The Fall of the Geocentric Theory The Fall of the Geocentric Theory, and the Rise of Heliocentrism The geocentric theory reached its pinnacle with the system devised by Ptolemy. Ptolemy's geocentric theory continued to be the system of choice as the Roman empire succeeded that of the Greeks. With the fall of the Roman empire (circa 450 AD), it was left to the Arabs to keep the Ptolemaic view of the universe alive. In 622 AD, the Prophet Mohammed launched his holy war against the infidels. Within a century, the Islamic Empire extended eastwards across northern India to the borders of China, and westwards across Asia Minor, to north Africa. With the Arabic conquest of Spain and Sicily, the empire made it into western Europe. Alexandria (Egypt), the center of classical learning, fell to the Arabs in 642. When the period of military expansion ended, Islamic scholars became enthusiastic students of classical philosophy. Many important manuscripts were translated from Greek into Arabic. In the world of medieval Islam, Aristotle and Ptolemy were the supreme authorities in matters of natural science and astronomy.

They continued to make observations, and to refine the data that went into the model while streamlining/advancing some of the calculation techniques. But they did not make any modifications to the underlying philosophy.1 "In 999 AD, Gerbert of Aurillac, the most accomplished mathematician, musician, astronomer and classical scholar in Europe, ascended to the papal throne as Sylvester II, known as 'the magician Pope' to his contemporaries. His papacy, at the symbolic date 1000 AD marks the turning point of the European 'dark ages'. Contact was established with Arabic centers of learning in Spain , where Muslim, Christian and Jewish scholars congregated. During the following centuries, Hebrew and Arabic versions of ancient Greek texts were translated into Latin and began to circulate in Europe. The works of Aristotle were translated from around 1200. The translation of Ptolemy's Almagest into Latin in 1175 re-vitalised European astronomy. King Alfonso X of Castile (1122-1184) commissioned new astronomical tables calculated according to Ptolemy's theory with Arabic mathematical refinements.

Completed in 1252, the Alphonsine Tables remained the best astronomical tables available in Europe for the next three centuries. The complexities of the Ptolemaic system exasperated King Alfonso however. When the intricacies of epicycles, deferents and equants were explained to him Alfonso 'the Wise' is said to have remarked that if the Almighty had consulted him on the matter, he would have recommended something a little simpler... "1 Eventually, with the re-emergence of European learning in the 13th century, the geocentric view of the universe would be adopted by the Catholic church. It is interesting that in the early European universities, Ptolemy's theory was relegated to the world of mathematics, calendars, and astrology. It was purely a mechanical model of the celestial motion, and not the "true" nature of the universe as described by Aristotle. The latter would be given a more revered place in higher learning, and especially in questions of philosophy and theology. The Copernican Revolution In the fifteenth century, a reform of European astronomy began. This was due to the fact that predictions made using the Ptolemaic system were less and less accurate.

With the advent of ocean-going vessels, and the expansion of global trade and exploration, navigation using astronomical knowledge had become extremely important. Also, the calendar implemented in 44 BC by Julius Caesar was 10 days off, with the spring equinox now occurring on the 11th of March instead of the 21st (used to fix the date of Easter). Astronomical help was needed! Two astronomers, Peurbach and Regiomontanus (who set up the first European observatory at Nuremburg in 1474) took on the task of locating errors in the works of Ptolemy, as well as errors in published tables and in observations. They had refined some of astronomy, but they had not gotten rid of all of the mounting problems. Copernicus (1473 to 1543) learned of the works of Peurbach and Regiomontanus while an undergraduate at the University of Cracow (Poland), then spent eight years studying in Italy (five years in Bologna studying liberal arts, and three years at the University of Ferrara where he got a degree in canon law) before returning to a position in the cathedral at Frombork, Poland.

Here he spent the majority of his time as a physician, lawyer, and church administrator. In his spare time he dabbled in astronomy. Copernicus was very interested in the Pythagorean mathematics, for he also believed in a harmony of the cosmos. He was, however, not apparently very interested in making new astronomical observations. By 1514 Copernicus had laid out his heliocentric view of the universe in a manuscript entitled Commentariolus. This short work would put forward most of the elements of the heliocentric system some 39 years before his major manuscript on the theory, De revolutionibus orbium coelestium ("On the Revolutions of the Heavenly Spheres"), was published. While many of the ideas Copernicus was proposing were radical, he still adhered to the Aristotelian view that everything moved in perfect circles, on solid celestial spheres, and moved via the physics espoused by Aristotle. Indeed, he even kept Ptolemy's epicycles in modified form in his new model. But Copernicus knew that his new theory would upset the Church, and he kept it relatively quiet.

By moving the Sun to the center of the universe, man was no longer so important, and this could not stand in the view of the Church. In the intervening years, Copernicus worked very hard at fully developing his view, and this included a number of mathematical devices that greatly advanced the art of calculation. In fact, De revolutionibus closely resembled Almagest in its structure and content. Copernicus feared the repercussions of his work, and was extremely reluctant to publish it. Only after the publication of a summary of Copernicus' system by an enthusiastic supporter named Rheticus in 1540, called Narratio prima, did the aging Copernicus agree to publish his theory. The story goes that Copernicus received a printed copy of his De revolutionibus on his deathbed in 1543. A diagram from De revolutionibus orbium lays out his system: Note that this system proposed a radical new idea: the Earth spun on its axis once per day! His theory also gave a simple explanation for the retrograde motions of the planets: the Earth catches up and passes them once each year. He also argued that his system was more elegant than the traditional geocentric system.

However, the predictive power of his model was not substantially better than its competition. Besides removing humanity from the central place in God's creation, there were some obvious "problems" with this theory: 1) If the Earth is spinning so fast, how do we remain attached to it--how do birds find their way home again with all of this spinning? [Of course, the counterpoint is what keeps us attached in the Geocentric Universe, where some people must be on "top" or "bottom" of the spherical Earth?] 2) Why do the stars not show a parallax? They have to be at immense distances to show no parallax, and thus there is this great empty space in between the last sphere (Saturn) and that containing the stars. [The counter-argument to this is that if all of the stars are at the same distance fixed to a crystalline sphere, no parallax can be measured since all stars would shift the same amount!] All in all, the Copernican heliocentric model of the universe was very slow to gain acceptance. In fact, during his lifetime and after his death, Copernicus was often the subject of ridicule.

But he was never formally charged with any heresies, as the heliocentric model would not really make it on the "radar screen" of the church for another 50 or 60 years (note also that De revolutionibus orbium was dedicated to Pope Paul III!). While the model may not have been accepted, much of the new tabular material and calculation methods were adopted by geocentrically-oriented astronomers for their own calculations on planetary motion. Tycho, Galileo, and Kepler The next player in the Copernican revolution was Tycho Brahe (1546 to 1601) . Tycho was from a privileged background of Danish aristocracy, and thus had a good education and the resources necessary to engage in a variety of pursuits: "He was brought up by his paternal uncle Jörgen Brahe and became his heir. He attended the universities of Copenhagen and Leipzig, and then traveled through the German region, studying further at the universities of Wittenberg, Rostock, and Basel. During this period his interest in alchemy and astronomy was aroused, and he bought several astronomical instruments.

