The Revival of an Ancient Science

One of the most powerful creations of Greek science was the mathematical astronomy created by Hipparchus in the second century B.C. and given final form by Ptolemy in the second century A.D. Ptolemy's work was known in the Middle Ages through imperfect Latin versions. In fifteenth-century Italy, however, it was brought back to life. George Trebizond, a Cretan emigre in the curia, produced a new translation and commentary. These proved imperfect and aroused much heated criticism.

But a German astronomer, Johannes Regiomontanus, a protege of the brilliant Greek churchman Cardinal Bessarion, came to Italy with his patron, learned Greek, and produced a full-scale "Epitome" of Ptolemy's work from which most astronomers learned their art for the next century and more. Copernicus was only one of the celebrities of the Scientific Revolution whose work rested in large part on the study of ancient science carried out in fifteenth-century Italy.

 In the thirteenth and fourteenth centuries, a number of recent Arabic and Persian astronomical works were translated into Greek by scholars who traveled to Persia under the Ilkhanid Empire.

George Trebizond, one of the notable Greek scholars who came to Italy in the early fifteenth century, made a new translation of the "Almagest" from the Greek for Pope Nicholas V between March and December of 1451. Due to a dispute about the quality of Trebizond's commentary on the text, the translation was never dedicated to Nicholas. This  very elaborate manuscript of the translation, with the figures drawn in several colors, was dedicated to Pope Sixtus IV  by George's son Andreas.

Nasir ad-Din at-Tusi was among the first of several Arabic astronomers of the late thirteenth century at the observatory  of Maragha in Persia who modified Ptolemy's models based on mechanical principles, in order to preserve the uniform  rotation of spheres. This early Arabic manuscript contains his principal work on the subject, the "Tadhkira fi ilm al-Haya"  (Memoirs on Astronomy).

The "Epitome of the Almagest" was written between 1460 and 1463 by Georg Peurbach and Johannes Regiomontanus at the suggestion of Cardinal Bessarion. It gave Europeans the first sophisticated understanding of Ptolemy's astronomy, and was studied by every competent astronomer of the sixteenth century.

Copernicus

Born: 19 Feb 1473 in Torun, Poland

Died: 24 May 1543 in Frombork, Poland

Nicolaus Copernicus was a proponent of the view of an Earth in daily motion about its axis and in yearly motion around a stationary sun. All his life Copernicus was a subject of the King of Poland, but it is possible that his native language was German (his writings are in Latin). Most of East Prussia, including the towns in which he lived, was ceded from Germany to Poland after the Second World War.

Copernicus came from a middle class background and received a good standard humanist education, studying first at the university of Krakow (then the capital of Poland) and then travelling to Italy where he studied at the universities of Bologna and Padua. He eventually took a degree in Canon Law at the university of Ferrara. At Krakow,Bologna and Padua he studied the mathematical sciences, which at the time were considered relevant to medicine (since physicians made use of astrology). Padua was famous for its medical school and while he was there Copernicus studied both medicine and Greek. When he returned to his native land, Copernicus practised medicine, though his official employment was as a canon in the cathedral chapter, working under maternal uncle who was Bishop of Olsztyn (Allenstein) and then of Frombork (Frauenburg).

While he was in Italy, Copernicus visited Rome, and it seems to have been for friends there that in about 1513 he wrote a short account of what has since become known as the Copernican theory, namely that the Sun (not the Earth) is at rest in the centre of the Universe. A full account of the theory was apparently slow to take a satisfactory shape,and was not published until the very end of Copernicus's life, under the title On the revolutions of the heavenly spheres (De revolutionibus orbium coelestium, Nuremberg, 1543). Copernicus is said to have received a copy of the printed book for the first time on his deathbed. (He died of a cerebral haemorrhage.)

Copernicus' heliostatic cosmology involved giving several distinct motions to the Earth. Itwas consequently considered implausible by the vast majority of his contemporaries, andby most astronomers and natural philosophers of succeeding generations before the middle of the seventeenth century. Its notable defenders included Johannes Kepler (1571 -1630) and Galileo Galilei (1564 - 1642). Strong theoretical underpinning for the Copernican theory was provided by Newton's theory of universal gravitation (1687).

