The imagined universe: From inception to Newton

Lost Civilizations (@lostcivilizations)

Published in 

lostworlds

 · 2 Sep 2023

Contents

1. Early astronomy: introduction
• 1.1 Astronomy in Mesopotamia
• 1.2 The Bible
• 1.3 Astronomy in Egypt
• 1.4 Astronomy in China
• 1.5 Astronomy in India
2. Astronomy in Classical Greece: introduction
• 2.1 The Pythagoreans and Philolaus
• 2.2 Plato's Timaeus
• 2.3 Aristotle's Heaven
3. Astronomy in the Hellenistic Age: introduction
• 3.1 Aristarchus of Samos
• 3.2 Eratosthenes and Hipparchus of Nicaea
• 3.3 Claudius Ptolemy
4. The astronomy of Islam and the Christian Middle Ages
• 4.1 Dante and theDivine Comedy
5. The astronomical revolution of the sixteenth century: introduction
• 5.1 Copernicus
• 5.2 Heliocentrism and geocentrism in the sixteenth century
• 5.3 Tycho Brahe
• 5.4 John Kepler
6. Galileo Galilei: introduction
• 6.1 Galileo: the astronomical discoveries and the Sidereus Nuncius
• 6.2 Galileo's scientific theories
• 6.3 TheDialogue on Major Systems
• 6.4 The conflict with the Church
7. Isaac Newton
• 7.1 The laws of motion
• 7.2 Experimental astronomy of the seventeenth and eighteenth centuries

1. Early astronomy: introduction

The origins of astronomy among primitive peoples are confused with those of civilization and religion.

In some countries the unfolding of celestial phenomena has suggested, with the possibility of predicting them, the concept of immutable natural law, thus paving the way for the passage from original forms of worship, such as fetishism, totemism, animism, to more complex in deities external to the terrestrial world and capable of acting upon it. Among the Israelites, monotheism is reached directly.

The multiplicity and the apparent independence of the movements observed in the sky, leads to the diffusion of mythologies rich in gods and demigods: polytheists are the Babylonians, the Egyptians, the Chinese, the Indians and the Greeks themselves, until the formation of a more advanced philosophical and religious consciousness does not lead to recognizing in the unity of the cosmos a single primary cause which is reflected in it.

A feature common to all primitive astronomical systems is given by the clear distinction between heaven and earth. In these conceptions, immutability is assigned to the sky, variability to the earth; freedom to heaven, dependence to earth; to heaven knowledge, to earth ignorance; impeccability to heaven, guilt to earth.

For the Jews (Genesis, 1) the detachment derives from successive differentiations in the creative act, while the Babylonians bring it back to the origin of the World and affirm its pre-existence to the Gods themselves.

For the history of astronomy those civilizations are of fundamental importance which, like the Babylonians, the Egyptians, the Greeks, supply the elements to the first great synthesis, the Alexandrian one; and those who, like the Arabs, prepare the second, begun in the fifteenth century and completed in the following centuries.

But other civilizations and cultures give rise to the independent development of as many astronomical concepts: the Chinese, the Persians, the Indians, the Jews, some Celtic and Scythian populations and, in the New Continent, the Aztecs of Mexico and the Incas of Peru.

1.1 Astronomy in Mesopotamia

Our knowledge of Mesopotamian mathematics and astronomy is based on the inscriptions on the thousands of clay tablets found at sites that were once the site of ancient cities.

The records belong to two separate periods, the "Old Babylonian" (c. 1800-1600 BC) and the "Seleucid" (the last three centuries before Christ).

Knowledge of mathematics developed in the earliest of these periods, as numbers were already represented as symbols, in a decimal and sexagesimal system. In later texts of the Seleucid period, we find the "zero" to indicate a sexagesimal empty place between two other digits.

Assyrian star planisphere found in the library of the Assyrian king Ashurbanipal (Aššur-bāni-apli – reigned 668-627 BCE) at Nineveh.

The astronomy of the Old Babylonian period contemplated only the observation of the brightest stars.

The later, or Seleucid, texts instead involve complicated systems of theoretical astronomy worked out by the priests. They are used to observing the sky from observatories or stepped temples, of which the biblical "Tower of Babel" is a reminder.

Their observations mostly concern the movements of the "seven planets" known since prehistoric times: the Sun, the Moon and five bodies (Mercury, Venus, Mars, Jupiter and Saturn).

Each planet appears to move across the sky, relative to the background of the stars. It is believed that the movements all lie within a certain area of ​​the celestial sphere, which for the purposes of calculation is imagined as a large circle: the Zodiac (from the Greek zodion, small animal figure). It will later be divided into twelve equal parts by the Babylonians, each of which bears the name of a corresponding constellation.

The periods of the revolution of the Sun and the Moon are used to measure time. The monthly events of the Moon, more evident than the annual course of the Sun, serve to regulate the most ancient lunar calendar. This division of time according to the Moon will be kept for religious purposes. There is no natural numerical relationship between the lunar month and the solar year, however Babylonian astronomy was pushed to develop also due to the need to find, through an effective rule, the connection between lunar and solar calculations.

Around the fifth century it is established that 19 solar years correspond to 235 lunar months, with the approximation of the fraction of a day.

1.2 The Bible

Genesis 1, 1-31. Creation of the world and humanity.

Creation of the world and humanity

“In the beginning God created the heaven and the earth. But the earth was bare and deserted: there was darkness on the surface of the deep, and the spirit of God hovered over the surface of the waters.
God said: Let there be light! And there was light. God saw that the light was good and God separated the light from the darkness. God called the light day and the darkness night. Then evening came, then morning came: one day.

God said: Let there be a firmament in the midst of the waters and separate the waters from the waters. And so it happened: God made the firmament and separated the waters which are under the firmament from the waters which are above the firmament. Then evening came, then morning came: second day.

God said: Let the waters, which are under heaven, be massed in one mass and dry land appear. And so it happened: the waters, which are under the sky, massed in their masses and dry land appeared. God called dry land earth and the mass of water he called sea. And God saw that it was good.

God said: Let the earth green with greenery, with graminaceous plants that produce seed and fruit trees, which make on the earth, each according to its kind, a fruit containing the seed. And so it was: the earth gave rise to greenery, grasses that produce seed, each according to its own species, and trees that each produce a fruit containing a seed according to its own species. And God saw that it was good. Then evening came, then morning came: a third day.

God said: Let there be luminaries in the firmament of heaven to separate the day from the night and they become signs for the holidays, for the days and for the years and they become luminaries in the firmament of heaven to shed light on the earth. And so it was: God made the two major lights, the big light to rule the day and the small light to rule the night and the stars. And God set them in the firmament of heaven to shed light on the earth and to govern day and night and to separate light from darkness. And God saw that it was good. Then evening came, then morning came: a fourth day. God said: Let the waters teem with a swarm of living and flying things fly above the earth, against the background of the firmament of heaven. And so it was: God created the great cetaceans and all the darting living beings with which the waters swarmed, according to their kind and all the winged birds according to their kind. And God saw that it was good. And God blessed them saying: Be fruitful and multiply and fill the waters of the seas, then the birds multiply on the earth. Then evening came, then morning came: a fifth day.

God said: Let the earth bring forth living things after their kind: cattle and reptiles and wild beasts of the earth after their kind. And so it was: God made the beasts of the earth after their kind and all the reptiles of the ground after their kind. And God saw that it was good.

God said: Let us make man in our image, after our likeness, and have dominion over the fish of the sea and the birds of the sky, over the cattle, over all the wild beasts of the earth and over all creeping things that creep on the earth.

God created man in his own image, in the image of God he created him; male and female he created them. God blessed them and God said to them: be fruitful and multiply, fill the earth and subdue it and have dominion over the fish of the sea and the birds of the sky, over the cattle and over all the wild beasts that creep on the earth. Then God said: behold, I give you all sorts of seed-producing grasses, which are on the surface of the whole earth, and also all sorts of trees in which there are seed-bearing fruits: they shall be your nourishment. But to all the wild beasts of the earth, to all the birds of the sky and to all the beings that crawl on the earth and in which is the breath of life, I give green herbs as nourishment. And so it was. And God saw all that he had made, and behold, it was very good. Then evening came, then morning came: the sixth day”.

Joshua 10, 10-15. Joshua's victory

“Jahve routed them in the face of Israel, which inflicted a great defeat on them at Gibeon, then pursued them in the direction of the slope of Bethoron and beat them as far as Azeka and as far as Makkeda. Now, when they fled before Israel and were on the descent of Bethoron, Jahve hurled from heaven above them, as far as Azekah, great stones which destroyed them. More died by the stones of the hail than by the sword of the children of Israel.
Then Joshua spoke to Jehovah, on the very day that Jehovah delivered the Amorites into the hand of the children of Israel, and he said before Israel's eyes:

O sun, stop on Gibeon

and you, moon, over the valley of Aialon!.

The sun stopped

and the moon stood still

until the people had avenged themselves on their enemies.

Isn't it written in the book of the Just? The sun remained motionless in the middle of the sky and did not hurry to set for almost a whole day.

There was never before or after a day like that, when Jahve heard the voice of a man, for Jahve was fighting for Israel! Then Joshua and all Israel with him returned to the camp at Galgal."

1.3 Astronomy in Egypt

Egyptian astronomy was empirical, like that of Asian peoples. The monuments of the Nile valley attest in very remote times significant knowledge of geometry applied to the art of construction, in relation to astronomy, as can be seen from the traces of exact orientations of the pyramids, temples and other buildings according to the cardinal directions, ecliptic or according to the culmination points of stars.