In a duel with another student, in Wittenberg in 1566, Tycho lost part of his nose. For the rest of his life he wore a metal insert over the missing part. He returned to Denmark in 1570. In 1572 Tycho observed the new star in Cassiopeia and published a brief tract about it the following year. In 1574 he gave a course of lectures on astronomy at the University of Copenhagen. He was now convinced that the improvement of astronomy hinged on accurate observations. After another tour of Germany, where he visited astronomers, Tycho accepted an offer from the King Frederick II to fund an observatory. He was given the little island of Hven in the Sont near Copenhagen, and there he built his observatory, Uraniburg, which became the finest observatory in Europe."2 Tycho went about building the finest astronomical instruments that he could ( read about them here ), he ran his own printing press, and he began to train astronomers from all over Europe. He was an excellent observer, and the quality of his observations were higher than any that came before him, and were much better than his contemporaries.

Two of his most important observations were of the "new star" of 1572 (now known to be a supernova ), and of the comet of 1577. In Aristotle's view, no new stars could occur, the heavens were immutable! He showed that the comet of 1577 had to be further away than the Moon, and that comets were not an atmospheric phenomena as previously believed. These two observations meant that Aristotle's view of the universe was incorrect, the heavenly realm could change. But Tycho could not accept the heliocentric view either, preferring the Aristotelian physics, and the view that man was important and at the center of the universe. What Tycho did to resolve this was a peculiar halfway step that was a hybrid of the old geocentric view, and Copernicus' new heliocentric view: the "Tychonic" model. In this model, he placed the Earth at the center, and the Moon and the Sun orbited about it. But the other planets all orbited around the Sun! Johannes Kepler After a falling-out with the King, Tycho left Denmark and moved to Prague in 1597.

There he hired Johannes Kepler (1571-1630) to help him in reducing the data he had collected at Uraniburg. This extensive data base would not get published until many years after Tycho's death (in 1601, tomb ). Kepler was born in Weil der Stadt in Swabia, in southwest Germany. "Kepler's teacher in the mathematical subjects was Michael Maestlin (1580-1635). Maestlin was one of the earliest astronomers to subscribe to Copernicus's heliocentric theory, although in his university lectures he taught only the Ptolemaic system. Only in what we might call graduate seminars did he acquaint his students, among whom was Kepler, with the technical details of the Copernican system. Kepler stated later that at this time he became a Copernican for "physical or, if you prefer, metaphysical reasons". In 1594 Kepler accepted an appointment as professor of mathematics at the Protestant seminary in Graz (in the Austrian province of Styria). He was also appointed district mathematician and calendar maker.

Kepler remained in Graz until 1600, when all Protestants were forced to convert to Catholicism or leave the province, as part of Counter Reformation measures. For six years, Kepler taught arithmetic, geometry (when there were interested students), Virgil, and rhetoric. In his spare time he pursued his private studies in astronomy and astrology. In 1597 Kepler married Barbara Müller. In that same year he published his first important work, The Cosmographic Mystery, in which he argued that the distances of the planets from the Sun in the Copernican system were determined by the five regular solids, if one supposed that a planet's orbit was circumscribed about one solid and inscribed in another."3 Kepler's peculiar construction actually produced very good results when predicting the positions of the planets (except for Mercury). Tycho was impressed with Kepler's mathematical skills, and invited him to Prague to be his assistant (where he lived ). When Tycho died, Kepler assumed the position of Imperial Mathematician. In 1604, just like Tycho had, Kepler discovered his own "New Star" (the last known supernova to occur in our Milky Way galaxy).

With Tycho's excellent observational data, Kepler had all the material he needed to launch a new heliocentric view of the universe. In 1609 he published Astronomia Nova ("New Astronomy") which contained his first two laws of planetary motion: 1. Planets move in elliptical orbits with the Sun at one of the foci: 2) A planet sweeps out equal areas in equal times: It was not until 1618 that Kepler came up with his final law (published in 1619 in Third Law in Harmonices Mundi): 3. The square of the planet's orbital period is proportional to the cube of the orbital size (semi-major axis). In equation form, P2 = K a3, where P is the period, a is the semi-major axis, and K is a constant. In a log-log plot, the relationship looks like this: The time taken to complete one orbit grows more than in direct proportion to orbital size. The orbital period is the circumference of the orbit divided by the planet's mean velocity.

Since the circumference of an orbit increases in direct proportion to its semi-major axis, the Third Law implies that the velocities of planets in larger orbits are slower than for planets nearer the Sun. A planet with an orbital diameter 5 times the Earth's will require 11 Earth years to complete an orbit. The timing of the publication (in 1609) of Kepler's original two laws could not have been better, for in 1610, Galileo, published the "Sidereal Messenger", describing his discovery of the four main moons of Jupiter (which we call the Galilean satellites after their discoverer). This discovery showed for the first time that not all celestial objects orbit around the Earth (more on this momentarily!). Kepler quickly published a letter supporting the author and the discovery of these moons. He obtained a telescope that year, and begun his own observations of these moons leading to a write-up describing his observations entitled Narratio de Observatis Quatuor Jovis Satellitibus ("Narration about Four Satellites of Jupiter observed"). These two manuscripts were published in Galileo's home city of Florence, and were a great relief to that beleaguered scientist.

By 1611 Kepler had published a preliminary description of how a telescope works in Dioptrice. Kepler's crowning achievements were his publications entitled Epitome Astronomiae Copernicanae ("Epitome of Copernican Astronomy") in 1621, and his Tabulae Rudolphinae ( "Rudolphine Tables" ) in 1627. In Epitome Astronomiae Copernicanae, Kepler fully laid out a new heliocentric model for the universe with the planets on elliptical orbits. This was the first accurate description of how the planets moved. Unfortunately, during the period of 1615-16 there was a witch hunt in Kepler's home country, and his mother was accused of being a witch. Kepler spent several years defending her in court, finally winning her freedom in 1620. On top of this, in 1618 the "Thirty Years War" broke out. Most of Germany and Austria were affected.

Kepler suffered some persecution during these years due to the fact that he was a protestant, and during this time the Catholic counter-reformation movement, that was attempting to keep people from leaving the church (as well as attempting to quash the Protestant movement), was raging through Europe. During these years he was attempting to have his new tables on the motions of the planets, the Tabulae Rudolphinae, published in Linz, but a peasant revolt broke out, and the printer's shop where the manuscript was being printed was burned. He left Linz, and finally had the Tabulae Rudolphinae published in Ulm in 1627. The Tabulae Rudolphinae were the most accurate predictions for the motions of the planets that had ever been published, and Kepler had laid the theoretical foundation for the acceptance of the heliocentric theory. This does not mean, however, that Kepler's new theory was quickly adopted as the correct view of the universe--it was not! Galileo While Kepler had escaped much of the wrath of the Church, his contemporary, and probably the staunchest supporter of his work, Galileo, would not.

