Annex 1 - Great Scientists

Aristotle
Aristotle was born in 384 BC in Stagira, Chalcidice, Greece, and he died in 322 at Chalcis, Euboea. He was a philosopher, scientist, one of the greatest Greek intellectual figures of all times. He studied the whole field of human knowledge that was known in the Mediterranean world in his days; and his writings long influenced Western and Muslim thought. The son of the court physician to the king of Macedonia, Aristotle was probably introduced to Greek medicine and biology at an early age. Following the death of his father, he was sent to the Athenian Academy of Plato and there engaged in dialogues for 20 years. On Plato's death in 348/347 he left Athens and travelled for 12 years, establishing new academies at Assus and at Mytilene. He lived at Pella, the capital of Macedonia, for about three years, tutoring the future Alexander the Great. He retired to his paternal property at Stagira in about 339. In 335 he returned to Athens and, at nearly the age of 50, opened the Lyceum, an institution to rival the Academy. For the next 12 years he organized it as a centre for speculation and research in every field of inquiry; the chief contributions of the Lyceum are in biology and history. On the death of Alexander in 323, an anti-Macedonian agitation broke out in Athens, and Aristotle withdrew to Chalcis where he died the following year. Aristotle's extant works comprise mostly notes used in giving courses at the lyceum.

In his book "On the Heavens", Aristotle said that, in his opinion, the earth was a sphere and not flat. He based this affirmation on the following observations:
- He realised that the eclipses of the moon were due to the earth coming between it and the sun. As the shadows of the earth on the moon are always round, this implies that the earth is a sphere. If it had been flat the shadows would have been elliptical.
- He knew from other Greek scientists that the North Star appeared lower in the sky when seen from southern countries that it did in the north. From these observations he was able to calculate an approximate value for the circumference of the earth. He quoted it as being 400,000 "stadia". Unfortunately we do not know the length of the stadia in modern units.
- He also had noted that one first sees the sails of a ship coming from far away, and only later on the hull.

Like all the people of his time -and for many centuries after him- he believed that the earth was at rest and that the sun, the moon, the other planets, and the stars were rotating on circular orbits around it. This was due to the fact that he believed that the earth was the centre of the universe.

Aristotle suggested that everything is made of four elements (earth, air, fire and water). This theory does not explain many observations, and does not allow any prediction and, if only for these reasons, it was rejected later on.

Bohr, Niels
Bohr was born October 7, 1885, in Copenhagen, Denmark and he died November 18, 1962, in Copenhagen. Bohr, a Danish physicist, was the first to apply the quantum theory -which restricts the energy of a system to certain discrete values- to the problem of atomic and molecular structure. For this work he received the Nobel Prize for Physics in 1922. He developed the so-called Bohr Theory of the atom and the liquid model of the atomic nucleus.

Bohr's scientific interests and abilities were evident early, and they were encouraged and fostered in a warm, intellectual family atmosphere. Bohr distinguished himself at the University of Copenhagen, winning a gold medal from the Royal Danish Academy of Sciences and Letters for his theoretical analysis and precise experiments of the vibrations of water jets as a way of determining surface tension. In 1911 he received his doctorate for a thesis on the electron theory of metals. He then went to England, intending to continue this work with Sir J.J. Thomson at Cambridge but the British scientist never showed much interest in Bohr's ideas on electrons in metals. Bohr moved to Manchester in March 1912 and joined Ernest Rutherford's group studying the structure of the atom. At Manchester Bohr worked on the theoretical implications of the nuclear model of the atom recently proposed by Rutherford. Bohr was among the first to see the importance of the atomic number, which indicates the position of an element in the periodic table. Rutherford's nuclear atom model was mechanically and electromagnetically unstable, but Bohr imposed stability on it by introducing the new ideas of the quantum theory developed by Max Planck, Albert Einstein, and other physicists. Bohr postulated that any atom could exist only in a discrete set of stable or stationary states, each characterized by a definite value of its energy. Bohr postulated that an atom would not emit radiation while it was in one of its stable states, but only when it made a transition between states. The frequency of the radiation emitted is equal to the difference in energy between those states divided by Planck's constant. This meant that the atom could neither absorb nor emit radiation continuously, but only in finite steps or quantum jumps.