This ritual practice will also be used outside Egypt, but no one applies it more widely than the Egyptians, from whom the Greeks and the first Christians will learn it.

Much of the astronomical interest of the Egyptians coincided with the invention of their calendar: and this for two distinct reasons. First of all, the economic and social life of that people is dominated by the periodicity of the variations in the flow of the Nile: hence the need to make the norms of the alternation of occupations and religious rites depend on a sure knowledge of the periods which reduce the floods. Furthermore, the preservation of priestly dominance over the nation and over the civil rulers themselves, the pharaohs, is entrusted to an occult doctrine, of which astronomy is an integral part. Therefore the control over the calendar constitutes the surest instrument of dominion of the populations of the valley of the Nile.

Egypt has in use in civil life "the vague year". It is 365 days. To the traditional year of 360 days, in use in the most ancient times, the five “epagomenan” days were added, probably as early as the fourth or fifth millennium B.C. However, the Egyptians also know the solar or "fixed" year consisting of 365 days and a quarter. The coexistence of the two calendars has led to dating problems for the older periods. Egyptian priests use three methods to determine the length of the solar year: first, through observations of the onset of flooding of the Nile; the second, based on the reappearance of the star Sirius on the eastern horizon in the morning twilight; the third, determined by the passage of the Sun through the hinges of the ecliptic.

A particular feature of later Egyptian astronomy is the concept of the thirty-six decans (or decans), a series of constellations rising at regular intervals, which serve to determine time during the night hours. This suggests that the institution of the decans is prior to that of the five epagomena, thus resulting very ancient.

The stars and major groups are dedicated to divinities: Sothis (or Sirius) to Isis, Orion to Osiris, The Pleiades, The Hyades and other stars to unidentified gods. Real observatories at Dendera, at Thinis, at Memphis, at Heliopolis, wait with regularity to follow the course of the stars, building tables of their passage across the horizon.

1.4 Astronomy in China

The Chinese already reached a rather elaborate conception of celestial phenomena in very ancient times, but their knowledge tends to crystallize, so that other peoples will carry on the research on the cosmos.

Astronomy in the ancient China

Under the Yao dynasty, in the 24^th century BC, the systematic observation of the sky was entrusted to carefully trained and chosen men, especially taking into account the sharpness of sight necessary for this function. This activity leads to a first important classification of the constellations.

China appears to be the only country that has set up a real "Astronomical Court", to which the sovereign directly refers the solution of important questions connected with science and its applications to the general good.

A second phase in the work of star classification dates back to the Han dynasty, around the year 120 BC Compared to Ptolemy's synthesis, which identifies 48 constellations, the groupings are generally smaller, reaching more than 300 constellations. For example, the two major stars of the Lira form the "Embroiderer"; Ursa Major is identical with a "Casserole" and even the individual stars with their characteristic configuration take on special names: Alpha is the "Pivot of Heaven", Beta and Y are "Precious Stones", Enne the "Shaken Light", Alpha and Beta of Ursa Major the "Sovereigns of the Sky". Although the Chinese travel in regions from which it is possible to see stars not visible below the latitude of Beijing,

Instead, their attention is focused on the variations in the position of the Sun, deduced rather from the observation of the shadows during the day, than from the investigation of the groups of stars. The procedure followed by the Babylonians and the Egyptians, which allowed them to make enormous progress in the field of solar astronomy, i.e. the observation of the "Eliacus" of some stars, is not followed by the Chinese, who preferentially stick to the shadow sundials. The frequency given to the nocturnal observations is not limited to those performed during the day using gnomons, but also extends to nocturnal observations.

It is the Chinese who precede all other peoples in the use of instruments for astronomical and nautical observations. The use of hourglasses with two superimposed containers, pointing tubes, concave and convex mirrors dates back to the 22^nd century BC.

More recent is the knowledge of magnetic polarity, with the consequent application to the construction of the compass and to the use of this instrument for the orientation of ships.

Chinese astronomers of the century XVII they appreciate the translations of European texts made by the Jesuits, but their science remains stationary, without further contact with the movement of Western thought and without their knowledge constituting an organic body of doctrine.

1.5 Astronomy in India

The possibility of a reciprocal influence of the ancient Greek and Indian cultures seems proven. There are traces of verbal derivations up to the sec. XVII BC, but the direct relations between the two peoples originate in the fourth century BC; the lack of a southern astronomy is determined by the migration of these people from the north. Certainly, in the southernmost lands of the peninsula, the very ancient belief could not have been born and strengthened according to which the South-West is the region of the Mani, of the goddess Nirrti and of Yama, god of death: a region where the Sun "dies" and descends underground.

Astronomy in ancient India

Very soon the stars and the main constellations encountered by the Moon in its monthly path and which constitute the Indian Zodiac were known and identified with names: there are 28 groups (Nakshatra) of stars crossed by the Moon along the zodiac; the place that the full moon occupies among the Nakshatras defines the season of the year.

Sky observers seek real or supposed connections between the movements of the stars and earthly and human events: astrologers have a system of fixed rules for the interpretation of each given event. Furthermore, a link is created between astronomical periods and conceived cycles for liturgical reasons and widely applied in every Indian philosophical and mystical system, while there appears a tendency to study divine and human things from a numerical point of view.

Another characteristic of Indian thought is the relationship between the use of cycles and the alternation between opposites, as in the alternation of day and night. Days and nights of different lengths are formed with multiples of the common days: a month of thirty days gives, divided by half of the new moon, the day and night of the Pitris, rulers of the lunar tasks: a year of 360 days (Institutes of Manu) gives the day and night of the Gods, which begin respectively at the spring and autumn equinox.

12,000 "years of the gods" make a "kalpa" or day of Brahma, a period which includes all the evolution of the world, created from scratch at the beginning of each kalpa, and brought to dissolution when, with the falling asleep of Brahma in a night of equal length, the kalpa ends.

Cosmic and astronomical phenomena separate the various subdivisions of each kalpa, over which special divinities preside. Thus the deluges at the end of each of the 14 'manavantra' into which the kalpa is divided: for each deluge the different species are gathered in an ark by a Manu, who becomes the ruler of the following period. This complex system of cycles is found described in the Mahabharata and the Puranas, ancient sacred books.

2.0 Astronomy in classical Greece: introduction

It is in Greece that astronomy makes an important qualitative leap, presenting itself for the first time with a "scientific" system and overcoming the mainly empirical motivations and the subordination to religious thought that had characterized it among the peoples of Mesopotamia and the Egypt.

Astronomy in classical Greece

Already with Thales, who with his stay in Egypt comes into contact with the knowledge of that country, we have the first cosmological speculations. The main exponents of astronomy in classical Greece, between the sixth and fourth centuries BC, are the philosophers of the Pythagorean school, mainly Philolaus, Plato and Aristotle.

Filolao is the first to spread the knowledge of the Pythagorean doctrines outside Magna Graecia and he is also the first among the followers of the sect to publish his writings in contravention of the prescription of silence.

He has a particular conception of the universe with two fires: one central and one located in the outermost part; around the central one the ten divine bodies rotate in a circular orbit. The peculiarity of his system is that the Earth is not placed at the center of the universe, an idea that will be resumed only in the sixteenth century by Copernicus. Another great Greek philosopher is Plato, who, arguing with the sophists, builds a complex philosophical theory which is the " doctrine of ideas".

In the Timaeus he formulates the principle according to which everything that is born must have a cause, that is, it must have been created from something. God is the creator of the world and created it in his image and likeness. He thinks of a spherical universe, with the Earth at the centre, the "fixed" and "wandering" stars (the planets) inserted in concentric spheres. Influenced by the doctrines that come from the East, he thinks of a "Great Year" of indefinite duration, which would end with a cataclysm that would renew the world, to then repeat a new cycle.

It was up to Aristotle to build the first lasting cosmological system, which would cross the ancient world, to be recognized as the most authoritative astronomical construction, together with that of Ptolemy, until the Copernican revolution of the sixteenth century. Dante's Paradise itself is inspired by his system.

In Heaven, his major astronomical work, he increases the number of spheres surrounding the Earth and justifies their movement with the presence of a "prime mover", i.e. the outermost sphere. He also provides evidence of the sphericity of the Earth, explains the nature of comets, the Milky Way and other Earth-related phenomena.

It will be in Alexandria of Egypt, in the following centuries, that the Greek synthesis will come to fruition.

2.1 The Pythagoreans and Philolaus

Filolao di Crotone is a philosopher of the Pythagorean school, born a few decades after Pythagoras, around 470 BC, he lives until the end of the 5^th century. He escapes persecution and the destruction of the Pythagorean circles of Crotone and around 450 he takes refuge in Greece where he lives for mostly in Thebes.

It is very important in the history of Pythagoreanism because it is the first to spread the Pythagorean doctrines outside Greece; he is also the first among the true followers who publishes writings in contravention of the prescription of silence.

According to Filolao, the universe is a sphere and does not include only the earth and stars, but also the formative principle of everything, the essence of things, the celestial vault and also what is around it, such as the purest fire, or ether, or soul, or God. This conception constitutes the most ancient non-geocentric astronomical system and will then be developed by the neo-Pythagoreans in the Hellenistic and Roman age.

Filolao shares the conception of the number 10, or the "tetractys" or decade, as a perfect number, he states that this number is:

“great, almighty and creator of all things, the principle and guide of both divine and earthly life”.