Galileo was born in Pisa in 1564, twenty one years after the publication of Copernicus' De revolutionibus orbium, and seven years before Kepler's birth. Galileo's early years would show the personality that would come back to haunt him later in life: "Galileo received an excellent education at a monastery near Florence, and in 1581, aged 17, showed enough talent for his father to send him to the University of Pisa to study medicine. Though born into the ranks of lower nobility, the Galilei family struggled to make ends meet and were unable to afford the university fees. It was hoped that Galileo would secure one of 40 scholarships available. [he did] In the second year he showed enough promise to discover that a pendulum of any given length swings at a constant frequency, which led to the invention of the 'pulsilogium', a medical device used for timing the pulse of patients. However, Galileo was already attracting animosity by his reluctance to accept the common philosophy and the scholarship was refused, forcing him to leave the university without attaining his degree.

Naturally, biographers have looked upon this as an early resistance to his liberal ideas, though Arthur Koestler in his book, The Sleepwalkers, writes: "It is more likely that the refusal of the scholarship was not due to the unpopularity of Galileo's views, but of his person - that cold, sarcastic presumption, by which he managed to spoil his case throughout his life". Excluded from university life, Galileo tutored privately and managed to maintain his studies. He developed his interest in mechanics, writing treatises on his inventions which he circulated in manuscript. Another early invention was a hydrostatic balance which attracted the attention of a number of scholars, one of whom, Marchese Guidobaldo del Monte, befriended Galileo and began a chain of recommendations that brought him to the attention of Ferdinand de Medici, the Duke of Tuscany. In a rather ironic twist of fate the Duke was so impressed with Galileo that he appointed him as a lecturer at the university which four years earlier had refused his scholarship. Just three years on, aged 28, he rose to the position of Chair of Mathematics at the esteemed University of Padua, where he remained until 1610.

One of the experiments Galileo is famous for is dropping rocks off of the leaning tower of Pisa. He did this to test Aristotle's view that the heavier an object, the faster it will fall. It is re-created here . It is hard to do this on Earth due to air resistance. A better, but fuzzier, demonstration was done by the Apollo astronauts . In 1597, Galileo was to receive his first contact from Johannes Kepler, then aged 26 and employed as Professor of Mathematics at Gratz in Austria. Kepler had completed The Cosmic Mystery, a treatise which expressed arguments in favor of Copernicus' Sun-centered universe. He sent a copy as a gift to the Chair of Mathematics at Padua, anxious for academic feedback. Galileo replied immediately, and wrote in cordial terms: "I indeed congratulate myself on having an associate in the study of Truth who is a friend of Truth. For it is a misery that so few exist who pursue the Truth and do not pervert philosophical reason.... I adopted the teachings of Copernicus many years ago, and his point of view enables me to explain many phenomena of nature which certainly remain inexplicable according to the more current hypotheses.

I have written many arguments in support of him and in refutation of the opposite view - which, however, so far I have not dared to bring into the public light, frightened by the fate of Copernicus himself, our teacher who, though he acquired immortal fame with some, is yet to remain to an infinite number of others (for such is the number of fools) an object of ridicule and derision. I would certainly dare to publish my reflections at once if more people like you existed; as they don't. I shall refrain from doing so." Although Kepler replied, imploring him to take a different stance and air his views, Galileo ignored his letter and ended the correspondence. It was 16 years before he would produce the first public indication of his beliefs; throughout the interim he continued to teach, and appeared to endorse the traditional Aristotelian arguments that the Earth did not move."6 The letter to Kepler provides us with excellent insight into the political realities of life in the late 16th century--you had to be careful what you said in a public forum, for you could face serious penalties for going against Church doctrine.

But Galileo would not remain quiet for too much longer, for he was a brilliant experimentalist, and as his fame and reputation grew, so did his confidence that he could challenge the status quo. The problem was that while the Copernicun system might be more elegant in explaining the motions of the planets than the Ptolemaic system, these were mere mechanical details, and were not sufficient reason for the Church and others to overthrow the established system--what was needed were observations that could not be explained by a geocentric view. We have already noted the two discoveries by Tycho (the supernova and comet) that showed the "superlunary" world was not immutable, contrary to the view of Aristotle. But again, this did not violate the geocentric model for the motions of the planets. Other evidence was needed. This evidence required a new instrument, the telescope. The invention of the telescope has been credited to Hans Lippershey, a Dutch spectacle maker. But this may or may not be correct (go for here for a bit more). The story goes that in July of 1609 Galileo had heard that a Dutchman had devised an instrument composed of two lenses that made objects appear closer.

Not wanting to be scooped, Galileo quickly came up with his own version and: "In August 1609 he invited the Venetian senate to inspect his own 'spy-glass' which, through a combination of a convex and concave lens, was able to magnify objects nine times greater than normal vision. The senate was greatly impressed, particularly by his suggestion that in matters of defense it would enable them to see the sails of ships two hours before they could be seen by the naked eye. When he presented his spy glass to them as a present they expressed their appreciation by doubling his salary to a thousand scudi a year and guaranteeing his position at Padua for the rest of his life. No doubt he felt some embarrassment when local spectacle makers were soon able to replicate his instruments for just a few scudi, but he committed himself to improving the power of his instruments and began to turn his attention to the heavens. In March of the following year, 1610, he published Sidereus Nuncius, the 'Messenger of the Stars', which revealed the fruits of his observations. The tract was kept deliberately short in order to make it widely accessible and the style of language was uniquely devoid of philosophy.

Combined with explosive contents, it made a remarkable impact worldwide. He wrote about the surface of the Moon, dismissing the common view that it was perfectly smooth, and describing it as full of lofty mountains and deep hollows. He wrote about the fixed stars, and told how he had witnessed "other stars, in myriads, which have never been seen before, and which surpass the old, previously known stars in number more than ten times". Most importantly, he wrote of his discovery of four new planets, the Moons of Jupiter which had never been imagined before. With this, he justified his first ever 'outing' of his heliocentric beliefs, writing: "Moreover, we have an excellent and exceedingly clear argument to put at rest the scruples of those who can tolerate the revolution of the planets about the Sun in the Copernican system, but are so disturbed by the revolution of the single moon around the earth while both of them describe an annual orbit around the Sun, that they consider this theory to be impossible."6 Galileo was assembling the ammunition to mount the final assault on the geocentric model. That objects could orbit Jupiter instead of the Earth, showed that the Earth could in no way be considered the sole center of the universe.

A page from Galileo's journal showing some observations of the movements of the moons of Jupiter: But this, by itself, was not quite sufficient to de-throne the geocentric model, since Tycho had already proposed a hybrid model where Mercury, Venus, Mars, Jupiter and Saturn orbited the Sun, while the Moon and Sun orbited the Earth. Galileo's observations continued to mount, and one of the most important came in late 1610 when he found that the planet Venus showed phases just like those of the Moon: [The top part of this figure also shows Galileo's impression of (from left to right) Saturn, Jupiter and Mars.] This observation finally ruled out the Ptolemaic system (but, unfortunately, not the Tychonic system!). He also showed that neither the Sun nor the Moon were perfect, as envisioned in the Aristotelian view of the universe: Galileo published these findings, and the Church found them offensive--as they violated the Aristotelian view. Galileo eventually was punished, and forced to recant his beliefs, and spent the rest of his life under house arrest.