Bohr returned to Copenhagen from Manchester in 1912. In 1916, he was appointed to a professorship in his native city. The university created a new Institute of Theoretical Physics in 1921 and Bohr was its director for the rest of his life. In the 1920s, Bohr tried to develop a consistent quantum theory that would replace classical mechanics and electrodynamics at the atomic level. His institute became an international centre for work on atomic physics and the quantum theory. During the next few years, a genuine quantum mechanics was created, very similar to what Bohr had been expecting. The most famous and most outspoken dissenter of Bohr's theories was Einstein. Although he greatly admired Bohr's early work, he never accepted Bohr's claim that quantum mechanics was the "rational generalization of classical physics" required for the understanding of atomic phenomena. They never agreed, but Bohr emphasized how important Einstein's challenging objections had been to the evolution of his own ideas. During the 1930s Bohr continued to work on the problems raised by the quantum theory and also contributed to the new field of nuclear physics. His liquid-drop model of the atomic nucleus was a key step in the understanding of many nuclear processes and in particular in 1939 in the understanding of nuclear fission. In 1943, under threat of arrest because of his Jewish ancestry and his anti-Nazi views Bohr, together with his wife and some other family members, escaped to Sweden in a fishing boat. He then flew to England. During the next two years, Bohr and his son Aage took part in a nuclear fission bomb project. They worked in England for several months and then moved to Los Alamos, New Mexico, USA, with a British research team. Bohr was concerned about the terrifying prospects for humanity posed by such atomic weapons; he tried to persuade British Prime Minister Winston Churchill and US president Franklin D. Roosevelt of the need for international cooperation in dealing with these problems. Bohr was convinced that free exchange of people and ideas were necessary to achieve control of nuclear weapons. He led in promoting such efforts at the First International Conference on the Peaceful Uses of Atomic Energy, held in Geneva (1955), and in helping to create the European Council for Nuclear Research (CERN).

Copernicus, Nicholaus
Copernicus received his university education at Kraków (1491-94?) in Poland, Bologna and Padua in Italy (1497-1503). In 1503 he returned to Poland and took up residence in Frauenburg where, in 1497, he had been elected a canon of the cathedral, a post ensuring lifelong financial security. In 1497 he made the first of his few recorded astronomical observations. Becoming increasingly dissatisfied with earth-centred ideas of the universe, he spent years developing the theory that earth and the other planets revolved about a point in space near the Sun.

Copernicus proposed that the planets have the sun as the fixed point to which their motions are to be referred; that the earth is a planet which, besides moving on a circular orbit around the Sun annually, also turns once daily on its own axis; and that very slow, long-term changes in the direction of this axis account for the precession of the equinoxes. This representation of the heavens is usually called the heliocentric, or "Sun-centred" system. Copernicus's theory had important consequences for later thinkers, including such major figures as Galileo, Kepler, Descartes, and Newton. Copernicus probably hit upon his main ideas sometime between 1508 and 1514, and during those years he wrote a manuscript, the "Commentariolus" ("Little Commentary"). However, the book that contains the final version of his theory, "De revolutionibus orbium coelestium libri vi" ("Six Books Concerning the Revolutions of the Heavenly Orbs"), did not appear in print until 1543, the year of his death. It took one century for his theory to be accepted.

Albert Einstein
Albert Einstein was born March 14, 1879, in Ulm, Württemberg, Germany and died April 18, 1955, in Princeton, New Jersey, USA. He was the physicist who developed the special and general theories of relativity. He won the Nobel Prize for Physics in 1921, not for his main work on relativity that was not yet fully accepted, but for his explanation of the photoelectric effect. He was recognized in his own time as one of the most creative intellects in human history. In the first 15 years of the 20th century Einstein proposed a series of theories that led to entirely new ways of thinking about space, time, and gravitation. His theories of relativity and gravitation were a profound advance over the old Newtonian physics and revolutionized scientific and philosophic inquiry. Almost reluctantly he admitted that he had a "passionate sense of social justice and social responsibility." His celebrity gave him an influential voice that he used to champion such causes as pacifism, liberalism, and Zionism. His famous energy-mass equation, which states that a particle of matter can be converted into an enormous quantity of energy, was at the base the atomic and hydrogen bombs.