In the composition of the universe there is a "fire" in the center which he calls: "hearth of the universe" and also ''house of Zeus'' or ''mother of the gods'' or ''bond'' or ''altar'' or ''measure of nature''. Then there is another fire in the highest part, which is the envelope: he maintains that, first by nature, it is the middle fire, around which 10 divine bodies move in a circle, i.e. Olympus and the 5 planets (Mercury, Venus, Mars, Jupiter, Saturn), after these there is the Sun with the Moon below, below that is the Earth followed by the Anti-Earth. After all these is placed the hearth fire with the place in the centre.

“The Pythagoreans say that in the center of the universe there is fire around which the Anti-Earth rotates, so called because it is opposed to the Earth. The Anti-Earth revolves around the center following the Earth, but it is not seen by us due to the continuous interposition of the terrestrial mass (...). The highest part, that of the envelope, in which the elements reside in their purity, he calls "Olympus"; the one under the circle of Olympus, in which the five planets are arranged together with the sun and the moon, he calls "cosmos"; finally the sublunar and circumterrestrial part, in which mutable things are generated, he calls it "sky".

(Aetius,Philolaus)

...

“The Italic philosophers called "'Pythagoreans'' support the theory of fire in the middle, and that the earth is a star which, moving in a circle around the center, produces night and day; they also suppose another earth opposite to this one , the anti-earth. However, they try to adapt the phenomena to their theories and not the other way around. They believe that it is the fire that should be in the center rather than the earth because that is the noblest place, where the most important part must be kept everything".

(Aristotle, De Caelo)

“ Philolaus Pythagoras says that the sun is glassy and porous in nature, it absorbs the reflection of the fire that is in the cosmos and transmits its light and heat to us”.

(Aetius, Philolaus)

“Some Pythagoreans, including Filolao, say that the moon is made up of earth and for this reason it is inhabited by animals and plants like our earth; but they are bigger and more beautiful; in fact they say that the animals found on it are fifteen times larger and do not excrete excrement, and that the day is as many times longer”.

(idem)

In Philolaus' system the earth takes 24 hours to revolve around the central fire; the moon takes a synodic month, i.e. 29 and a half days. The peculiarity of the moon to always turn the same face towards the inside of the orbit is known, and it is perhaps from it that Filolao draws the conviction that also the earth and the anti-earth always turn the same face to the central focus.

Furthermore, it had been observed that the Sun, the Moon and the five planets move by their own motion from west to east on the plane of the zodiac, successively traversing the zodiacal constellations; with Filolao also the earth participates in the rotary motion from west to east around the central focus, according to the oblique circle in a similar way to the Moon and the Sun.

2.2 Plato's Timaeus

Plato (Athens 427-347 BC) is a Greek philosopher, disciple of Socrates. Starting from the thought of Socrates and arguing with the sophists he builds a complex philosophical theory which is the "doctrine of ideas".

The Platonic idea transcends reality. The idea has characteristics such as universality, immutability and eternity that do not coincide with those of reality, which appears to be particular and transitory instead. Reality is but a copy of the ideal form.

For Plato, the only science that represents knowledge of the universal is mathematics. Only with an accurate study of mathematics can one dedicate oneself to philosophy. However, mathematics has its limits, because it starts from some assumptions that it is unable to justify. For Plato there are sensible things, ideas and mathematical entities, which differ from sensible things because they are eternal and immutable.

The "Timeus"

Timaeus was a Greek historian who is used by Plato in one of his dialogues to explain the origin of the world. In the Timaeus a principle is formulated according to which everything that is born must have a cause, that is, it must have been created by someone. A distinction is made between:

''that which always is and has no birth, and that which is always born and never is not. The one is apprehensible by the intelligence by reasoning, because it is always in the same way; the other, on the other hand, is questionable by opinion through irrational sensation, because it is born, dies, and never really exists”.

Therefore things that have no origin and have always been so are apprehended with intelligence, while things that are born and die are perceived through opinion. We need to understand if the world is one of those things that has always been like this or if it was generated by some principle.

“But the maker and father of this universe is difficult to find, and, having found him, it is impossible to point him out to everyone.”

God is the creator of the world and he generated it in his image and likeness and since he wanted all things to be good and none bad, he took everything that was agitated in a wild and disorderly way and transformed it into order. Among all that he created he thought he was making the most beautiful thing and to make it so he gave it intelligence and soul. For this reason he created only one world and created it perfect.

"God wanting all things to be good and, as far as possible, none bad, therefore took what was visible that was not still, but moved wildly and disorderly, and reduced it from disorder to order, judging this completely better than that (...) composing the intelligence of the soul and the soul of the body, he built the universe, so that the work he accomplished was the most beautiful according to nature and the best that could be (...) What is born must be physical and visible and tangible. But nothing could be visible, separated from fire, nor tangible without solidity, nor solid without earth."

God created the world which is visible and therefore formed from fire and tangible and therefore formed from earth. Both of these substances are connected by air and water in such a way that the universe consists of four elements. Each of these elements was used entirely for the composition of the world in such a way that creation would be perfect and eternal. The shape that God attributed to the world was the spherical one, because of all shapes it is the most perfect.

The world was not endowed with any organ because being perfect it was sufficient unto itself. Circular motion was attributed to it and it was deprived of the other six movements to eliminate any type of error.

“The soul then God did not make it after the body as we who now take to speak of it last, because, having joined them, he would not have let the older be governed by the younger. But we who greatly depend on the fate of chance, thus also we speak at random. Instead he formed the soul before and older than the body by generation and by virtue, inasmuch as it had to govern the body, and this obeyed it, and he formed it of such elements and in such a way”.

God also created the soul of the world and this was certainly created before the body.

“Time therefore was made together with heaven, that being begotten together they also should dissolve together, if any dissolution ever then takes place; and it was made after the pattern of eternal nature to be like it as much as possible.”

...

“For the movable things of the universe he creates time, which consists in the division into day, night, months, years. All these parts of time make no sense when it refers to the universe which is eternal, so we will not speak of old or young." ... in order for time to be created, the Sun and the Moon and five other stars, which are called planets, were made to distinguish and observe the numbers of time”.

These seven bodies he set to revolve in seven orbits. In the first orbit the Moon revolved around the Earth; the Sun revolved in the second above the Earth; Lucifer and the planet sacred to Hermes revolved in the same orbit as the Sun, but in opposite directions. The orbits covered by the planets were not the same but those that covered a greater orbit rotated more slowly than those that covered a smaller orbit. To gauge the speed with which the planets make their revolution, God lit the sun and made it shine throughout the sky.

Time was defined in this way: night and day are determined by the single circular motion; the month is the orbit traveled by the Moon until it reaches the Sun; The year is the time it takes for the Sun to travel around its orbit.

“And all the rest up to the generation of time had already been accomplished in the likeness of its model: but the world was still dissimilar to it in that it did not yet include within itself all the animals, which were then generated in it. Once the world was created he decided to put four types of species: the celestial species of the gods he made of fire, so that it was splendid and beautiful to see. To make it more similar to the universe he made it round”.

2.3 Aristotle's Heaven

Aristotle (384-322 BC) was born in Stagira, a Greek colony near present-day Mount Athos. A pupil of Plato in Athens, in 342 he became the tutor of the young prince Alexander of Macedonia and remained in Macedonia until 336. He later returned to Athens to undertake the profession of public teacher. Aristotle's writings span every region of knowledge. Most of his works are composed during his second Athenian sojourn in the twelve years preceding his death. In his work he clarifies the relationship between physics, which for him is a general description of the universe, and the study of living beings.

From Heaven

"Heaven in its totality is not generated, but is one and is eternal, it has no beginning or end, rather it contains and embraces within itself all the infinity of time".

The sky is spherical, like the bodies that occupy the center of the universe, since if water surrounds the earth, air water, fire air and the superior bodies which have a similar disposition, are not continuous to the first, but are in contact with them, consequently the surface of the water will be spherical

"and what is continuous with a spherical body is necessarily so too, and for this reason the sky will be considered spherical".

..

“Everything that has a function exists in view of this function”,

since the sky is also of this nature, for this reason it has a circular body, which by nature moves in a circle

“in a body that moves in a circle there is necessarily a part that remains stationary, and that is the one that is in the center; while in the circular body there is no part that can remain stationary, neither absolutely nor in the centre”.

Aristotle considers the fall of a heavy object towards the center of the Earth as an example of natural motion and is convinced that any object left to itself quickly reaches a constant rate of fall and maintains it until the end. He deduces that the weight of an object helps determine the speed of fall and that this must be proportional to the weight of the object and inversely proportional to the ratio between weight and resistance. He also examines violent motion, i.e. the motion of an object that is not moving freely towards its natural place. According to his theory such a motion must be caused by a force: if the force increases the speed must increase, if the force ceases the motion must cease.

Aristotle, unlike Plato, suffers from Pythagorean influences in his scheme of the physical world. In particular he, considering the circle and the sphere as more perfect geometric figures, places them at the foundation of the structure of the world

"since it [the sphere] does not possess any organ capable of movement", for example"the Moon which is spherical it is demonstrated to us by the phenomena that we perceive with the sight, otherwise it would not assume a mostly lunar shape with waxing and waning and a half-moon shape only once, since if one of the stars has this shape, it is clear that also the others will be spherical”. He was thus led to consider the cosmos as a series of concentric spheres with the Earth in the centre, stating that if there is earth there must also be fire: "since one of two opposites is according to nature, the other too it must be according to nature".