You can read more about the trials and tribulations of Galileo at my website for the Astronomy 301 course here . Newton and His Laws Kepler had taken the Copernican proposal and provided a mathematical basis for understanding the motions of the planets, and all observations confirmed this model. This was the confirmation and proof that the heliocentric model was correct. But he did not have an understanding of why the planets moved, and what kept them in their orbits. It was Isaac Newton that put forward the first explanation of why the planets moved by invoking a "force" called gravity. Like Kepler, Newton also had three laws: I. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it . II. The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma; in this law the direction of the force is the same as the direction of the acceleration. III. For every action there is an equal and opposite reaction. The origin of this mysterious force called gravity was the subject of intense debate.

The true understanding (at least to the point of what is going on, but not why mass actually exerts a force called gravity---a very deep, and difficult subject) had to wait until Einstein's theory of General Relativity in 1916. But Newton's approach, that mathematics can be used to understand the Universe, was the true beginning of modern physics. To understand a little about gravity, we need to discuss some new terms. First let's tackle "mass" and "weight". You are probably familiar with these two terms, but they have completely different meanings. In the English system, weight is measured in "pounds". In the metric system "mass" is measured in kilograms. You may have even seen the conversion 1 kg = 2.2 lbs. But this conversion only works at the Earth's surface. Why? Because mass is an intrinsic property of the object--whether a grain of sand, a rock, a human being, a car, a planet, etc. They all have a "mass" that is always the same number of kilograms, no matter where they are located. But an object's weight depends on where it is located.

On the Earth's surface, an object with a mass of 100 kg has a weight of 220 lbs. But on the Moon, the weight of that object is only 36.5 lbs. On Jupiter (which has 318 times the Earth's mass) that weight would be 520 lbs! (To see what you would weigh on other worlds go here .) So for an astronaut orbiting the Earth in the Space Shuttle, we talk about them being "weightless". But obviously, they have not lost any mass! Weight is what a bathroom scale reads, and it comes about through the gravity from the Earth's mass pulling on objects. We talk about the "acceleration" of gravity. You are familiar with the term acceleration---you hit the gas pedal ("accelerator") in your car and you go faster, and faster. An acceleration is the changing velocity of an object (also read section 4.1 to see the real definitions of "speed" and "velocity"--we will just consider them to be the same thing for our discussion here, but technically they are not quite the same thing).

As shown in Figure 4.1, an object that is speeding up is accelerating--but so is a car going around a corner, or one that is slowing down, "decelerating". A car that is speeding up has a positive acceleration, one that is slowing has a negative acceleration. So, how do we accelerate a car? We push on the gas, using more and more of our gasoline (energy!) to speed up. To decelerate we push on the brake---we are again using energy, but this time the brake heats up from the friction to dissipate the speed of the car. If you have ever pulled a heavy load, or descended down a very steep hill, you can smell your brakes when you try to slow down---the energy contained in your motion, the "momentum", has to be dissipated, and in slowing it is transfered to heat, and this creates a smell as the brake pads/shoes heat up. Ok, now we know from experience that "what goes up, must come down". So, let's climb to the top of a tall building and drop a rock. What happens?

Initially, for just an instant, the rock is not moving, but then it falls, and as it falls it speeds up---it is accelerating. Not only that, it is accelerating at a specific rate. This is shown in Fig 4.2: After one second (t = 1s), the rock is moving at a velocity of 10 m/s, after two seconds (t = 2 s) the rock is moving with a velocity of 20 m/s. We can write this as an equation: v = 10 x t. Using this equation, we know that if t = 4 s, then v = 40 m/s. Ok, so velocity is measured in meters per second (or kilometers per second, or kilometers per hour, or miles per hour, etc.). The "10" in our equation (which is actually 9.8) has to have the weird units of m/s2 ("meters per second squared") to get the units on the equation to work out. This "10" is called the gravitational acceleration constant, abbreviated "g". So, in actuality, the equation is v = gt. And "g" depends on the local gravity.

On Jupiter "g" is bigger, on the moon "g" is smaller. On the Earth g = 9.8 m/s2. Of course, with an atmosphere, you cannot continue to go faster and faster as you fall, you eventually reach something called "terminal velocity," where the friction caused by your motion pushes back against your motion. A real world example of how the air causes friction is this Space Shuttle re-entry video . This gravitational constant also is what determines your weight! In fact, weight = mass x g. Let's be more general now, and revert to calling "g" the acceleration, abbreviated by "a". Now our equation becomes w = ma. And, calling weight the "force of gravity", abbreviated by "F", we get the equation F = ma. This is the second of Newton's laws that we listed above: force = mass x acceleration. A "Force" is something that tries to change the acceleration of a mass. When you jump up into the air (to dunk a basketball), the force of gravity changes your acceleration: you go up for a while all the time slowing, stop, then go back down, accelerating as you fall.

This force of gravity is what keeps the planets orbiting around the Sun on elliptical orbits. But this is just part of the explanation (and it was Newton that developed and used the theory of gravity to explain Kepler's laws). To understand why planets orbit the Sun (or why the moon orbits the Earth) we have to talk a little more about motion. Newton's first law states that "in the absence of a net force acting upon it, an object in motion moves with constant velocity". This is kind of hard to envision on the surface of the Earth. If we were to throw a baseball, it would go a little ways, but eventually crash into the surface of the Earth. Why? Because the Earth's gravity is a force that changes the motion of the baseball. But, if we could move into deep space and then throw our baseball, then without any nearby masses, it would move at a uniform velocity through space. But near a large mass, the path of the baseball is altered--it is curved. We have had to play a thought game to understand this motion---let's make some more mental leaps and imagine shooting a cannonball off a very tall mountain . This is shown in the figure, below.

If we use a little bit of powder, and the ball comes out slowly, it will crash close to the mountain. Let's add more powder and blast it out at a higher velocity---the ball travels further. But Earth's gravity wins and the ball eventually crashes back to Earth. Now, what happens if we shoot the ball to a very high speed so much so that it doesn't crash back into the Earth. Is this possible? Yes, it is called orbital velocity! This is what rockets like the Space Shuttle do, they go fast enough to reach orbit. What is an orbit? Well it is the speed at which the cannonball (or spacecraft) is going where it "continuously falls around the Earth" without hitting it. The gravity of the Earth continually curves the motion of the ball, but at just the right rate so that the cannon ball never hits the Earth. Of course we could use so much explosive that the cannon ball is not captured by the Earth but blasts itself into deep space---just like we must do to launch a space probe to another planet.

We call the velocity where the object permanently leaves the Earth, the "escape velocity" (this is a very high speed: 40,000 km/hr!): So, how can we understand this curvature thing? Let's look at a simple example, a ball attached to a string that is spun around our head, as in Figure 4.6: As long as the string holds, the ball will circle our head---but if it breaks, the ball flies off! What is the force acting on the ball? Well it is the string! The string is the force acting to keep the ball in motion around our head (though we supply the energy). If we could keep spinning the ball faster and faster it would eventually break the string--it would "escape". This is just like gravity---gravity is the invisible string that keeps the ball (or satellite) orbiting the Earth. We can now expand upon this demonstration to understand Kepler's third law. If we suddenly shorten the string, what happens? The ball goes around faster! If we lengthen the string, the ball goes around more slowly--just like planets.