Einstein published four research papers in 1905 in what is now a collector item volume 17 of "Annalen der Physik"-including the Special Theory of Relativity-, each containing a great discovery in physics:
- The first paper deals with statistical mechanics and shows that any gas consists of a lot of molecules or atoms bouncing off each other and from the walls of their container in random motion. This proved the existence of atoms although they are to little to be seen.
- The second paper deals with the photoelectric effect. If a beam of light hits a metallic surface, the metal emits particles carrying a negative electrical charge-electrons- and this creates an electric current. Using Planck's quantum hypothesis he went further assuming that light must, for some applications, be seen as quantised particles (photons) while for others it behaves like waves. Einstein received the Nobel Prize for Physics for this work.
- The third paper was on the special theory of relativity that changed the way we look at space and time. In it he showed that the speed of light is an absolute constant, that moving clocks go slower that those at rest, and that objects decrease in length when moving. These effects are only noticeable at speed close to the velocity of light.
- In his fourth paper Einstein showed that mass and energy are the same (this is shown by the well-known equation linked for ever to Einstein, E=mc²).

They were followed by his General Theory of Relativity in 1915. International fame came to Einstein in 1919 with the announcement that a prediction of his general theory of general relativity was verified. In 1933 Einstein joined the Institute for Advanced Study in Princeton, New Jersey, USA, and became a US citizen in 1940. At the institute Einstein continued his work on general relativity, the unified field theories, and the critical discussion of the interpretation of quantum theory. He also cooperated with charitable and social organizations to help the large number of refugees who were arriving in the United States from Nazi Germany. In 1939 two German physicists discovered the fission of uranium. Enrico Fermi, a Jewish Italian physicist who was also in the United States, thought that the fission of uranium and plutonium through chain reaction would release enormous quantities of energy. Fermi and the Hungarian physicist Leo Szilard informed the US government. Szilard and Eugene Wigner, another Hungarian physicist, asked Einstein to appeal directly to President Franklin D. Roosevelt, pointing out the dangers if Germany succeeded in developing a bomb based on these principles. Einstein's letter to President Roosevelt resulted in the Manhattan Project and in the development of the atom bomb. In 1945 Einstein retired from his position at the institute but continued to work there until his death.

Euclid
Euclid lived in Alexandria, Egypt, around 300 BC. He was the most prominent mathematician of Greco-Roman antiquity, best known for his treatise on geometry, the Elements.

Of Euclid's life nothing is known except what the Greek philosopher Proclus (c. AD 410-485) reports in his "summary" of famous Greek mathematicians. According to him, Euclid taught at Alexandria in the time of Ptolemy I Soter, who reigned over Egypt from 323 to 285 BC.

Euclid drew upon all his predecessors, but his most important work, "Elements", was his own; it does not concern only geometry, as reading no further than Books I through IV, which cover elementary plane geometry, would suggest. Building a logical and rigorous geometry (and mathematics) depends on the foundation -a foundation that Euclid began in Book I with 23 definitions (such as "a point is that which has no part" and "a line is a length without breadth"), five unproved assumptions that Euclid called postulates (now known as axioms), and five further unproved assumptions that he called common notions. Book I proves elementary theorems about triangles and parallelograms and ends with the Pythagorean theorem. The subject of Book II is geometric algebra; it contains the division of a line into two parts such that the ratio of the larger to the smaller segment is equal to the ratio of the original line to the larger segment. This division was renamed the golden section in the Renaissance after artists and architects rediscovered its pleasing proportions. Book II also generalizes the Pythagorean theorem to arbitrary triangles. Book III deals with properties of circles and Book IV with the construction of regular polygons, in particular the pentagon. Book V shifts from plane geometry to expound a general theory of ratios and proportions. While Book V can be read independently of the rest but its solution to the problem of irrational numbers is essential to later books. In addition, it formed the foundation for a geometric theory of numbers. Book VI applies this theory of ratios to plane geometry, mainly triangles and parallelograms; it also contains a procedure for solving quadratic problems by geometric means. Books VII-IX contain elements of number theory, where number means positive integers greater than 1. Beginning with 22 new definitions -such as unity, even, odd, and prime-these books develop various properties of the positive integers. For instance, Book VII describes a method for finding the greatest common divisor of two or more numbers; Book VIII examines numbers in continued proportions, now known as geometric sequences; and Book IX proves that there are an infinite number of primes. Book X deals with the classification of incommensurable lines and areas. Books XI-XIII examine three-dimensional figures. Book XI concerns the intersections of planes, lines, and parallelepipeds. Book XII prove that the areas of circles are to one another as the squares of their diameters and that the volumes of spheres are to one another as the cubes of their diameters. Book XIII culminates with the construction of the five regular Platonic solids (pyramid, cube, octahedron, dodecahedron, icosahedron) in a given sphere.

