planets not just our moon around the earth.
2. The change of phase in Venus just as we observe it in the moon. If Venus was moving on an epicycle between earth and sun, we will only observe its crescent.
3. Our moon to contain mountains, huge craters and valleys on its surface, instead of it being a perfectly smooth heavenly body.
4. The Milky Way filled with myriad of stars that were not visible with naked eye being too faint. This is an intriguing discovery.
5. The moving sunspots, raising the question that sun is also not perfect. Also, the sun rotates about its axis.
Sir Isaac Newton (1642 - 1727 A.C.): From his study of the work of Galileo, Kepler and others, Newton realized that the force responsible for an apple to fall off a tree branch is the same force that pulls the moon towards earth. He explained the difference between mass (as being the same everywhere in the universe) and weight (as being force due to pull of earth's gravity). He enunciated three laws of physics.
1. Law of Inertia: A body at rest remains at rest unless force acted on it changes it. A body moving at constant speed does not change its state of motion unless acted on by an external force.
2. Law of Force: This law may be stated as, the force (F) applied on a body is equal to product of mass (m) and acceleration (a).
F = ma
3. Law of Action and Reaction: Every force has an equal and opposite reaction.
Newton gave the universal law of Gravitation. It states that force of gravitation on one body due to the presence of another body is directly proportional to the product of the two masses and inversely proportional to the square of the distance between the two.
Force, F = G[Mm/r^{2}] where, "G" is universal gravitational constant and "r" is the distance between the two bodies.
Newton showed that an object can be projected outward to send it into the orbit around earth. The speed required is called "escape velocity."
Newton was able to explain the motion of all objects in the heaven and the earth by his universal law of gravitation. If an object is projected from the surface of the earth with sufficient force, it is expected to orbit around the earth. Newton's laws of gravity and general motions concerning the mutual attraction of two bodies were applied to Astronomy with great success.
NEW TERMS:
parallax, geocentric universe, uniform circular motion, retrograde motion, epicycle, deferent, equant, heliocentric universe, paradigm (example or model), hypothesis, theory, natural law, ellipse, mass and Inverse square law.
Updated 01/14/2014