Mercury is close to the Sun, it's "string" is short (in reality the force of gravity of the Sun is larger), so it has to go around fast (to balance the larger gravitational force) or else it will crash into the Sun (Mercury's orbital period is only 88 days). Jupiter is five times further from the Sun then the Earth, its string is long, so it moves slowly--it takes Jupiter more than 11 years to go around the Sun. Kepler's third law, P2 = a3, says the longer the string ("a") the slower the planet moves and the longer the orbital period ("P"). It is the force of gravity that keeps planets and comets in orbit around the Sun, and the various moons in orbit around their planets. Newton realized that to explain Kepler's third law, the "force of gravity", that is the force that attracts two bodies with "mass", must be directly proportional to their masses, but inversely proportional to the square of the separation between them: Fgrav = G(m1x m2)/r2 The "G" in this equation is the "gravitational constant" that makes the equation work. It is something that must be experimentally measured .

Here is a figure showing the geometry of gravitational attraction: The force of gravity is also the cause of the tides. As discussed in section 4.5, the gravities of the Moon and Sun distort the shape of the Earth, and create the rising and falling tides that coastal dwellers are familiar with. There are other forces in nature, and we will encounter them shortly. Gravity is the weakest of all of nature's forces, but because the others are strong, and have both positive and negative "charges", they quickly cancel themselves out. Gravity is an odd force in that it is only attractive--thus even though it is weak, it is the force the controls how matter behaves in our Universe. There is a lot more to gravity that we do not have time to discuss, we are glossing-over most of the subject here. To get a full flavor for this subject, read Chapter 4 in its entirety. To get more requires you to take a physics class (for a simple tutorial, go here ). Note that Newton's laws work pretty well for navigating through the solar system. But when you get very close to the Sun, or to other large bodies (such as black holes), all sorts of weird affects reveal themselves.

Einstein showed that Newton's laws were not the correct description of gravity, and they only worked fairly well for (and near) "low mass" objects like planets. Objects of higher masses and densities (stars and remnants of stars) require Einsten's theory of general relativity where the gravitational force is actually due to the curvature of empty space! This is a subject beyond our abilities to discuss in this class, but a site like Wikipedia can supply additional details. It is interesting to note that without taking the effects of general relativity into effect, the GPS system that we use for navigation would not work. To read more about this, go here . Geocentric and Heliocentric Models Nicolaus Copernicus Polish astronomer, mathematician, and canon Modeled the movements of the Sun, the Moon, and the five known planets in the skies above, using a heliocentric system of orbits. Born: 1473 in Torun, Poland Died: 1543 in Frombork, Poland Quotation: Finally we shall place the Sun himself at the center of the Universe.

All this is suggested by the systematic procession of events and the harmony of the whole Universe, if only we face the facts, as they say, `with both eyes open'. The advances in cosmology of the sixteenth century were built upon a strong framework. They combined the mathematical advances of the Greeks with the significant advances in observation and instrumentation of the Islamic world . Al-Haitham (965 – 1040) was born in Basrah, part of present-day Iraq. He promoted the scientific method of inquiry, and developed the field of optics in its infancy. His astronomical work included a strong argument that the Milky Way galaxy extended far beyond the Earth an estimation of the height of the Earth's atmosphere of 32 miles, good to within 5%. In the heliocentric system , the Sun is considered to be the center of the solar system. All of the planets rotate about the Sun. The Moon rotates around the Earth, and thus moves around the Sun with the Earth. An illustrationof the heliocentric model of the solar system, from the Harmonia Macrocosmica star atlas of Dutch-German cartographer Andreas Cellarius, circa 1660.

Tycho Brahe (1546 – 1601) developed a comprehensive method of recording precise observations of the skies, before the advent of the telescope. His many detailed observations included: the discovery of a supernova (a new star, to all appearances, which shone brightly and then faded away) in the heavens, in 1572 measurements of parallax for comets, showing that they were further away than the Moon extensive measurements of the position of Mars in the skies; these data led in time to Kepler's three laws of planetary motion the most detailed measurements of stellar parallax to date, which still showed no effect Tycho proposed an intermediate model of the universe, where the Earth was still the center point, but the other planets were allowed to rotate around the Sun as it rotated around the Earth. This was an intermediate solution, designed to explain the observational evidence that the planets moved around the Sun while preserving the sacrosanct notion that the Earth was the center of the Universe. Copernicus was willing to move one step further away from orthodoxy.

By removing the Earth from its central position he freed the orbital paths of the planets from the extremely convoluted models of the Ptolmeic system, paving the way for Kepler's laws of elegant symmetry. Galileo Galilei (1564 – 1642) was the first to provide strong, compelling evidence in favor of this system. He made a number of observations with the (newly invented) telescope, and discovered: mountains and volcanoes on the Moon sunspots, which moved, on the Sun individual stars within the Milky Way phases for Venus, like those of the Moon moons orbiting Jupiter Geocentric Model [NMSU, N. Vogt] The diagram drawn above shows Venus as it could appear in the heliocentric system and in the geocentric system. The magenta portion of each image of Venus (in positions 1 through 12, forming a circle) represents the side which faces the Sun, while the green line divides the side which faces toward Earth (the side that we see) from the side which is hidden from us.

The row of images across the top of the frames shows Venus as it would appear from Earth if visible (note: in positions 1 and 5 through 9, Venus would be lost in the sunlight if viewed by eye). In the heliocentric system, the twelve positions cover an entire range of the possible locations of Venus around the Sun as viewed from Earth. In the geocentric system, the twelve positions cover an entire range of the possible locations of Venus on its epicyclic path as it travels around the Earth. Under the geocentric model, could Venus ever appear even near to fully illuminated (as a filled magenta circle) to us on Earth? Because this model requires that Venus always lie closer to the Earth than the Sun does (Venus can never pass behind the Sun), Venus can never be illuminated with more than a crescent portion. What Is The Geocentric Model Of The Universe? - Universe Today Universe Today What Is The Geocentric Model Of The Universe? Article Updated: 4 Feb , 2016 by Matt Williams During the many thousand years that human beings have been looking up at the stars, our concept of what the Universe looks like has changed dramatically.

At one time, the magi and sages of the world believed that the Universe consisted of a flat Earth (or a square one, a zigarrut, etc.) surrounded by the Sun, the Moon, and the stars. Over time, ancient astronomers became aware that some stars did not move like the rest, and began to understand that these too were planets. In time, we also began to understand that the Earth was indeed round, and came up with rationalized explanations for the behavior of other celestial bodies. And by classical antiquity, scientists had formulated ideas on how the motion of the planets occurred, and how all the heavenly orbs fit together. This gave rise to the Geocentric model of the universe, a now-defunct model that explained how the Sun, Moon, and firmament circled around our planet. The notion that the Earth was the center of the Universe is certainly an understandable one. To ancient people, looking up at the skies, it seemed evident that the Sun, the Moon and the stars rotated around the Earth once a day. For the Earth-bound observer, the ground that they stood on seemed like a fixed point of reference, a flat plane from which to watch the circling cosmos.