Galileo Galilei
Galileo was born in Pisa, Tuscany, Italy, on February 15, 1564. The family moved to Florence in the early 1570s, where the Galilei family had lived for generations. In his middle teens Galileo attended the monastery school at Vallombrosa, near Florence, and then in 1581 matriculated at the University of Pisa, where he was to study medicine. However, he liked mathematics more and decided to make mathematics and philosophy his profession. Galileo then began to prepare himself to teach Aristotelian philosophy and mathematics, and several of his lectures have survived. In 1585 Galileo left the university without having obtained a degree, and for several years he gave private lessons in mathematics in Florence and Siena. During this period he began his studies on motion that he pursued steadily for the next two decades. In 1588 Galileo applied for the chair of mathematics at the University of Bologna but was unsuccessful. His reputation was, however, increasing, and later that year he was asked to deliver two lectures to the Florentine Academy, a prestigious literary group, on the arrangement of the world in Dante's Inferno. He also found some ingenious theorems on centres of gravity (again, circulated in manuscript) that brought him recognition among mathematicians. As a result, he obtained the chair of mathematics at the University of Pisa in 1589. But his attacks on Aristotle made him unpopular with his colleagues and, in 1592, his contract was not renewed. His patrons, however, secured him the chair of mathematics at the University of Padua, where he taught from 1592 until 1610.

At the University of Pisa Galileo demonstrated, by dropping bodies of different weights from the top of the famous Leaning Tower, that the speed of fall of a heavy object is not proportional to its weight, as Aristotle had claimed. The manuscript tract "De motu" (On Motion), written during this period, shows that Galileo was abandoning Aristotelian notions about motion and was instead taking an Archimedean approach to the problem. Galileo developed the astronomical telescope, with which he discovered craters on the Moon, sunspots, phases of Venus, and the satellites of Jupiter. The discovery of these satellites showed that all the heavenly bodies did not have to rotate around the earth as Aristotle and Ptolemy thought. Many scientists had doubts about his findings. He showed that the Milky Way is composed of stars. His astronomical observations led him to espouse the Copernican theory that the planets revolve around the Sun. This conflicted with the teachings of the Roman Catholic Church and Galileo was forced to recant his findings. He was put under house arrest for the final eight years of his life for having "held and taught" Copernican doctrine. In 1992 the church formally acknowledged its error in condemning Galileo. Galileo's major works were Dialogue Concerning the Two Chief World Systems-Ptolemaic and Copernican (1632) and Dialogue Concerning Two New Sciences (1638).

Heisenberg, Werner
Heisenberg was born December 5, 1901, in Wurzburg, Germany and died February 1, 1976, in Munich. Heisenberg was a physicist and philosopher who discovered a way to formulate quantum mechanics in terms of matrices (1925). For that discovery, he was awarded the Nobel Prize for Physics for 1932. In 1927 he published his "uncertainty principle." His philosophy is based on it. He also made important contributions to the theories of the hydrodynamics of turbulence, the atomic nucleus, ferromagnetism, cosmic rays, and elementary particles. He was involved in the design of the first post-World War II German nuclear reactor, at Karlsruhe. In his philosophical and methodological writings, Heisenberg was much influenced by Niels Bohr and Albert Einstein. He was co-author with Bohr of the philosophy of complementarity. In his later life he conceived of a central order in nature, consisting of a set of universal symmetries that can be expressed in a single mathematical equation for all systems of particulate matter. As a public figure, he actively promoted the peaceful use of nuclear energy after World War II and, in 1957, led other German scientists in opposing a move to equip the West German Army with nuclear weapons. He was, in 1954, one of the organizers of the Conseil Européen pour la Recherche Nucléaire (CERN; later, Organisation Européene pour la Recherche Nucléaire) in Geneva Switzerland.