The Earth was the fixed center of the universe until Polish astronomer Nicolaus Copernicus ventured the idea that the sun was at the center of the solar system, with the earth and the planets revolving around it. Copernicus, a student of mathematics and astronomy, began to amass evidence disputing the geocentric universe of Aristotle and Ptolemy. But he was also a cautious, one might say a wise man at a time when heretics were put to death. Copernicus didn't publish On the Revolutions of the Celestial Spheres, which would revolutionize our concept of the world, until 1543, when he was on his deathbed.

Galileo

An abstract on Galileo's work with Mechanics

By challenging views of the natural world that had prevailed for 1500 yrs, Italian astronomer, physicist and mathematician, Galileo Galilei changed the way we think. By inventing a mathematical approach to everyday experience, he discovered the laws of inertia, falling bodies and the pendulum. With a telexcope he built, he also made astronomical discoveries that convinced him of the heliocentric view of the universe, which Copernicus had formulated earlier but been hesitant to publish. Galileo took the chance but was forced to retract his findings before a Catholic Church tribunal in 1633. Nonetheless, his beliefs and discoveries lived on, opening the door for modern physics and a new aproach to scientific thought.

The following picture illustrates one of Galileo's experiments

Kepler

Johannes Kepler (1571-1630) was born in the small barony of Württenberg. He originally studied for a theological career. There he learned the principles of the Copernican system. He became an early convert to the heliocentric hypothesis and he defended it in arguments with his fellow scholars.

In 1594, because of his expertise in mathematics, he was offered a position teaching mathematics and astronomy in Graz. While there, he prepared almanacs that gave astronomical and astrological data. Eventually, however, the power of the Catholic church in Graz grew to the point were Kepler, a Protestant, was forced to quit his post. From there, her went to Prague to serve as an assistant to Tycho Brahe.

His first assignment by Brahe was to work on finding a satisfactory theory of planetary motion- one that was compatible with the long series of observations made at Hveen. He worked on this until Brahe's death, at which time he succeeded him as mathematician to the emperor Rudolph. At that time her obtained possession of the majority of Brahe's records. Their study occupied most of Kepler's time for most of 20 years.

Kepler's most detained study was of Mars, for which the observational data was the most extensive. He spent several years trying to fit various combinations of circular motion , including eccentrics and equants, to the observed motion of Mars, but without success. At one point, he found a hypothesis that agreed with observations to within 8 minutes of arc, but he believed that Tycho's observations could not have been in error by even this small amount, so he discarded the hypothesis. Finally, Kepler tried to represent the orbit of Mars with an oval, and soon discovered that the orbit could be fitted very well by a curve known as an ellipse.

1st Law:

2nd Law:

 

3rd Law:

Newton

Coincidentally, Isaac Newton was born in the same year that Galileo died. Newton finished the revolution that was started by Copernicus and, more importantly, firmly established the scientific process that was created by Galileo.

Galileo constantly referred to experiments that would check his hypotheses. This was a new procedure in the study of nature. Prior to his time, the primary method of discussing nature was to refer to the authorities, primarily Aristotle.

Such a reliance on observation and experimentation rather than authority is a cornerstone of science today. Its beginning is usually credited to Galileo, but its preeminence was established by its use by Newton.

A passionately religious man in a time of great scientific discovery, Isaac Newton wanted to know how God's universe worked. His quest for answers gave us the law of universal gravitation, calculus, a new theory of color and light, and the three laws of motion that form the basis of modern mechanics. Brilliant and creative, the English physicist and mathematician synthesized the discoveries of Galileo, Kepler and others, formalizing and transforming physical science. Yet, looking back, Newton said

1st Law of Motion

The most important results of Newton's work are his three laws of motion and his law of universal gravitation. Let's look at the three laws of motion first. The first law of motion was essentially a restatement of Galileo's law of inertia:

Unless an object is acted upon by a net, outside force, the object will maintain a constant velocity. Beyond just restating Galileo's work, Newton used the first law as an opportunity to define a new quantity, momentum.

Momentum is a measurement of an object's tendency to maintain its specific state of motion. In other words,momentum is a measurement of the fact that a moving object tends to keep moving and a stationary object tends to remain at rest. Momentum depends on velocity, for clearly a body moving at 50 km/hr has more "motion" than one moving at 10 km/hr. But momentum also depends on the amount of matter in the moving object and automobile going 30 km/hr certainly has more "motion", and is harder to speed up, stop, or turn than a bicycle moving with the same speed.