But if Earth and fire are present, there are also intermediate bodies to these:

"each element in fact is in a contrariety relationship with every other element".

But once the existence of these is posited, it is clear that there must also be generation, since

“none of them can be eternal; in fact, the opposites are subjected to each other's action, and have the virtue of causing one to corrupt the other”.

This conception of his will dominate the idea that men will form of nature for two thousand years and it can be summarized in various definitions:

• Matter is continuous; Aristotle with this principle opposes Democritus and agrees with Socrates and Plato.
• All terrestrial things are made up of four elements: Earth, Air, Water and Fire, which, in turn, contain the four qualities: hot, cold, dry and wet combined in pairs. This conception of matter is taken from Empedocles and is probably of more ancient origin, but it is also the Aristotelian expression of the Pythagorean conception that all things are in a relationship of love and discord.
• Stars and planets move in circular motion in crystalline spheres around the Earth; each sphere is subject to the influence of the outermost ones. This scheme would remain in effect until Kepler's time.
• The circular motion is perfect as the circle is the perfect figure. At the end of the seventeenth century Newton will succeed in expressing the movements of the celestial bodies in known and experimentally demonstrated terms.
• The universe is limited in space in the sense that it is contained within an external sphere; it is unlimited in time in the sense that in its entirety it is subject neither to creation nor to destruction. This theory of Aristotle will not be accepted entirely because the finiteness of the universe could not be imagined both in space and in time, therefore it will be based on the philosophical conception of the infinite universe.
• The movements of each star take place according to a ratio proportional to the distance as to being one faster, the other slower. In fact, the closest body is more subjected to the action of the first heaven; while the farthest is so to a minimum degree, due to the effect of distance.

3. Astronomy in the Hellenistic Age: introduction

With the birth of the school of Alexandria in Egypt, in the third century BC, the Greek philosophical and scientific tradition reached its highest results. Astronomy is one of the most representative sciences of Hellenistic culture. The studies carried out by the scientists of the school, in addition to leading to a significant increase in knowledge of the sky and the stars, results obtained thanks to the development of instruments and observation methods typical of experimental science, provide systems of ideas and cosmologies that will be considered valid beyond the astronomical revolution of the sixteenth century.

Aristarchus of Samos is a contemporary of Euclid and bases his conclusions on coherent logical procedures. He conceives, like Philolaus, a universe with the central Sun. He also studies the distances and relationships between the Earth, the Sun and the Moon. His theories are condemned by the majority of other scientists, so his positions are known thanks to the writings of those who fought against him, while his works have not survived.

Eratosthenes, librarian of the school of Alexandria, accurately measures the earth's radius.

Hipparchus of Nicaea is considered the greatest astronomer of antiquity. His method of investigation, which seems to anticipate the Galilean one, starts from the collection of observation materials, which are reworked, ordered and studied; so he tries to express the results achieved in geometric form. He studies the precession of the equinoxes and the solar motion.

Claudius Ptolemy concludes the great Alexandrian research, one of the most important astronomers, he is known above all for his "great mathematical composition", the Almagest, in which he collects his studies on the Earth and the universe.

Between the fourth and fifth centuries the Alexandrian school dies out, its knowledge will pass to Arab culture and, through the latter, to the medieval West, after the year 1000.

3.1 Aristarchus of Samos

Aristarchus of Samos (310 - about 230 BC) teaches in Alexandria after Euclid.

He develops Philolaus' idea that the Earth revolves around a central fire, arguing that the Sun itself is stationary and all the planets revolve in circular orbits around it. He also claims that the earth rotates on itself.

We owe Aristarchus the first scientific attempt to determine the distances of the Sun and the Moon from the Earth and their relative sizes.

In the treatise "On the size and distance of the Sun and the Moon" (about 260 BC), based on the hypothesis of a geocentric universe, Aristarchus asserts that the Sun is about 19 times the distance from the Earth to the Earth.

He develops a reasoning that would allow him to calculate the dimensions of the celestial bodies: when the Moon presents the first and last quarter, i.e. when we see only half of its face illuminated by the Sun, the visual axis that goes from the terrestrial observer to center of the lunar disk must intersect at right angles the axis of illumination which runs from the center of the solar disk to the center of the lunar disk. Knowing the relative distances of the Sun and the Moon from the observer, the respective dimensions of these bodies can be determined, assuming the relative dimensions of their disks as they appear to an terrestrial observer are known.

In reality, the Sun-Earth distance is almost 400 times greater than the Moon-Earth distance.

Although Aristarchus' results are distant from the current ones, they are still better than those of his predecessors. Furthermore, his method is irreproachable in the procedure and the result is vitiated by an observation error consisting in measuring the Moon-Earth-Sun angle in 87 degrees (while in reality it is about 89 degrees)

In order to arrive at a real evaluation of the distance between the Sun and the Moon, it is necessary to measure the radius of the Earth. This calculation is due to Eratosthenes, a contemporary of Aristarchus.

The mathematical reasoning of Aristarchus

Indicated with S,T,L respectively Sun, Earth, Moon, when the Moon has the first or last quarter, the angle included between the visuals of the Sun and the Moon is equal to approximately 87¡, i.e. LTS~87¡. Having set LT and ST respectively the distance Moon-Earth and Sun-Earth, knowing that sen3¡~1/19, Aristarchus concludes that LT/ST~1/19.

Having determined the ratio LT/ST, Aristarchus maintains that the magnitudes of the Moon and the Sun are in the same ratio. This derives from the fact that the Sun and the Moon have almost identical apparent magnitudes, i.e. they subtend the same angle as seen by an observer on Earth. Therefore, positing Rl as the radius of the Moon and Rs as that of the Sun, Rl/Rs=1/19 results.

On the basis of this ratio, which expresses in particular the size of the Sun compared to that of the Earth, Aristarchus determines the size of the Moon compared to that of the Earth. In particular he obtains the approximation Rl = 20 / 57Rt.

The mathematical calculation developed for this purpose is based on figure 2, which constitutes a geometric model of a lunar eclipse. Figure 2 is drawn by tracing the tangent to the circles with centers S and T (center of the Sun and of the Earth) and setting A and B as the respective points of contact; on this tangent the point C is determined such that LC is parallel to TB (L is the center of the Moon). Then EB and DC are drawn such that they are parallel to the line passing through S,T,L.

From the consequent similarity of the triangles EAB and DBC, follows the proposition DB/EA=DC/EB.

Having Aristarchus available the experimental datum according to which the amplitude of the shadow projected by the Earth at the distance of the Moon is 2 times the size of the Moon, according to figure 2 the result is LC+2Rl. Taking advantage of this last equality and bearing in mind that the quadrilaterals EBTS and DCLT are parallelograms, the previous proportion (DB/EA=DC/EB) is transformed into the following (Tr-2Rl)/(Rs-Rt)=LT/ST.

Knowing that LT/ST~1/19 and Rs~19Rl, the approximation Rl~20/57Rt is obtained.

3.2 Eratosthenes and Hipparchus of Nicaea

Eratosthenes (c. 276 - 194 BC) is librarian of Alexandria. The most important investigation of him is the measurement of the earth's radius; from this data he calculates the Earth-Moon distance and the Sun's radius.

Eratosthenes observes that at noon on the summer solstice, the Sun sends its rays directly to the bottom of a deep well at Syene (modern Aswan). At the same time, at Alexandria, which lies on the same meridian as Syene, at a distance of 5,000 stadia, the Sun casts a shadow (relative to the zenith) of a magnitude which can be accurately measured. He calculates the measure of the angle in one fiftieth of a circumference. This leads to the result that the circumference (that of the earth) must measure 250,000 stadia, or 25,000 miles.

Hipparchus of Nicaea (about 190 - 120 BC) is the greatest astronomer of antiquity and is considered the founder of scientific astronomy. He carries out his activity in Rhodes, where he establishes an observatory for his research. Hipparchus develops trigonometry and makes numerous and precise astronomical observations which lead him to two brilliant astronomical intuitions.

He discovers the precession of the equinoxes, observing the movement of the stars over time and comparing the position of about 1,000 stars he studied with the observations made by other scholars 150 years earlier. He demonstrates that in a given time there are shifts in the distances between the stars from given fixed points, shifts that can only be explained by the rotation of the Earth's axis in the direction of the apparent diurnal motion of the stars. As a result, the equinoxes fall slightly earlier each year.He develops his own theory on the apparent motion of the planets based on eccentric movement: the planets would draw circular orbits around the Earth whose center would not coincide with that of the Earth; this second center can be represented as moving in a circle. Hipparchus' very accurate calculations make it possible to predict lunar eclipses with an accuracy of one or two hours.

3.3 Claudius Ptolemy

Claudius Ptolemy (Ptolemais of Egypt, 90 AD, Canopus 168) lives in Alexandria. He elaborates the most complete astronomical and geographical synthesis and carries out the most remarkable experimental optical research of antiquity.

He formulates the proportionality rule of the angles of incidence and refraction (approximately true for small angles) and applying it he intuits that the light of a star, entering the atmosphere, is deflected or refracted so as to appear closer to the zenith than it is. really be.

He writes a work of enormous scientific importance which will later be recognized as the Almagest.

The Ptolemaic work will be given the name of Almagest only in the Middle Ages. This name derives from the Greek expression "Megalé Mathematikè Syntaxis" that is "Great mathematical syntax", also used in the superlative form "magisté syntaxis", from which the Arabic translation "Al-Magiste", which becomes Almagestum in medieval Latin.