Hipparchus
Hipparchus was born in Nicaea, Bithynia and died after 127, BC, probably in Rhodes. He was a Greek astronomer and mathematician who discovered the precession of the equinoxes, calculated the length of the year to within 6 1/2 minutes, compiled the first known star catalogue, and made an early formulation of trigonometry. Hipparchus carried out his observations in Bithynia, at Rhodes, where he spent much time, and also, it seems, at Alexandria. The year 127 BC is usually cited as the last date known for his actual work, and a French astronomer, Jean-Baptiste-Joseph Delambre (1749-1822), clearly demonstrated that some observations of Hipparchus on the star Eta Canis Majoris could well have been carried out in that year.

Hipparchus is best known for his discovery of the precessional movement of the equinoxes. The term is still in current use, although the phenomenon is more usually referred to merely as "precession." Hipparchus observed the positions of the stars and then compared his results with those of Timocharis of Alexandria about 150 years earlier and with even earlier observations made in Babylonia. He discovered that the celestial longitudes were different and that this difference was of a magnitude exceeding that attributable to errors of observation. He therefore proposed precession to account for the size of the difference and he gave a value of 45² or 46² (seconds of arc) for the annual changes. This is very close to the figure of 50.26² accepted today. Observations of star positions measured in terms of celestial latitude and longitude, as was customary in antiquity, were carried out by Hipparchus and entered in a catalogue-the first star catalogue ever to be completed. Hipparchus measured the stellar positions with greater accuracy than any observer before him, and his observations were of use to Ptolemy and even later to Edmond Halley. Hipparchus had been stimulated in 134 BC by observing a "new star." Concluding that such a phenomenon indicated a lack of permanency in the number of "fixed" stars, he determined to catalogue them, and no criticism was able to deflect him from his original purpose. Hipparchus' catalogue, completed in 129 BC, listed about 850 stars the apparent brightness of which was specified by a system of six magnitudes similar to that used today.

Hipparchus studied the motion of the sun and the moon. The motion of the Moon is more complex than that of the Sun, owing to the perturbations that the Moon suffers from both Earth and Sun; in consequence, there are more irregularities to be taken into consideration. Hipparchus accounted for that inequality of the Moon's motion that is now known to be due to the elliptical form of its orbit. His theory gave reasonably satisfactory results for the motion at Full and New Moon. Hipparchus also attacked the problem of the relative size of the Sun and Moon and their distance from the Earth. It had long been appreciated, of course, that the apparent diameter of each was the same, and various astronomers had attempted to measure the ratio of size and distance of the two bodies. Eudoxus obtained a value of 9:1, Phidias (father of Archimedes) 12:1, Archimedes himself 30:1; while Aristarchus believed 20:1 to be correct. The present-day value is, approximately, 393:1. Hipparchus followed the method used by Aristarchus but he obtained no satisfactory result from his efforts. At least he appreciated that the distance of the Sun was very great indeed. Hipparchus was unsuccessful in forming a satisfactory planetary theory and was scientist enough to avoid building hypotheses on insufficient evidence. In his work Hipparchus adopted the generally accepted order for the Sun, Moon, and planets. With the Earth as the centre, they were, in order from the Earth, the Moon, Mercury, Venus, the sun, Mars, Jupiter, and Saturn.

Kepler, Johannes
Kepler, a German astronomer, discovered that the Earth and planets travel about the Sun in elliptical orbits. He transformed the old, geometric description of the heavens into dynamical astronomy. After studying astronomy at the University of Tübingen under Michael Mästlin, who believed in the Copernican theory, Kepler wrote a paper that came to the attention of Galileo and Tycho Brahe. Subsequently, while lecturing on mathematics, rhetoric, and Virgil at the Lutheran high school in Graz, Austria, Kepler was invited to join Tycho's research staff at the observatory outside Prague. In the following year (1601) Tycho died and Kepler was appointed his successor as imperial mathematician of the Holy Roman Empire. Using Tycho's extraordinarily accurate collection of astronomical observations, Kepler was able to deduce three fundamental laws of planetary motion that later enabled Sir Isaac Newton to formulate his theory of gravitational force. Kepler also founded modern optics by postulating the ray theory of light to explain vision. In 1627 Kepler published his Tabulae Rudolphinae, containing tables that held their place for more than a century, being universally used in calculating planetary positions and an extended catalogue of 1,005 stars based on Tycho's observations of 777 star positions.

