Tag Archives: Aristarchus

The Astronomical Renaissance

by Tim Harding BSc BA

(An edited version of this essay was published in The Skeptic magazine, March 2015, Vol 35 No 1, under the title ‘Rebirth of the Universe’.  The essay is based on a talk presented to the Mordi Skeptics, Tuesday 11 November 2014).

This article follows on from my previous one on ancient astronomy and astrology (‘An Eye to the Sky’, The Skeptic, Vol. 33, No. 4, December 2013).  That story began about 4000 years ago in Babylon, then moved to the first scientific revolution in ancient Greece, ending with Ptolemy’s complicated geocentric (Earth-centred) model of the cosmos in the 2nd century CE.

We now make a great leap forward to the second scientific revolution beginning with the publication of Nicolaus Copernicus’ heliocentric (Sun-centred) model of the cosmos in 1543 CE.  Why the huge gap?  Because astonishingly, nothing much happened in cosmology for about 1400 years between Ptolemy and Copernicus.  (The reasons for this are complex and best left to a possible future article).

After the Fall of Constantinople in 1453 CE, there was a rediscovery of ancient Greek texts written by philosophers and scientists such as Plato, Aristotle, Aristarchus, Archimedes and Ptolemy.  That is why this subsequent period is described as an astronomical renaissance (alongside the cultural renaissance), from the French word meaning ‘re-birth’.  The midwives of this re-birth were the development of scientific methods and the invention of printing, which would improve access to learning, allowing a faster propagation of new ideas.

Copernicus’s astronomical observations were complemented and improved in accuracy by those of Tycho Brahe.  His heliocentric model was later adopted by Galileo Galilei and then refined by Johannes Kepler.

Nicholas Copernicus (1473- 1573 CE)

Copernicus was born 1473 in the Polish city of Torun.  His father was copper merchant – the name ‘Copernicus’ is thought to be derived from this occupation.  He studied mathematics, philosophy and astronomy at the University of Krakow; then medicine at Padua in Italy.  He was also a lawyer, physician, classics scholar, translator and economist.

copernicusatwork2 crop

Nicolaus Copernicus

As well as being a polymath, Copernicus was also a polyglot, which gave him access to the ancient Greek texts.  From these writings he would most likely have known that Aristarchus of Samos had some 1800 years earlier proposed a heliocentric model of the cosmos in the third century BCE.  Aristarchus had also calculated the diameters of the Sun and Moon, as well as their distances from the Earth in Earth radii.  This regression from the correct heliocentric to the incorrect geocentric model presents a serious challenge to our notions of inevitable human progress.

In around 1510, Copernicus moved to one of the defensive towers of the cathedral town of Frombork on the Baltic Sea coast, where he did most of his astronomical observations and writing.  His attempts at retrofitting cosmological theory to seemingly endless observational anomalies eventually became just too complex.  Simplification became a major motivation for Copernicus to construct his revolutionary heliocentric model.  His colleague Andreas Osiander, a Lutheran theologian, wrote an anonymous preface to Copernicus’ published major work De Revolutionibus.  This preface stated that Copernicus’ system was merely mathematics intended to aid computation and not an attempt to declare literal truth.  Both Copernicus and Osiander probably feared the reaction not only of other astronomers but also the Roman Church – a fear that was later justified by the trial of Galileo, of which more will be said later.  The delay in publication until the eve of Copernicus’ death is thought to be due to these fears.

Thirty years earlier in about 1514, Copernicus had written the Commentariolus – an unpublished outline of his later De Revolutionibus. In this outline, he proposed seven axioms, all of which are true:

  1. Heavenly bodies do not all move around same centre.
  2. The Earth is not centre of the cosmos – only the Moon’s orbit.
  3. The Sun is the centre of the planetary system.
  4. The Stars are much further away than the Sun.
  5. The apparent daily revolution of the stars and planets is due to the Earth’s rotation on its own axis.
  6. The apparent annual motion of the Sun is due to the revolution of Earth around the Sun.
  7. The apparent retrograde motion of the planets has same cause.