It is not possible to know exactly which part of the work is due to Ptolemy's personal merit and how much instead should be ascribed to that of his predecessors, such as Hipparchus, which the author himself sometimes suggests. It is probable that even to the planetary mathematical theory he brings only the latest refinements.

In the Almagest Ptolemy mathematically presents the apparent orbits of the planets. He takes into account all observed planetary motions, with an accuracy of about five seconds of arc more than the naked eye. This theory will remain unchanged as far as the mathematical part is concerned even after Copernicus will modify its theoretical system (1543). Only after Kepler, in the seventeenth century, will substantial changes be made, in order to take account of the more exact observations of Tycho Brahe.

Ptolemy presents the scheme of the universe as a unified whole, placing the Earth within the principal circle of the planets' orbits, but in an eccentric position, while the planets make their rotation around the equant, a point located at equal distance from the Earth, but on the other side of the center of the circle. The result of these studies is so close to that obtained by Kepler fifteen centuries later.

In the Almagest "epicycles" are used, i.e. circles described by the planets around an ideal point called "equant", which in turn describes a circle around the Earth called "deferent", to explain the second periodic variation of the position of a planet (which is really caused by the movement of the earth around the sun), but for mathematicians it is indifferent to consider the Earth at rest like Ptolemy, or the Sun like Copernicus.

The Almagest also contains a detailed and precise list of the Stars, partially adapted from Hipparchus.

Finally, the main tools used by Ptolemy in his studies are described:

• THE METAL RING, used for observing the meridian altitude of the sun. It is composed of an internal ring with two indicators, placed inside another graduated ring, placed vertically on the plane of the meridian;
• A WOODEN BLOCK sliding on a long frame with a hole in one of the two ends to fit the eye, so that by sliding the block you can measure small angles and evaluate the apparent size of the sun;
• A SIMPLE RING placed on the plane of the equator, used to determine the equinoxes;
• THE TRIQUETRUM (Latin term meaning triangle) which is used to determine the center of the Moon even when only part of it is visible. It consists of an axis for aiming at the Moon which is framed by a large hole at the lower end, and has the advantage that the graduations are marked on a straight shaft and therefore can be more easily determined than on the circular scales of other instruments;
• THE ARMILLARY ASTROLABON is the most important instrument used by Ptolemy. Formed by a series of metal rings inserted one into the other, the innermost of which carries an alidade (a mobile index which, sliding on a graduated circle, allows you to measure the opening of an angle) with two small holes (through which to carry out the observations) while the outermost is fixed to a heavy support; one axis of rotation is parallel to the polar axis of the earth, and a second axis is inclined like the ecliptic axis 23.5 degrees to the polar one. This is used to directly measure angles, while with any other less complicated instrument it would take long and complex calculations to transform the height and azimuth data, or equatorial coordinates, in the ecliptic coordinates essential to the theory. With this instrument, Ptolemy also manages to measure the "inhabitable" world; these results are reported in another work by him: the Geography.

The Almagest is characterized by Ptolemy's major concern: that of finding a particular mathematical theory for each planet. But when he comes to the problem of considering the planetary system as a whole, he notes that no observations known to him can throw much light on this point, and any hypothesis could not much alter his conclusions. Thus he falls back into the traditional view that the speed with which the planets move proves their proximity; in this way he places the Earth in the centre, and the Moon, Mercury, Venus, the Sun, Mars, Jupiter, Saturn and the fixed Stars in ever more outward orbits. Therefore, even if the Almagest he speaks little of cosmology, Ptolemy's name remained with the major pre-Copernican system.

The Almagest will be translated into Latin towards the end of the 12^th century (around 1175) by Gerardo, a monk from Cremona, therefore it will not be able to have a direct influence on the science of the High Middle Ages. In its place will spread the simpler scheme of the universe from Aristotle. At the end of the Middle Ages the conflict between the Aristotelian and the Ptolemaic conception was destined to assume great importance for the history of science.

4.0 The astronomy of Islam and the Christian Middle Ages

The Romans make no original contribution to astronomical science. They have a good practice of some fundamental tools such as the sundial, which they have known since the third century BC, and which they apply to calculating the calendar. They also possess considerable mechanical ability that allows them to make and frame fundamental astronomical observations. More significant is the influence of astrology which, although forbidden at the time of the empire, was particularly widespread among the popular classes.

Connected to Alexandrian astronomical research are the Arabs who, through trade with the Indians, starting from the 9^th century, can use their knowledge in the field of arithmetic and algebra to reconsider the knowledge of the Hellenistic Age. They translate and popularize Ptolemy's work, transmitting it to the Christian West, while developing the use of particular instruments such as the astrolabe, an ancient instrument used by sailors to determine the position of the stars, later replaced by the sextant. It is a system for transporting a curved surface on a flat one.

The instrument essentially consists of a circular map of the firmament that rotates around the north pole, resting on a celestial plane corresponding to the view of an observer at a given latitude. This astronomical instrument was used between the 7^th and 16^th centuries and is of inestimable value for astronomical research.

Among the major Arab astronomers are Al-Farghani and Al-Battani, who lived in the 9^th century, who compiled summaries of the Almagest. The philosopher Averroes will be the mediator of Aristotelian thought between Arab and Christian culture.

Only in the thirteenth century the works of Aristotle and those of Ptolemy are known in Europe, determining the recovery of Western thought. A reflection on these themes is developing within European universities and the Dominican and Franciscan orders. Among the personalities who propose the first Christian astronomical syntheses is the Sacrabosco, active in Paris in the thirteenth century.

With the spread of Christianity and the disappearance of Stoic philosophy, astrology fades into the background to return with the Arabs and with the rise of the University of the thirteenth century.

4.1 Dante and the Divine Comedy

In Dante's Divine Comedy we find the medieval cosmological vision synthesized. It is a direct derivation of the Aristotelian conception, in part different from the Ptolemaic one, filtered through the theological reflection of Thomistic derivation, operated in the first half of the XIII century by Thomas Aquinas. In the Divine Comedy, and particularly in the third canticle, Paradise, astronomical and cosmological elements are an integral part of the poetic construction. In numerous places in the poem, the Author presents well-defined and recognizable astronomical situations and indicates their influences on the behavior and fate of humans. Astronomy and astrology are merged into a single conception, poetic and existential.

This is all the more true in the cantica del Paradiso, where souls appear to Dante in different heavens. But Dante's cosmology is, at the same time, a moral vision of the world. For the author, divine virtue is the cause and creation of all that exists. The heavens and their influences act as causes arising from creation. Their motion is not a purely mechanical fact, but they are presided over by the individual celestial hierarchies or intelligences, each one for a specific sky. Each planet and each constellation has a specific influence on terrestrial creatures.

The work of Alfragano, Ptolemy's commentator, and the Etymologiae of Isidore of Seville exerted a significant influence on Dante's astronomical-astrological vision.

Heaven. Canto XXII

Verses 133-150

“With my face I returned for all of themthe seven spheres, and I saw this globe such, that I smiled at his vile semblance; and that advice for the better I approve who has it for less; and who else thinks you can really call it honest.

I saw the daughter of Latona incense without that shadow that was my causewhere fore I already thought it rare and dense.

The appearance of your offspring, Hyperion, I stood there, and saw how it moves around and near him Maia and Done.

Then the temper of Jupiter appeared to me between father and son; and then it was clear to me the variation they make of their where; and all seven proved themselves to me how big they are and how fast they areand how they are in a distant shelter”.

Heaven. Canto XXVIII

Verses 22-39
Perhaps as much as it appears below halo will cigner the light that paints it 24 when the vapor that carries him is most often, distant around the point a circle of igne he turned around quickly, who would have won that motion which more quickly surrounds the world; and this was of another circumcinto, and that from the third, and the third then from the fourth, from the fifth the fourth, and then from the sixth the fifth.

Above followed the seventh Spartan self already in breadth, than the messenger of Juno whole to contain it would be limb.

So the eighth and ninth; and each one later it moved, according as it was in number more distant from one; and that had the most sincere flame from which the pure spark was least distant,I believe, however, that more than her it becomes true.”

5 The astronomical revolution of the sixteenth century: introduction

The astronomy of the early sixteenth century has its own characteristics that distinguish it from the medieval one. Knowledge of the work of Regiomontanus stimulated the resumption of astronomical studies.

However, the merit of having started the "astronomical revolution" of the century belongs to the Polish Nicolaus Copernicus. He is above all a theorist and deals with mathematics, astronomy, medicine, law and theology, while as a researcher of astronomical phenomena his activity is very scarce. After having taken into consideration the various movements of the celestial bodies, he finds a starting point for his theory of him in the classical tradition which had handed down the ideas of the Pythagorean Philolaus and Aristarchus. The new Copernican system retains much of the old theories: it continues to consider the universe as spherical, finite and as concluded by the sphere of fixed stars.

Among the most relevant critical contributions appears that of Giordano Bruno (1547-1600). A teacher at various universities (Lyon, Toulouse, Montpellier and Paris), an expert in mnemonics (i.e. the techniques to activate memorization), in his work. De l'infinito universo e mondi he exposes his vision of an infinite universe without a center, formed by infinite worlds. God would not act from outside this universe, but would identify himself with it, animating it from within.

Another very important character is the German Johannes Kepler (1571-1630), the first to apply mathematics in the study of celestial motions, convinced that the pattern of the universe and its parts must respond to an abstract numerical and geometric criterion. The structure of the universe is explained according to a unitary system, even if Kepler soon discovers that he was wrong in calculating the distance of the planets from the center of their orbit.