Kepler discovered three major laws of planetary motion:
- The planets move in elliptical orbits with the Sun at one focus
- The time necessary to traverse any arc of a planetary orbit is proportional to the area of the sector between the central body and that arc (the "area law")
- There is an exact relationship between the squares of the planets' periodic times and the cubes of the radii of their orbits (the "harmonic law").

Kepler himself did not call these discoveries "laws," as would become customary after Isaac Newton derived them from a new and quite different set of general physical principles. He regarded them as celestial harmonies that reflected God's design for the universe. Kepler's discoveries turned Nicholaus Copernicus' Sun-centred system into a dynamic universe, with the Sun actively pushing the planets around in noncircular orbits. Among Kepler's many other achievements, he developed a new explanation for the behaviour of light in the newly invented telescope and he suggested a new theoretical foundation for astrology while at the same time restricting the domain in which its predictions could be considered reliable.

Newton, Isaac
Isaac Newton was born December 25, 1642, [January 4, 1643, New Style], in Woolsthorpe, Lincolnshire, England. He died March 20 [March 31], 1727, in London. A physicist and mathematician, he invented the infinitesimal calculus, laid the foundations of modern physical optics, and formulated three laws of motion that became basic principles of modern physics and led to his theory of universal gravitation. He is regarded as one of the greatest scientists of all time. Newton received a bachelor's degree at Trinity College, Cambridge, in 1665. During the next two years while the university was closed because of plague, Newton returned home. There he thought about how certain natural phenomena might be explained and he formulated the bases of his first major discoveries. He returned in 1667 as a fellow to Trinity College where he became Lucasian professor of mathematics in 1669. In 1666 Newton discovered the nature of white light by passing a beam of sunlight through a prism. He invented the calculus about 1669 but did not formally publish his ideas until 35 years later. He built the first reflecting telescope in 1668. Newton's most famous publication, "Philosophiae Naturalis Principia Mathematica" (1687; Mathematical Principles of Natural Philosophy), contains his work on the laws of motion, the theory of tides, and the theory of gravitation. His laws of motion laid the basis for classical mechanics, and the theory of gravity was particularly important in working out the motions of the planets. The Principia has been called one of the most important works of science ever written. In another book, Opticks (1704), Newton described his theory of light as well as the calculus and other mathematical researches. Newton served as warden of the Royal Mint from 1696 and became president of the Royal Society in 1703, holding this office until his death. In 1705 he became the first British scientist ever to receive a knighthood for his researches.

Law of gravitation
Any particle of matter in the universe attracts any other with a force proportional to their masses and inversely proportional to the square of the distance between them. In mathematical form, the attractive force F is equal to G (the gravitational constant, a number the size of which depends on the system of units used and which is a universal constant) multiplied by the product of the masses (m1 and m2) and divided by the square of the distance R that is: F = G*m1*m2/R². Isaac Newton put forward the law in 1687 and used it to explain the observed motions of the planets and their moons, which had been reduced to mathematical form by Johannes Kepler early in the 17th century.

Law of motion
The relations between the forces acting on a body and the motion of the body, formulated first by Isaac Newton, had been discovered experimentally by Galileo about four years before Newton was born. The laws cover only the overall motion of a body that is the motion of its centre of mass. This concept is equivalent to assuming that the body is a particle with a definite mass, but no size. Strictly speaking, the laws are valid only for motions relative to a reference frame (coordinate system) attached to the fixed stars. Such a reference frame is known as a Newtonian, Galilean, or an inertial frame. Because the Earth rotates, a reference frame attached to the Earth is not inertial, and in some cases this rotation must be considered when applying Newton's laws. In most applications, however, the Earth's rotation can be neglected.
- Newton's first law states that if a body is at rest, or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless a force acts it upon. This postulate is known as the law of inertia. It is a description of one of the properties of a force: its ability to change rest into motion, or motion into rest, or one kind of motion into another kind. Before Galileo's time it was thought that bodies could move only as long as a force acted on them and that in the absence of forces they would remain at rest.
- Newton's second law is a quantitative description of the changes that a force can produce in the motion of a body. It states that the change of velocity, or acceleration, a, is directly proportional to the force F and inversely proportional to the mass m of the body; a = F / m or F = ma; the larger the force, the larger the acceleration; the larger the mass, the smaller the acceleration. Both force and acceleration have direction as well as magnitude, and are represented in calculations by vectors having lengths proportional to their magnitudes. The acceleration produced by a force (or more forces) is in the same direction as the force or in the direction of their resultant. A simple case is a freely falling body. Neglecting air resistance, the only force acting on the body is its weight acting down, and it produces a downward acceleration equal to the acceleration of gravity, symbolized as g, which has an average value of 9.8 metres (32.2 feet) per second per second near the surface of the Earth.
- Newton's third law states that the actions of two bodies upon each other are always equal and directly opposite that is, reaction is always equal and opposite to action. The proposition seems obvious for two bodies in direct contact; the downward force of a book on a table is equal to the upward force of the table on the book. It is also true for gravitational forces; a flying airplane pulls up on the Earth with the same force that the Earth pulls down on the airplane. The third law may not hold for electromagnetic forces when the bodies are far apart.