And over time, thanks to centuries of record-keeping by various civilizations – from ancient Babylonian and Egyptian astronomers to contemporary Mediterranean ones – a formalized system began to emerge that put the Earth at the center of all things. This would continue to endure well into the 17th and 18th centuries, by which point, the model’s inherent inconsistencies would lead to it being abandoned in favor of the heliocentric mode l. A comparison of the geocentric and heliocentric models of the universe. Credit: history.ucsb.edu Ancient Greece: The earliest recorded example of a geocentric universe comes from around the 6th century BCE. It was during this time that Pre-Socratic philosopher Anaximander proposed a cosmological system where a cylindrical Earth was held aloft at the center of everything. Meanwhile, the Sun, Moon, and planets were holes in invisible wheels surrounding the Earth, through which humans could see concealed fire. During this same century, the Pythagoreans began to propose that the Earth was circular, based on observation of eclipses (and in all likelihood, observations of the zodiac from different latitudes).

By the 4th century BCE, this idea combined with the concept of a geocentric universe to create the cosmological system that most Greeks subscribed to. It was also during the 4th century BCE that Plato and Aristotle would create works on the geocentric universe that would secure its place as the predominant cosmological theory. According to Plato, the Earth was a sphere and the stationary center of the universe. The stars and planets were carried around the Earth on spheres or circles, arranged in the order of distance from the center. These were the Moon, the Sun, Venus, Mercury, Mars, Jupiter, Saturn, fixed stars, and the fixed stars. His system was expanded by Eudoxus of Cnidus, a contemporary of Plato’s who developed a less mythical, more mathematical explanation of the planets’ motion based on the Platonic idea of uniform circular motion . Aristotle elaborated on Eudoxus’ system, placing a spherical Earth at the center and all other heavenly bodies arranged in concentric crystalline (i.e. transparent) spheres around it. Illustration of Anaximander’s models of the universe. On the left, daytime in summer; on the right, nighttime in winter.

Credit: iep.utm.edu/Dirk L. Couprie These spheres all moved at different uniform speeds to create the rotation of bodies around the Earth and were composed of an incorruptible substance called “aether”. He further described his system by explaining the natural tendencies of the terrestrial elements, which in accordance with contemporary belief were earth, water, fire, air; though Aristotle included a fifth element of “celestial aether”. Earth was the heaviest element, hence why it moved towards the center; whereas water, fire and air formed layers around it. Beyond these layers, the solid spheres of aether in which the celestial bodies were embedded lay. Another important aspect of his model was the inclusion of the “Prime Mover”, a sort of deistic concept whereby all motion in the Universe is initiated by a being or force that is themselves “unmoved”. Support for this cosmological principle was based on a number of accepted theories. For one, if the Earth were to move, scholars believed that there would be an observable change in the positions of the fixed stars and constellations (aka. stellar parallax ). This could be explained by reasoning that they were either motionless, or much further away than believed.

Naturally, they chose to believe the former, as it was the simpler explanation. Another observation that supported geocentric theory was the apparent consistency in Venus’ luminosity, which was interpreted to mean that it was the same distance from Earth at any given time. While this would later come to be explained as the result of Venus’ phases compensating for its increase in apparent size, ancient astronomers lacked the means to see this taking place (i.e. telescopes). The cosmological model of Aristotle, with a spherical Earth at the center surrounded by the Moon, Sun, planets and “fixed stars”. Credit: csep10.phys.utk.edu Ptolemaic Model: This is not to say, however, that the Eudoxian-Artisotelian model was without its share of flaws. For example, the apparent luminosity of Mercury, Mars and Jupiter were subject to change over time. In addition, the passage of Mars and Jupiter through the sky was subject to “ retrograde motion “, a phenomena where they would appear to slow down, move backwards, and then move forwards again through the zodiac.

All of this contradicted the belief in uniform circular motion, which would have meant that there should be changes in apparent luminosity or changes in the apparent motion of the planet’s across the sky. Resolving these issues, and standardizing the many aspects of the Aristotelian system, would become the work of Egyptian-Greek astronomer Claudius Ptolemaeus (aka. Ptolemy). In his treatise Almagest , which was released in the 2nd century CE, Ptolemy unveiled his concept for a geocentric universe, which would remain the accepted view for the next 1500 years. Drawing on centuries of astronomical traditions, ranging from Babylonian to modern times, Ptolemy argued that the Earth was in the center of the universe, the planets and Sun revolved around it, and the stars were all at a modest distance from the center. Each planet in this system is also moved by a system of two spheres – a deferent and an epicycle . The deferent is a circle whose center point is removed from the Earth, which was used to account for the differences in the lengths of the seasons.

The epicycle is embedded in the deferent sphere, acting as a sort of “wheel within a wheel”. The purpose of he epicycle was to account for retrograde motion, where planets in the sky appear to be slowing down, moving backwards, and then moving forward again. Unfortunately, these explanations did not account for all the observed behaviors of the planets. Most noticeably, the size of a planet’s retrograde loop (especially Mars) were sometimes smaller, and larger, than expected. To alleviate the problem, Ptolemy developed the equant – a geometrical tool located near the center of a planet’s orbit that causes it to move at a uniform angular speed. To an observer standing at this point, a planet’s epicycle would always appear to move at uniform speed, whereas it would appear to be moving at non-uniform speed from all other locations.While this system remained the accepted cosmological model within the Roman, Medieval European and Islamic worlds for over a thousand years, it was unwieldy by modern standards. Granted, it did manage to predict planetary motions with a fair degree of accuracy, and was used to prepare astrological and astronomical charts until replaced by the heliocentric model of the Universe.

At the same time, however, every planet in the model required an epicycle revolving on a deferent and offset by an equant, which were also different for each planet. In time, these complexities would come to be challenged. Medieval Geocentrism: During the Middle Ages, the geocentric model gained new power and as it became synthesized with Christian theology to become an essential canon. As part of a general trend whereby classical knowledge was being rediscovered by the 13th century and after, the adoption of the Aristotelian-Ptolemiac model of the Universe was part of a marriage between Faith and Reason champion by scholars like St. Thomas Aquinas. Pages from Sacrobosco’s “Tractatus de Sphaera” (1550), showing the Ptolemaic system. Credit: Wikipedia Commons For starters, the separation of the Universe into the “heavens” and the Earth, with the Earth at the center of creation and the heavens beyond, agreed with the Christian view of mankind being the pinnacle of God’s creation.

Second, the Prime Mover of Aristotle’s cosmos was interpreted as being the God of Christian theology, and the outermost sphere of the Prime Mover was equated with the Christian Heaven. As a result of this, challenging the view that the heavens revolved around the Earth was not merely a scientific matter, but a matter of heresy. Hence why it did not come to be challenged until the 16th century with the publication of Nicolaus Copernicus ‘ De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres), which he only published posthumously to avoid controversy. It is also why support for the heliocentric model of the Universe was also carefully tempered and its adoption gradual. The geocentric view of the Universe was also the accepted cosmological model in the Islamic world during the Middle Ages. However, beginning in the 10th century CE, there were several Muslim astronomers who challenged one of more aspects of Ptolemy’s work. For instance, Iranian astronomer Abu Sa’id al-Sijzi (ca. 945 – ca.