However, in Prague he collects important observations together with another protagonist of this century: Tycho Brahe, with whom he corrects the cosmic theories. He works for ten years on an island supplied to him by his king and his observations are the most extensive and accurate that have ever been made up to that time.

5.1 Copernicus

The Polish Nicolaus Copernicus (Thorn 1473 - Frauenberg 1543) to respond to the difficulties of the Ptolemaic system regarding the apparent motion of the stars, in his work De revolutionibus orbium coelestium (1543), denied the Earth the central position in the universe affirmed by traditional conceptions, while he maintains that it rotates, like the other planets, around the Sun, motionless.

Copernicus states that, having found the traditional theories inadequate, he set out to read the books of all the philosophers he could procure, to see if anyone had ever thought of motions of the spheres of the world other than those taught in schools. In Cicero he finds that Nicetas had admitted the motion of the Earth. He later learns that others, such as Filolao, had done so. Thus he meditates on what he has learned and manages to explain celestial motions satisfactorily.

According to the beliefs accepted since Plato's time, the motions of celestial bodies had to be circular or composed of circular motions. Copernicus accepts the circularity of the motion of the celestial bodies as an indisputable principle, adding however a practical reason: only a circular motion, or one made up of several circles, can account for the periodic movement of the celestial figures.

Ptolemy had saved the circularity of celestial bodies, but not their uniformity, as the motion has a uniform angular velocity but does not coincide with its center, therefore it was necessary for the celestial bodies to move with a motion composed of uniform circular motions. It is from this problem that the search for Copernicus begins.

Copernicus' solution to the problem of the cause of celestial motions is based on the following axioms.

1. The celestial orbits and spheres do not have a single center.
2. The center of the Earth is not the center of the world, but only of gravity and the orbit of the Moon.
3. All orbits revolve around the Sun as it is placed at the center of all things.
4. The ratio between the Sun-Earth distance and the height of the firmament is less than that between the Earth radius and the Sun-Earth distance, so that this is insensitive with respect to the height of the firmament.
5. Whatever motion is observed in the firmament, does not belong to it but to the Earth. So the Earth, with the elements that surround it, rotates in diurnal motion on its immutable poles, while the firmament and last sky remains motionless.
6. All the motions that we see in the Sun are due to the Earth and to our orbit, with which we rotate in the manner of any other planet around the Sun.
7. The retrograde and direct motion that is observed in the planets does not belong to them, but to the Earth. The motion of this alone is sufficient to explain all the inequalities that are observed in the sky.

Even if the Copernican revolution will appear as a frontal contestation of Aristotelianism, in reality it was born from Copernicus' attempt to solve the practical difficulties of the Ptolemaic system and contains, in opposition to Aristotelianism, only some particular conclusions, such as the centrality of the Sun Copernicus, on the other hand, will not lose faith in Aristotelian physics and philosophy which he continues to consider valid.

In Ptolemy's conception, the astronomical world does not constitute a system: the planetary motions, although similar to each other, are independent of each other and are united only by their common centre, the Earth. Copernicus, on the other hand, gives an organic and architectural structure to the universe, and the motions of the planets are not simply traced on the sphere, but constitute a system according to a necessarily determined disposition. Kepler can argue that the Copernican hypothesis is more true than the Ptolemaic one because, of the two, it alone arranges the planets around the Sun in an order that accords with their periods.

5.2 Heliocentrism and Geocentrism in the sixteenth century

The refutation by the traditional culture of the Copernican theory is articulated in six points.

1. If the Earth were not located in the center of the world, the eclipses of the Moon would not be explained when the Sun and the Moon are not in opposite places of the zodiac, which is in contradiction with the experience of astronomers, who teach that eclipses occur when the Moon is in opposition to the Sun, and never otherwise.
2. The second argument is taken from Aristotle and Regiomontanus: all bodies in free fall along the diameter of the world meet the surface of the Earth at equal angles, in whatever part of the orb they descend, consequently they tend towards the center of the Earth; from this it follows that the center of the Earth and the world are identified.
3. The third argument, also taken from Aristotle, places the Earth at the center because,“being very heavy, it must tend towards the lowest place; and this, having to be as far from heaven as possible, can only be placed in the center of the world”. Furthermore, the Earth, 'being the most ignoble body, had rightly to be placed in the centre, in order not to cause harm to other bodies by its proximity'.(De caelo). Copernicus replies to the first part of this objection with his definition of gravity and with the hypothesis of the existence not of a single center of gravity, but of a plurality of centres; to the second he had opposed the greater nobility of the inside compared to the other parts of the universe, thus justifying the centrality of the Sun.
4. The fourth argument is taken from Alfragano and from Sacrobosco: once all the vapors, mists and exhalations that can impede our vision are removed, in any place on the surface of the Earth we find ourselves, the stars always appear to us of the same size, to rise, to set, to the zenith: which would not be possible if the Earth were not placed at the center of the universe, exactly equidistant from all parts of the sky.
5. The fifth argument, taken from Sarobosco, states that if the Earth weren't at the center of the universe, there wouldn't be six signs of the zodiac above the horizon and six below. Copernicus replies to these two arguments by reversing his reasoning: from the observation that the horizon divides the starry sphere into two exactly equal portions, and that he does the same with the zodiac, so that when the diameter of the circle of the horizon begins for example in the Cancer in the east, ending in Capricorn in the west, we deduce that the sky is immense compared to the Earth and that the Earth is in relation to the sky like a point compared to a body and the finite to infinity.
6. The sixth argument is deduced from Ptolemy: if the Earth were not at the center of the universe, it would have to be either in the plane of the equinoctial circle outside the axis of the world (in fact if it were on the axis of the world and in the plane of the equator would be in the center), or on the world axis outside the equinoctial plane or, finally, neither on the equinoctial plane nor on the world axis.

In the times of Copernicus and Galileo, heliocentrism can only be based on a series of arguments with a more or less high degree of probability.

1. The movement of the Earth makes it possible to explain all the appearances observed in the sky, including the precession of the equinoxes and the variations of the eccentricity.
2. The same decrease in the eccentricity of the Sun is found unchanged in the eccentricity of the other planets.
3. The planets have the centers of their deferents around the Sun as the center of the universe.
4. The fourth reason is of a philosophical nature and concerns the uniformity of the circular motion with respect to its own center and not to an arbitrarily introduced point (as in Ptolemy).
5. Then there is the conviction of the simplicity and economy of nature. Without the conviction of the rationality and perfection of nature, Copernicus would not have committed all his energies to the search for a simple and exact constitution to be applied to the celestial spheres.
6. The last reason lies in the fact that the previous astronomers, in elaborating their theories, did not take into account that rule which warns that the order and the motions of the celestial orbits are included in an absolute system.

5.3 Tycho Brahe

Tycho Brahe (1546-1601) unlike Copernicus is rather an observer than a theorist. The king had made available to him a well-equipped observatory located on an island where he remained for ten years. Later, in Prague with Kepler, he collects astronomical observations which allow him to correct traditional knowledge. His information is the most extensive and accurate of any made up to then. He is not concerned with giving life to a new theory of knowledge, but with accounting for his investigations into sensible evidence.

Brahe's findings can be summarized as follows:

• He illustrates the planetary system with the Earth at the center of the orbits of the Moon and the Sun and at the center of the fixed Stars. The Sun revolves around the earth in twenty-four hours taking all the planets with it. From a mathematical point of view, the system is identical to that of Copernicus.
• In 1502 he observed a new star and in 1577 he was able to determine its parallax and demonstrate that it was much further away than the moon and therefore beyond the sphere of the "elementary" world. This means introducing the principle of change into the sphere considered immutable, thus contradicting Aristotelian principles.
• Formulates the hypothesis that the motion of a comet maybe “not exactly circular but slightly oblong”. This is the first hypothesis that the movement of a celestial body can follow an orbit other than the circular one.
• Describes with great accuracy the alterations in the motion of the moon (1599), which will then be explained by successive generations of astronomers.
• His multiple observations of the planets allow Kepler to reveal the true nature of their orbits.
• He corrects the values ​​of many astronomical data and in a work published by Kepler (Prague 1602) he determines the position of 719 stars, which Kepler will later lead to 1005.

5.4 John Kepler

John Kepler (1571-1630) is convinced that the scheme of the universe can be expressed in numerical and geometrical relationships. He is the first to apply mathematics as a practical tool for studying the laws that regulate celestial motion. His idea of ​​the universe is at first substantially Platonic and Pythagorean. He is convinced that the pattern of the universe and its parts must respond to an abstract criterion of beauty and harmony. On the other hand, in accordance with the spirit of the time, he did not give up considering the relationship between science and astrology: through astrological calculations he sought in the events of his own life a verification of the theory of the influence of celestial bodies. Kepler soon adopted the Copernican point of view, always aiming to find a law that brings together the elements of the solar system. Thus he arrives at a first solution (1596), in which he connects his reflections to convictions that come from tradition. There are five possible regular solids, the so-called "Platonic bodies" and there are only five intervals between the six planets that he knows. According to Kepler's calculations, the five regular solids can be placed between the spheres of the planets so that each is inscribed in the same sphere as the next outer planet was circumscribed, according to the following scheme:

• Sphere of Saturn
• Cube
• Sphere of Jupiter
• Tetrahedron
• Mars sphere
• Dodecahedron
• Sphere of the Earth
• icosahedron
• Sphere of Venus
• Octahedron
• Mercury sphere

However Kepler soon discovers that he was wrong in estimating the distance of the planets from the center of their orbit and the unitary structure of the system cannot be conserved. Despite the failure of his first attempt, Kepler continues to seek the constitution of an astronomy in which hypotheses are replaced by demonstrable mathematical principles. He examines the relationships between the distances of the planets and their times of revolution around the Sun and it becomes clear to him that since the outer planets move too slowly, those times are not proportional to the distance.