From his laws Newton showed that:
- As a result of gravity the moon moves around the earth on an elliptical orbit and the earth and the planets also move on elliptical orbits around the sun.
- Together with Copernicus, Newton's laws showed that the concept of Ptolemy's celestial spheres was wrong, and that the universe had no natural boundary.
- Due to the gravity, the stars attract each other so they cannot stay at rest. However Newton explained that this does not happen only because there are an infinite number of them distributed more or less uniformly over infinite space. This infinite universe, and infinite number of stars, is difficult to imagine. Moreover, as a consequence, the universe is not static and, if the gravity is always attractive, it must expend or contract.

Planck, Max
Planck was born April 23, 1858, in Kiel, Schleswig, Germany, and died October 4, 1947, Göttingen. Planck, a theoretical physicist, introduced, among other things, the quantum theory, which made him famous and which won him the Nobel Prize for Physics in 1918. This theory revolutionized our understanding of atomic and subatomic processes, just as Albert Einstein's theory of relativity revolutionized our understanding of space and time. Together they constitute the fundamental theories of 20th-century physics.

Max Karl Ernst Ludwig Planck was the sixth child of a distinguished jurist and professor of law at the University of Kiel. The long family tradition of devotion to church and state, excellence in scholarship, incorruptibility, conservatism, idealism, reliability, and generosity became deeply ingrained in Planck's own life and work. When Planck was nine years old, his father received an appointment at the University of Munich, and Planck entered the city's renowned Maximilian Gymnasium, where a teacher, Hermann Müller, stimulated his interest in physics and mathematics. But Planck excelled in all subjects, and after graduation at age 17 he faced a difficult career decision. He ultimately chose physics over classical philology or music. Planck entered the University of Munich in the fall of 1874 followed by a year spent at the University of Berlin (1877-78). His intellectual capacities were brought to a focus as the result of his independent study, especially of Rudolf Clausius' writings on thermodynamics. Returning to Munich, he received his doctoral degree in July 1879 (the year of Einstein's birth) at the unusually young age of 21. The following year he completed his Habilitationsschrift (qualifying dissertation) at Munich and became a Privatdozent (lecturer). In 1885, with the help of his father's professional connections, he was appointed ausserordentlicher Professor (associate professor) at the University of Kiel. In 1889 Planck received an appointment to the University of Berlin. In 1892 he was promoted to ordentlicher Professor (full professor). He remained in Berlin for the rest of his active life.