Thus, Newton defined momentum to be proportional to velocity, and defined the constant of proportionality as mass. Mass is a quantity that characterizes the total amount of material in the body and is the property that gives the body its inertia.

Once we have this definition of momentum, we can restate Newton's first law as follows:

2nd Law of Motion

The second law of motion deals with changes in momentum. It states that if a force acts on a body it produces a change in the momentum of the body that is in the direction of the applied force. The second law, then, defines force. The magnitude or strength of a force is defined as the rate at which it produces a change in the momentum of the body on which it acts.

Some familiar examples of forces are the pull of the Earth, the friction of air slowing down objects moving through it, the friction of the ground or floor similarly slowing bodies, the impact of a bat on a baseball, the pressure exerted by air, and the thrust of a rocket engine.

Note that Newton's first law of motion is consistent with the second. When there is no force, the change in momentum is zero. There are three ways in which the momentum of an object can change. Its velocity can change, its mass can change, or both. most often the mass of a body does not change when a force acts upon it. A change in momentum usually results from a change in velocity. Thus, in the vast majority of examples, the second law can be written as the simple formula.

                                     Force = mass x acceleration

because acceleration is the rate at which velocity changes. If the acceleration occurs in the same direction as the velocity, the body simply speeds up. If the acceleration occurs in the opposite direction to the velocity, the body slows down. If acceleration occurs at right angles to the velocity, only the direction of motion of the body, and not its speed, changes.

The acceleration of falling bodies is downward (in the direction toward which the gravitational pull of the Earth is acting). Gravity accelerates a body in the direction it is already moving, and so simply speeds it up.

If a body is slid along a rough horizontal surface, it slows down uniformly with time. It is therefore accelerated in the direction opposite to its velocity. The acceleration is produced by the force of friction between the moving body and the rough surface.

In general, both the speed and direction of a body may change. Acceleration is the rate at which the velocity changes, so we reason that if the velocity of a body changes by an amount v in time t, the rate at which it changes, that is its acceleration, is v/t. If the force, (and hence acceleration) were not constant in magnitude and direction, v/t would be only the average acceleration over the time t. However, if the interval t, and hence v, is very small, v/t becomes a good approximation to the instantaneous acceleration.

3rd Law of Motion

Newton's third law of motion was a new idea. It states that all forces occur as pairs of forces that are mutually equal and opposite each other. If a force is exerted on an object, it must be exerted by something else, and the object will exert an equal and opposite force back on that something. All forces, in other words, must be mutual forces acting between two objects or things. Simply stated,

If a man pushes against his car, the car pushes back against him with an equal and opposite force, but if the man has his feet firmly set upon the ground, the reaction force is transmitted through him to the Earth. Because of its enormously greater mass, the Earth accelerates far less than the car.

A more obvious example of the mutual nature of forces between objects familiar to those who have fired a gun is shooting a rifle. When the rifle is discharged, the force pushing the bullet out the muzzle is equal to that pushing backward upon the gun and shooter.

Here, in fact, is the principle of rockets- the force that discharges the exhaust gases from the rear of the rocket is accompanied by a force that shoves the rocket forward. The exhaust gases need not push against the air or the Earth; a rocket operates best of all in a vacuum.

In all the examples discussed, a mutual force acts upon the two objects concerned; each object always experiences the same total change in momentum, but in opposite directions. Because momentum is the product of velocity and mass, the object of lesser mass will end up with proportionally greater velocity.

In fact, a system may be far more complex than just a pair of bodies exerting mutual forces on each other. Suppose, for example, that a rocket in space were to explode into thousands of pieces. Each of the remnants of the explosion has exerted a force on each other in such a way that all the forces balanced each other. Each particle has suffered a change in momentum, but the sum total of all changes in momentum of particles accelerated one way will be equal and opposite to the total change in momentum associated with all the particles going the opposite direction. All these changes in momentum balance each other, so that the total momentum of the entire system, as long as it has not been acted on by external forces, is the same as before the explosion.

In other words, Newton's third law can be thought of as a generalization of his first. The first law states that in the absence of a force, a body's momentum is conserved. The third law means that if we isolate an entire system from outside forces, the total momentum of the system is conserved. Internal forces in the system may result in changes of momentum within it, but these are always accompanied by equal and opposite changes. The total momentum of a rocket, for example, does not change, so long as we always include the momentum of its exhaust gases and any other object that may have come into contact with these gases.

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