He supposes the existence of a motor intellect within the sun which moves all things around it, but above all the closest ones, weakening instead for the more distant ones, due to the diminishing of its influence. So he devoted himself to the study of conics. The idea of ​​parables with two foci, one of which is at infinity, allows him to approach the solution of the problem. Since 1604 Kepler has been interested in conic sections, which he prefers to consider as distributed in five species, all belonging to a single family. Kepler formulates the principle of continuity for conics. From the conical section formed by two intersecting straight lines, in which the two foci coincide with the point of intersection, one gradually passes through an infinite number of hyperbolas as one focus moves further and further away from the other. When a focus is infinitely distant, there is no longer a hyperbola with two branches but a parabola. When the focus, continuing to move, passes beyond infinity and approaches again on the other side, we pass through an infinite number of ellipses, until, when the focuses coincide again, we reach the circle.

Kepler's three laws

Kepler develops a useful method for dealing with the problem of the infinitely small in astronomy.

In his Astronomia nova of 1609 he announced his first two planetary laws:

1. the planets move around the Sun in elliptical and non-circular orbits, with the Sun at one of the foci;
2. the ray vector joining a planet to the Sun covers equal areas in equal times. Another ten years pass before Kepler enunciates in his Epitome astronomiae (1618) his third law according to which;
3. the squares of the periods of revolution around the Sun are proportional to the cubes of the distances.

6 Galileo Galilei: introduction

Galileo Galilei (Pisa 1564 - Arcetri 1642) physicist and astronomer, initiator of the modern experimental method. In 1589 he obtained the chair of mathematics at the University of Pisa; in 1592 he moved to Padua, where, in 1604, he began his activity as an astronomer.

Galileo, in addition to being important for his scientific theories, must be considered one of the first scientists in the modern sense of the term. In fact, with his way of reasoning and using mathematics, with his beliefs on the need to use experimental controls, he creates the working method of modern science.

Galileo shows that natural phenomena can be expressed quantitatively in mathematical terms.

Furthermore, science must consider that the natural events we observe are not simple and elementary, as Aristotle believed, but very complex.

Galileo's previous science is based on Aristotelian theories from which medieval physics derives which makes a clear distinction between terrestrial and celestial bodies, whose natural motion is a perennial revolution on circular orbits around the center of the universe. This coincides with the center of the earth.

It takes the work of a complex personality like Galileo's to question Aristotelian theories and thus lay the foundations of modern physics.

6.1 Galileo: the astronomical discoveries and the Sidereus Nuncius

The first celestial phenomenon that attracts his attention is probably the comet of 1577, while he becomes aware of the Copernican hypothesis on 5 September 1581 at the Studio in Pisa, if not earlier.

Galileo's activity as an astronomer began in 1604, when a new luminous body appeared in the constellation Serpentarius. He demonstrates that it does not have a parallax, that is, no variations of its apparent position in the firmament are noticed, from whatever point it is observed. The parallax decreases as the distance increases and, in Galileo's time, while that of the planets is well known, the parallax of the fixed stars is so small, due to their enormous distance, that it cannot be detected with instruments for measuring the era.

Consequently, the new celestial body must be found in the remote region of the fixed stars, that is, in that external zone, which Aristotle and his school had considered as absolutely immutable. Until then it had been assumed that new stars, such as meteors and comets, were found in the least elevated and least perfect regions of the universe, that is, in those closest to the Earth. Tycho Brahe demonstrates that the new star is beyond the Moon and Galileo succeeds him in the fight against the idea of ​​incorruptibility and immutability of the universe, bringing a blow to the solidity of the Aristotelian scheme.

In 1609 Galileo invents two instruments that will have enormous importance in the subsequent evolution of science: the telescope and the microscope. While the Flemish eyeglass makers Lippershey and Jansen, having discovered by chance the combination of glass that forms the telescope, limit themselves to making the indispensable improvements to their reinforced glasses, Galileo, from the moment he receives the news of the approach glasses, builds the theory. And starting from this theory, pushing the precision and power of his glasses ever further, he builds his own series of optical instruments.

If the Dutch lens is a practical device, in fact it allows us to see at a distance that exceeds that of human sight, Galileo tries to give, with the use of these instruments, an answer to purely theoretical needs.

In January 1610 Galileo, thanks to the telescope, discovered four satellites of Jupiter. There are reactions of both enthusiasm and controversy. There are those who refuse to use the new instrument, who question the validity and the results of the observations carried out up to then. Others argue that the discovery of Jupiter's satellites is insignificant.

His first discoveries are published in Sidereus Nuncius, of 1610. The first part is occupied by observations on the Moon, whose surface, far from being smooth and polished, as it appears to the naked eye, is described as rich in relief, with high mountains and deep depressions which Galileo thinks are rivers, lakes and seas.

But Galileo is not limited to direct observations of space. He considers it essential, in his research, to interpret natural phenomena, observed and measured with precision with his tools, by means of mathematics, and in particular geometry. Mathematical language loses its abstractness and allows the scientist to detach himself from appearances and from the occasional and sensitive elements of knowledge, in order to formulate general laws.

The use of mathematics is not just a working method, it reflects a particular conception of the universe and divine action.

“Philosophy is written in this enormous book which is continually open before our eyes (I mean the universe), but it cannot be understood unless one first learns to understand the language, and to know the characters in which it is written. It is written in mathematical language, and the characters are triangles, circles, and other geometric figures, without which means it is humanly impossible to understand a word of it" (Il Saggiatore)

6.2 Galileo's scientific theories

Galileo's intellectual development is already accomplished many years before his works, the De Motu, the Massimi Sistemi and the Nuove Scienze, are written. Numerous indications, in fact, confirm that:

in 1602, Galileo had already considerably deepened the study of the pendulum and inclined planes, as well as the effects of the blow on the motion of bodies;

in 1604, he is in possession of the law of acceleration of fall (which he will fully discover in 1609);

in 1607 it is thought that the scientist had already reached a first formulation of the principle of inertia and of relativity;

in 1609 Galileo worked on the motions of projectiles and deepened the already stated principle of relativity; now at a good point is the intellectual elaboration of his work on motion.

The discovery of the law of acceleration of fall in 1609.

The position of the scientific community

The starting point is Aristotle's formulation, which is not very clear, namely that every motion needs an engine to maintain itself. According to the philosopher, every body removed from its natural place tends to rejoin it.

A radically different explanation appears only in the fourteenth century in Paris, where a substantially new dynamic arises in opposition to the Aristotelian one. Giovanni Buridano is its founder. He explains the acceleration of fall through the acquisition, by the falling object, of a series of impetuses which add to its gravity: as the body continues its fall, its motion becomes faster and faster because further and further away from the point from which it began to fall. Nicola Oresme introduces the graphic representation of motion in relation to two orthogonal axes which he calls Longitudo and Latitudo.

Galileo's position

In De Motu, Galileo explains the acceleration of a fall as the result of two contrasting forces, one of which, the imprinted virtue (impetus), wears itself out over time, and the other, the weight, exerts a constant action. For Galileo the impetus, instead of accentuating the action of gravity, hinders it, first to a very strong extent and then less and less sensitively. As a result, if natural motion could continue indefinitely, its velocity would not increase at that time.

Without this discovery, neither the exact treatment of the composition of motions in general nor the mathematization of the science of motion would be possible. Through the link with the composition of the motions, the importance that the exact formulation of the law has for the solution of the cosmological problem comes into full light.

Another theory: the principle of inertia

Galileo argues, in various contexts, the impossibility of a truly inertial motion. He states that only circular motion can be conserved indefinitely.

It is appropriate to keep in mind a fundamental distinction between the cosmological-architectural plan and the dynamic one.

When Galileo maintains that only circular motion is perpetual, because rectilinear motion would introduce an element of disorder into the well-ordered structure of the cosmos, he is not making use of a dynamic but an architectural consideration, the truth of which cannot be denied by anyone.

When, on the other hand, explaining how the diurnal rotation of the Earth does not have ruinous effects, Galileo shows that the circular motion is actually the result of a "projection by the tangent" and of the "own gravity" of the moving object, he resorts to a consideration dynamic. Galileo also clearly understood the principle of inertia on a cosmological scale and this results from his theory of tides, in which he applies that tendency of bodies to move in uniform rectilinear motion in which the principle of inertia is identified.

The motion of the Earth

Galileo develops a whole series of arguments to demonstrate the possibility of the motion of the Earth. He proposes to see if, in the bodies separated from the Earth, we perceive any appearance of movement, which equally pertains to all. To determine whether the Earth is moving, it is necessary to find, so to speak, a negative image of this motion in all the other bodies of the universe.

A motion common to all bodies external to the Earth is diurnal rotation, i.e. that apparent motion of the celestial vault by virtue of which all celestial bodies rotate from east to west in twenty-four hours. This motion will therefore be an appearance, a negative image of the rotation of the Earth from west to east. It is practically demonstrated that a possible motion does not influence the behavior of the bodies that are part of it, or that such an influence, if it exists, is practically insensitive; secondly, Galileo's intention is to show that the diurnal motion of the Earth can in practice be considered an inertial motion, even if on our planet the only truly horizontal plane is the spherical surface.