In 1859-60 Kirchhoff had defined a blackbody as an object that reemits all of the radiant energy incident upon it; it is a perfect emitter and absorber of radiation. There was, therefore, something absolute about blackbody radiation. Planck was particularly attracted to the formula found in 1896 by his colleague Wilhelm Wien and he subsequently made a series of attempts to derive "Wien's law" on the basis of the second law of thermodynamics. By October 1900, other scientists had found indications that Wien's law, while valid at high frequencies, broke down completely at low frequencies. Planck knew how the entropy of the radiation had to depend mathematically upon its energy in the high-frequency region if Wien's law held there. He also saw what this dependence had to be in the low-frequency region in order to reproduce the experimental results there. Planck guessed that he should try to combine these two theories, and to transform the result into a formula relating the energy of the radiation to its frequency. The result, Planck's radiation law, was hailed as indisputably correct. To Planck, however, it was simply a guess, a "lucky intuition" and, to be taken seriously, it had to be derived somehow from first principles. By December 14, 1900, he had succeeded, but he had to relinquish one of his own most cherished beliefs, that the second law of thermodynamics was an absolute law of nature and not only a statistical law as other scientists believed. Planck had also to assume that the blackbodies re-emitting the radiant energy incident upon them could not absorb this energy continuously, but only in discrete amounts, in quanta of energy, each containing an amount of energy proportional to its frequency. In this way Planck derived the formula he had hit upon two months earlier. He used it to evaluate the constant h (his value was 6.55 ´ 10-27 erg-second, close to the modern value), as well as the so-called Boltzmann constant (the fundamental constant in kinetic theory and statistical mechanics), Avogadro's number, and the charge of the electron. As a consequence physicists recognized that -because Planck's constant was not zero- the world of atomic dimensions, could not be described by ordinary classical mechanics. Planck's concept of energy quanta, in other words, conflicted fundamentally with all past physical theory. It took years before the far-reaching consequences of Planck's achievement were generally recognized, and in this Einstein played a central role. In 1905 Einstein argued that radiant energy itself seemed to consist of quanta (light quanta, later called photons). In 1909 Einstein introduced the wave-particle duality into physics. In October 1911 he attended the first Solvay conference in Brussels where the discussions stimulated Henri Poincaré to provide a mathematical proof that Planck's radiation law necessarily required the introduction of quanta. In 1913 Niels Bohr also contributed greatly to its establishment through his quantum theory of the hydrogen atom. Planck was the first prominent physicist to champion Einstein's special theory of relativity (1905). "The velocity of light is to the Theory of Relativity," Planck remarked, "as the elementary quantum of action is to the Quantum Theory." In his later years, Planck devoted more and more of his writings to philosophical, aesthetic, and religious questions. Together with Einstein and Schrödinger, he remained adamantly opposed to the indeterministic, statistical worldview introduced by Bohr, Max Born, Werner Heisenberg, and others into physics after the advent of quantum mechanics in 1925-26.

Ptolemy
Ptolemy became famous in the years 127 -145 AD in Alexandria. Claudius Ptolemaeus was an astronomer, geographer and mathematician who considered the Earth the centre of the universe. Virtually nothing is known about his life.

In the 2d century AD Ptolemy developed Aristotle's theories into a cosmological model. According to him the immobile earth was at the centre of eight spheres on which the sun, the moon, the five planets known at that time (Mercury, Venus, Mars, Jupiter and Saturn) and the stars were moving. As the planets had rather complicated trajectory in the space there believe to move on small circles attached to their sphere. The stars are on the eighth sphere, they remain at the same position in relation to each other and, in consequence, move together on their sphere.

This simple cosmology allowed Ptolemy to predict the positions of all bodies in the sky; however he had to make some unproved assumptions on the moon trajectory. Most scientists accepted this theory for a long period of time. Even the Christian Church accepted it, as it did not contradict the Bible. This was also probably due to the fact that there were room in it for more spheres for Heaven and Hell!

Ptolemy's astronomical work was described in his book "He mathematike syntaxis" (The Mathematical Collection) -also known as, Ho megas astronomos ("The Great Astronomer") and the Almagest, the name still used today. 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 is a synthesis of the results obtained by Greek astronomy; it is also the major source of knowledge about the work of Hipparchus, a great astronomer of antiquity. Ptolemy extended some of the work of Hipparchus through his own observations. On the motions of the Sun, Moon, and planets, Ptolemy formulated his geocentric theory -known as the Ptolemaic system. In the first book of the Almagest, Ptolemy describes his geocentric system and gives various arguments to prove that, in its position at the centre of the universe, the Earth must be immovable. Ptolemy argued that since all bodies fall to the centre of the universe, the Earth must be fixed there at the centre, otherwise falling objects would not be seen to drop toward the centre 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. As a result of such arguments, the Christian Church accepted the geocentric system until the 15th century, when it was supplanted by the Sun-centred system of Nicolaus Copernicus. Ptolemy accepted the following order for celestial objects in the solar system: Earth (centre), Moon, Mercury, Venus, Sun, Mars, Jupiter, and Saturn.