1020) contradicted the Ptolemaic model by asserting that the Earth revolved on its axis, thus explaining the apparent diurnal cycle and the rotation of the stars relative to Earth. In the early 11th century, Egyptian-Arab astronomer Alhazen wrote a critique entitled Doubts on Ptolemy (ca. 1028) in which he criticized many aspects of his model. Around the same time, Iranian philosopher Abu Rayhan Biruni (973 – 1048) discussed the possibility of Earth rotating about its own axis and around the Sun – though he considered this a philosophical issue and not a mathematical one. Illustration from al-Biruni’s astronomical works, explaining the different phases of the moon, and suggestiing that the Earth rotated on its axis. Credit: Public Domain In the 11th and 12th centuries several Andalusian astronomers, centered in the Almohad (Moorish) territory of Spain, challenged the geocentric model of the Universe as well. For instance, 11th century astronomer Abu Ishaq Ibrahim al-Zarqali (aka.

Arzachel) departed from the ancient Greek idea of uniform circular motions by hypothesizing that the planet Mercury moves in an elliptic orbit. In the 12th century, fellow Andalusian Nur ad-Din al-Bitruji (aka. Alpetragius) proposed a planetary model that abandoned the equant, epicycle and eccentric mechanisms. This was followed by Fakhr al-Din al-Razi’s (1149–1209) publication of his treatise Matalib, which dealt with conceptual physics. In it, he rejected the notion of the Earth’s centrality within the universe and instead proposed a cosmology in which there were a “thousand thousand worlds beyond this world…” And at the Maragha Observatory in eastern Iran, the Damascus mosque, and the Ulugh Beg (aka. Samarkand) Observatory in modern-day Kazakhstan, the Earth’s rotation was discussed by several generations of astronomers between the 13th and 15th centuries. Though these were largely philosophical in nature and did not result in the adoption of heliocentrism, many of the arguments and evidence put forward resembled those used later by Copernicus.

The Heliocentric Model: In the 16th century, Nicolaus Copernicus began devising his version of the heliocentric model, which represented the culmination of years worth of research. Like others before him, Copernicus built on the work of a number classical astronomers who did not support the geocentric view, as well as paying homage to the Maragha school and several notable philosophers from the Islamic world. Andreas Cellarius’s illustration of the Copernican system, from the Harmonia Macrocosmica (1708). Credit: Public Domain By 1514 century, Copernicus summarized his ideas in a short treatise titled Commentariolus (“Little Commentary”), which he began circulating to friends. This forty-page manuscript described his ideas about the heliocentric hypothesis, which was based on seven general principles.

These principles stated that: Celestial bodies do not all revolve around a single point The center of Earth is the center of the lunar sphere—the orbit of the moon around Earth All the spheres rotate around the Sun, which is near the center of the Universe The distance between Earth and the Sun is an insignificant fraction of the distance from Earth and Sun to the stars, so parallax is not observed in the stars The stars are immovable – their apparent daily motion is caused by the daily rotation of Earth Earth is moved in a sphere around the Sun, causing the apparent annual migration of the Sun. Earth has more than one motion Earth’s orbital motion around the Sun causes the seeming reverse in direction of the motions of the planets Thereafter he continued gathering data for a more detailed work, and by 1532, he had come close to completing the manuscript of his magnum opus – De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres). In it, he advanced his seven major arguments, but in more detailed form and with detailed computations to back them up. By placing the orbits of Mercury and Venus between the Earth and the Sun, Copernicus was able to account for changes in their appearances.

In short, when they are on the far side of the Sun, relative to Earth, they appear smaller but full. When they are on the same side of the Sun as the Earth, they appear larger and “horned” (crescent-shaped). It also explained the retrograde motion of planets like Mars and Jupiter by showing that Earth astronomers do not have a fixed frame of reference but a moving one. This further explained how Mars and Jupiter could appear significantly larger at certain times than at others. In essence, they are significantly closer to Earth when at opposition than when they are at conjunction. However, due to fears that the publication of his theories would lead to condemnation from the church (as well as, perhaps, worries that his theory presented some scientific flaws) he withheld his research until a year before he died. It was only in 1542, when he was near death, that his treatise was sent to Nuremberg to be published. Thanks to the invention of the telescope, ongoing observations about the motions of the planets, and refined calculations, astronomers would come to understand that the Earth was not immovable.

Nevertheless, for thousands of years, the geocentric model of the universe would remain the accepted cosmological system, and was used to calculate the positions of the planet, eclipses, and other astronomical phenomena. In the end, the geocentric model of the universe succumbed to the same fate as many other accepted notions of its day. Much like the true age of the Earth, humanity’s biological origins, and astrology, the belief that the Earth was the center of the universe did not survive the expansion in learning that was taking place by the 17th century. Astronomy Cast also has an episode on the subject, titled Episode 77: Where Is The Center Of The Universe For more information, check out the NASA Earth Observatory’s page on Planetary Motion , and the Polaris Project’s page on the The Ptolemaic Model . Share this: Astronomy: cosmology, geocentric and heliocentric theories; Astrology: stars and planets from Crossref-it.info Astronomy studies the movement of the planets and stars. Astrology deals with the supposed influence of the stars on human life.

This distinction is a modern one, however: while astrology is regarded as a pseudo-science today, for centuries it was accepted as a way of explaining and predicting terrestrial events. Before the seventeenth century, astronomy and astrology were not usually separated, and observation of the ‘heavenly bodies' was accompanied by ideas about their effects on man and his earthly habitat. Astronomy A universal study All settled civilizations have studied astronomy: Knowledge of the movement of the moon and the sun was vital for a pre-industrial society, as a way of telling the time The codification of such knowledge produced a calendar, by which the best periods for sowing, reaping, herding and other activities could be determined Observation of the stars was also necessary for sea navigation and long land journeys The calculations involved in this study made astronomy a main stimulus for mathematics. Cosmology The accumulated knowledge of the stars gave a cosmology, a picture of the whole universe. Before modern science, cosmology was closely related to theology: as well as describing the physical shape of the universe, a cosmology also explained its meaning, and gave an account of man's nature and purpose. The two central cosmologies in Western history were the geocentric and the heliocentric universe.

Both were based on the basic shape of a wheel revolving around a hub. The geocentric (or Ptolemaic) universe In the geocentric universe the earth (geo) is at the centre, with other planets (the sun being counted as a planet) revolving around it in concentric circles. Looking out from the earth, astronomers noted the Moon, then Mercury, Venus, the Sun, Mars, Jupiter, and Saturn. Beyond these came the stars. These were held to be equidistant from the earth, and were placed on a further circle (hence the ‘Fixed Stars'). This was the conception of the cosmos held by the ancient Greeks, as described by Aristotle (384-322 BC). It is often referred to as the Ptolemaic universe after the Egyptian scientist Ptolemy (c.90-168). This cosmology persisted throughout the Middle Ages and much of the Renaissance, until the new science started to supplant it from about 1600. The influence of the geocentric view Christianity Though the geocentric universe was originally pre- Christian , it was comfortably Christianised.