Although the demonstration given by Galileo of why the rotation of the Earth does not have destructive effects is unsatisfactory, it remains nevertheless established that the motion along the tangent is that of diurnal vertigo and that the rotation of the Earth is not fast enough to cause the feared disastrous effects from Ptolemy.

6.3 The Dialogue on Major Systems

The Dialogo sopra i Massimi Sistemi (1632) is the work written by Galileo during his intellectual maturity, it summarizes the innumerable studies made during his life.

In this work and in the text The New Sciences (1638), Galileo summarizes all of his cosmological and scientific thought, a set of very complex, but sober and rational concepts, which form the basis of a new discipline, dynamics.

In Massimi Sistemi it is proposed to demonstrate the truth of the Copernican system and the first part is essentially a critical analysis of the two books of Aristotle's De Caelo. The scientist also introduces a concept of gravitation close to the Copernican one and highlights the fact that the Moon and the Sun are not unalterable, but rather that the former has numerous similarities with the Earth, which becomes a mobile and wandering globe like the Moon, Jupiter and Venus.

Assuming the motion of the Earth and placing the Sun at the center of the universe, the motion of the celestial bodies from east to west proves to be illusory. The universe acquires a rational architectural structure, while in the Ptolemaic world the planetary orbs had no relation to each other. At the time of Galileo, the attribution of the diurnal motion to the Earth represents a great advantage over traditional astronomy and the fundamental principle, in order to explain the diurnal motion and all the phenomena that occur on the Earth, is that of the composition and motion independence.

According to this principle a body, stimulated simultaneously by two different motions, moves according to the resultant. In this way Galileo abandons the Aristotelian-Telemaic conception of gravity. The main difficulty against adopting the annual motion of the Earth is the fact that in such a case some mutation of the fixed stars would also have to be observed. Galileo's solution to this problem is that the Earth's orbit is like a point with respect to the sphere of the fixed stars, consequently its projection onto the sphere is insensitive.

For Galileo, in the Earth-Moon-Sun system, the bond that unites bodies is not a "material" bond; this bond, as we now know, is gravitational.

The only certain proof of the motion of the Earth is seen by Galileo in the phenomenon of the tides, which flow consists of a sort of attraction that the Moon exerts on the water through a force deriving from an affinity of nature. The lunar attraction tends to give the fluid globe an elliptical shape, with the axis oriented in the direction of the force exerted. The monthly and annual periods are in turn explained by the position of the Earth, the Moon and the Sun during the month and the year.

Galileo seems to realize that the bond that unites the celestial bodies is of a gravitational nature, but he never tackles the technical problems of traditional astronomy, he does not elaborate a planetary "theory", not even in the case of the "Medici planets" he discovered. His interest is all in "philosophical" astronomy, ie in cosmology.

6.4 The conflict with the Church

But this interest of his puts him at odds with the Church, which does not tolerate questioning the interpretations of the sacred texts. For the Church, a supposition useful for interpreting phenomena should suffice for every mathematician, but it cannot accept that the philosopher questions the evidence on the centrality of the Earth. Galileo does not care too much about the very precise theoretical limits imposed by Pope Urban VIII, considering them basically a pure formality.

The work soon encounters serious obstacles for publication; at its appearance the Massimi Sistemi aroused the enthusiasm of the Galileans. On the contrary, the Jesuits immediately sensed the profound cultural significance that prevails over the scientific merits of the work itself and unleashed controversies destined to overcome any resistance on the part of the pope who, if at first was in favor of the scientist, now feels betrayed and becomes his opponent.

In October 1632 Galileo was summoned by the Inquisition to Rome; in the long months of the trial, theological and cultural reasons intertwined with the Church's need to publicly reaffirm the counter-reformist policy towards every heresy.

The pontiff remains disturbed by the violent accusations made against him for having favored Protestant heretics with his anti-Habsburg policy, favoring the political factor over the vital religious interests of the Catholic Church and its commitment to the fight against heresy.

Galileo's condemnation becomes inevitable. On 22 June, kneeling before the "solemn assembly congregation", the scientist, now seventy years old, pronounced, after reading the sentence, his public abjuration.

Years of long meditation followed, in which Galileo completed his Discourses and Mathematical Demonstrations on Two New Sciences; in this text, which the theologians strangely do not condemn, even though they are no less Copernican than the Maximal Systems, modern Galilean science now appears as a fait accompli; in the work the reader finds his new universe governed by those precise dynamic laws that the scientist had so skilfully derived.

7 Isaac Newton

Isaac Newton (Woolsthorpe, Lincolushire 1642; Kensington, Middlesex 1727) tells of having been attracted by the fall of an apple from a tree in his garden, so he elaborates the idea that there is a single universal gravitational force, such as that which holds the Moon along its orbit around the Earth and attracts bodies towards the ground.

After the discovery of the law of gravitation, he builds his first reflecting telescope, then exhibits the theory of the decomposition of white light: when a ray of white light passes through a glass prism, it will be possible to see the decomposition of the white light into other color rays of the rainbow due to the different angle of refraction.

Newton's studies on gravitation lead to the explanation of why a planet moves in an elliptical and non-circular orbit. However, the result that Newton obtains is not the one he desired, so he develops a new type of treatment of the curves, this method will become the "infinitesimal calculus".

Many scientists, including Newton, think that the solar system is a big machine, i.e. that the different parts of the solar system are held together by a gravitational force, their relative motion, according to Newton's theory, is determined once and for all when the parts of the solar system are put together. The machine-universe model is also adopted by other “religious” scientists such as Robert Boyle, who states:

“...God's wisdom stands out more in the construction of the factory of the universe, that is, the fact that He has created such a complex mechanism that, making use only of raw matter and its general and normal contribution, behaves as He has decidedly, more so than if He had used an intelligent supervisor to, from time to time, regulate, assist and control the motion of the various parts.”

7.1 The laws of motion

Newton is interested in dynamics; that is, the study of the causes that determine the motion of bodies, causing them to start moving instead of remaining stationary. This interest of him can be realized thanks to Galileo Galilei's studies on kinematics, that is the study of how objects move.

Through dynamics, Newton can explain the properties that characterize the motion of objects, formulate three principles of dynamics and manages to connect them to Kepler's laws on planetary movements, on the orbits of the planets and on the times of their revolution.

• First law of motion: Every body maintains its state of rest or uniform motion in a straight line unless a resultant force other than zero acts on it.
• Second law: the acceleration undergone by a body has the same direction as the resultant of the acting forces and is proportional to it, furthermore it is inversely proportional to the mass of the body.
• Third law: to every action there is always an equal and opposite reaction; in other words, the reciprocal actions of two bodies are always equal to each other and directed in opposite directions.

7.2 Experimental astronomy of the seventeenth and eighteenth centuries

Experimental astronomy, or the direct observation of celestial bodies by means of a telescope, greatly accelerated with the improvement of the telescope in the 17^th and 18^th centuries.

The greatest advances in this field occur thanks to the studies of the following astronomers.

• C. HUYGENS (1629-1695): perfected the telescope, introducing the micrometer. He demonstrates that Saturn's aspect variations are due to a ring inclined 28 degrees on the ecliptic. He also measures the acceleration due to gravity.
• O. ROEMER (1644-1712): provides proof that light propagates with a determined speed.
• GD CASSINI: demonstrates that the Earth is flattened at the poles; measures the parallax of Mars allowing an assessment of the distance of Mars from the Sun.
• J. FLAMSTEED (1646-1719): demonstrates that the system for detecting longitude in the open sea would be impossible if a way to establish the position of the fixed stars with greater precision was not found.
• E. HALLEY (1656-1742): perfected the second-hand pendulum and determined the position of 341 stars. Newton had hypothesized that comets moved along very elongated ellipses, Halley calculates the shape, position and size of the trajectory of the comet of 1682, which takes his name.
• J. BRADLEY (1693-1762): discovers that the axis of the Earth undergoes an oscillation under the influence of the Moon; he discovers the aberration of the fixed stars, an apparent change in their position due to the motion of the Earth relative to the speed of light.
• W. HERSCHEL (1738-1822): builder of highly precise telescopes, he discovered Uranus, 800 double stars and over 2000 nebulae. He describes the structure of the Milky Way and ascertains the translation motion of the Sun hypothesized by Bradley. He can be considered the founder of astrophysics, because he tries to discover the laws of groupings in systems in the apparent disorder according to which the stars are distributed in the sky.
• GW LEIBNIZ (1646-1716): arrives at the conception of differential calculus, which becomes an indispensable tool for later mathematicians.
• L.EULERO ( 1707-1783): demonstrates that certain irregularities in the movements of the Earth which occurred from the time of Ptolemy can be explained by assuming that our planet moves along a trajectory made up of a variable and not fixed ellipse.
• JL LAGRANGE (1736-1813): studied the perturbations of the solar system.
• PS LAPLACE (1749-1827): develops the investigations on the secular perturbations of the solar system identified by Lagrange and summarizes the results of the astronomical investigations of his century in the work Treatise on Celestial Mechanics (1799-1825). We owe him the "hypothesis of the nebula" on the origin of the solar system.
• G. PIAZZI (1746-1826): discovers the small planet Ceres, about 1/4 the size of the Moon and begins the discovery of asteroids.
• FW BESSEL (1784-1846): measures for the first time the distance of a star, obtaining the value of about eleven light years.