Aristotle had described a ‘Prime Mover', a force outside the heavens setting them in motion. To Christians, this Prime Mover corresponded to God . They believed that the universe involved human-like intentions: for example, the (presumed) circular orbit of the planets expressed the planets' desire to be close to God. The music of the spheres The planets were believed to revolve on invisible but solid crystalline spheres. Their combined movement made the music of the spheres , which expressed divine harmony. The entire design of the universe was seen to reflect the will of a perfect God. Geocentricity The central position of the earth reflected the idea that the human race were privileged creatures, and the cosmos literally revolved around them. But the geocentric universe also put Earth at the furthest possible distance from Heaven (the ‘empyrean'), which lay beyond the Fixed Stars. Thus it also suited ideas of humility, with humans as fallen sinner s. Dual nature The heavens were held to be perfect and unchanging. Earth, however, was mutable and corrupt. Earthly and heavenly natures were believed to be different, and therefore obeyed two sets of physical laws. Earth corresponded to the body, the heavens to the spirit.

Sublunar / superlunar Beyond the moon (superlunar), the heavens existed in the perfect atmosphere of ‘ether', the natural element of angels . Man occupied the sublunar sphere. Here the atmosphere was polluted, and matter was composed of the four elements (Earth, Air, Fire and Water). Beneath the moon, all things are liable to corruption and decay. Finite The cosmos was seen as vast but finite. Medieval man looking up at the stars imagined he was looking at the outermost edge of the universe. Heliocentric In the heliocentric cosmos, the sun (Greek helios) was believed to be at the centre, and the earth and other planets revolved around it. Copernicus 's On the Revolution of the Heavenly Spheres (1543) showed that apparent aberrations in planetary orbits on the old model could be better explained if the sun were put at the centre. Thus Earth spins around its axis and revolves around the sun, giving the appearance that the sun rises in the east and sets in the west.

Later astronomers continued this work: Kepler (1571-1630) worked out that orbits are elliptical, not circular Using the telescope, Galileo (1564-1642) observed sunspots and irregularities on the moon, showing that the heavens were not perfect. The response to the Heliocentric view Heretical The heliocentric cosmos was a matter of great controvesy. The Roman Catholic Church authorities condemned the theory, forcingd Galileo to recant in 1616, and banning Copernicus' book. The Ptolemaic model had informed Church teachings about God and man, thus the new model presented a challenge to the authority of the Church. Protestant reactions were very mixed; heliocentrism was enthusiastically adopted by some theologians and taught in some Protestant universities. New Science The heliocentric cosmos helped to pave the way for a fresh approach to science, based on mathematics and experiment: Newton (1642-1727) later demonstrated the physical rules underlying the behaviour of all matter.

Although most scientists before the twentieth century could be described as theist s, who believed that God was the reason behind the order observed within scientific laws, the sense that all aspects of cosmology were a reflection of theology was weakened. Increasingly, science studied only material things, while religion dealt with meaning and morality. Culture The heliocentric picture took centuries to be generally absorbed. Writers continued to use ideas and images drawn from the older picture, as is still common today in the words sunrise and sunset. Developments The heliocentric model has itself been altered by modern science, which places the solar system on the edge of the known universe. Newtonian physics has been revised by Einstein. Modern theories of parallel universes inspire science fiction in particular, while the relation of science and religion is frequently discussed. Astrology The influence of the heavenly bodies Astrology describes the influence of the stars on human life. It was generally accepted until about 1600. Because the sun is the source of life, and the moon causes tides, it was felt that other heavenly bodies must also influence the earth. In the absence of modern science, this would help explain human behaviour and terrestrial phenomena, and allow for predictions.

The planets Each planet has an individual influence: Jupiter (Jove) disposes someone to be merry or ‘jovial' Mars and Venus influence man to be warlike ('martial') or loving respectively The influence of Mercury is seen in the term ‘mercurial' (lively and unpredictable) A ‘lunatic' is affected by the lunar cycle of the moon The influence of Saturn is seen in the adjective ‘saturnine' (having a gloomy temprament or appearance) Planets also dominate particular days of the week (Sun-day etc.). Planetary influence is affected by the planets' relation to each other (their constellation or aspect). Though planets could influence human behaviour, they could not determine it since, in Christian thinking, man has free will (see Romanticism: Determinism and free will ). The stars By picturing the geocentric universe as a circle, it can be divided like a cake into twelve equal slices. For about a month (starting on March 21st) each ‘slice' will appear in the east where the sun rises. This segment is said to be ‘in the ascendant'.

Each segment has a distinct grouping of stars, referred to by the signs of the Zodiac : Aries (the Ram), Taurus (Bull) , Gemini (Twins), Cancer (Crab), Leo (Lion), Virgo (Virgin), Libra (Scales), Scorpio (Scorpion), Sagittarius (Archer), Capricorn (Goat), Aquarius (Water-carrier), Pisces (Fishes). The stars in the ascendant were believed to further affect the influence of the planets passing through them. Credibility There were some scholarly attacks on astrology in the sixteenth century, but in general people from all social ranks turned to astrologers to help them make important life decisions. The mathematics behind it seemed dazzling, and there was no alternative explanation of most events. Astrology also provided a satisfying link between the earth and the rest of the universe. Astrology thus formed part of the general way of thinking until it was displaced by modern science from the seventeenth century. In King Lear, Edmund laughs at his father Gloucester for ascribing events to the stars, a sign of a shift in belief at this time.

Language The impact of astrology can be traced in language: influence itself comes from the idea of power flowing in from the planets and stars; dis-aster refers to a ‘bad star' having a malign influence. Together with Plato, he was the leading Greek philosopher, whose works on literature and science have had an enormous influence on Western culture Name originally given to disciples of Jesus by outsiders and gradually adopted by the Early Church. The Bible describes God as the unique supreme being, creator and ruler of the universe. An ancient concept which regarded the orbits of the sun, moon and planets to be working in harmonious patterns. In many religions, the place where God dwells, and to which believers aspire after their death. Sometimes known as Paradise. Someone who disobeys God's will by their actions or failure to act. The Bible regards all human beings as predisposed to sin. Likeliness to change, inconsistence. The transitory nature of earthly life is a frequent theme in Renaissance writing. Supernatural beings closely linked with the work of God; his messengers, traditionally portrayed as having a winged human form.

Nicolaus Copernicus was a mathematician and astronomer who theorised that the sun, rather than the earth, was at the centre of the universe. Galileo Galilei, 1564 – 1642, was an Italian physicist, mathematician, astronomer and philosopher. A worldwide Christian church which traces its origins from Peter, one of the disciples of Jesus. It has a continuous history from earliest Christianity. Its centre is the Vatican Palace, Rome, where the Pope resides. To retract, to take back. Christians whose faith and practice stems from the Reformation movement in the sixteenth century which resulted in new churches being created as an alternative to the Roman Catholic Church. Sir Isaac Newton was an English physicist, mathematician and philosopher, noted for his theories of motion and gravity and scientific developments. A person who believes in the existence of a god who created the universe and continues to interact with it, intervening in certain situations. The Bible describes God as the unique supreme being, creator and ruler of the universe. The study of God.

The term refers to the 12 divisions through which the sun travels over the course of a year and is usually associated with horoscopes, astrology and the 12 signs of the zodiac, although the term was used in astronomy.

Question: The term geocentric places what as central?
Answer: Earth