Copernicus’ heliocentric model of the cosmos

However, Copernicus clung to the erroneous theological belief that all the orbits of celestial bodies must be perfect circles.  This forced Copernicus to retain Ptolemy’s complex system of planetary epicycles, thus leading him astray.  At first, Copernicus initially proposed that only 34 epicycles were needed in his model, but he was later forced to modify the model by increasing this number to 48 – eight more cycles than the 40 in Ptolemy’s model.  These anomalies led Kepler to subsequently propose elliptical rather than circular planetary orbits, as will be discussed later.

Copernicus also modified his model to account for the apparent absence of stellar parallax during the Earth’s orbit around the Sun.  He did this by postulating that the distance of the fixed stars was so immense compared to the diameter of the earth’s orbit that stellar parallax was unnoticeable by the accuracy of astronomical observations at that time.  This modification subsequently turned out to be correct in reality, but at the time it was an ad hoc modification made for the purpose of correcting an imagined observational anomaly.

Tycho Brahe (1546 – 1601 CE)

Tycho Brahe was a colourful character, born 1546 into an aristocratic family in Scania which was then part of Denmark but is now in Sweden. He studied law and astronomy at University of Copenhagen.  He is notorious for losing part of his nose in sword fight, so he had to wear a brass prosthetic nose.  Another piece of irrelevant trivia is that Tycho had a pet Elk that once drank too much beer at one of his friends’ dinner parties.  Sadly, the inebriated Elk fell down some stairs and died.

Tycho’s observatory on the island of Hven in Sweden

Tycho’s observatory on the island of Hven in Sweden

In 1597, Tycho fell out with Danish King Christian IV and became court astronomer to Holy Roman Emperor Rudolph II in Prague, who funded the building of a state-of-the-art new observatory for Tycho.  Johannes Kepler was employed as Tycho’s assistant, who later used Tycho’s more accurate observational data for his own astronomical calculations.  These more precise measurements clearly showed that the stars lacked parallax, thus confirming that either the Earth was stationary or the stars were a vast distance from the Earth.

Tycho proposed a hybrid ‘geo-heliocentric’ system in which the Sun and Moon orbited the Earth, while the other planets orbited the Sun (known as the Tychonic system). This system provided a safe position for astronomers who were dissatisfied with the Ptolemaic model but were reluctant to endorse the Copernican model.  The Tychonic system became more popular after 1615 when Rome decided officially that the heliocentric model was contrary to both philosophy and scripture, and could be discussed only as a computational convenience that had no connection to the truth.

Galileo Galilei (1564- 1642 CE)

Galileo Galilei was a physicist, mathematician, engineer, astronomer, and philosopher who arguably contributed more than anybody to both the second scientific revolution and the astronomical renaissance.  He was born 1564 in Pisa, Italy, and educated in the Camaldolese Monastery at Vallombrosa, 35 km southeast of Florence.  He enrolled at the University of Pisa for a medical degree, but switched to mathematics and natural philosophy.

Galileo Galilei

Galileo Galilei

Galileo’s contributions to observational astronomy include the telescopic confirmation of the phases of Venus, the discovery of the four largest satellites of Jupiter (named the Galilean moons in his honour), the roughness of the Moon’s surface, and the observation and analysis of sunspots. He also made contributions to physics, including the science of dynamics, leading to Newton’s laws of motion later on.

He championed Copernicus’ heliocentrism when it was still controversial – most astronomers at this time subscribed to either geocentrism or the Tychonic system.  They doubted heliocentrism due to the absence of an observed stellar parallax, without appreciating the enormous distances involved.

When confronted with this absence of stellar parallax, Galileo attempted an ad hoc modification to the Copernican model by incorrectly claiming that the tides are caused by the earth’s rotation combined with its orbit around the Sun.  This is despite the ancient Greek philosopher Seleucus some 1600 years earlier having correctly theorized that tides were caused by the gravitational effect of the Moon’s orbit around the Earth.  .

Galileo showing his telescope to the Doge of Venice

Galileo showing his telescope to the Doge of Venice

After the Roman Inquisition of 1615, works advocating the Copernican system were placed on the index of banned books and Galileo was forbidden from advocating heliocentrism.  This resulted in heated correspondence between Galileo and the Vatican.  Unfortunately, Galileo’s aggressive manner alienated not only the Pope but also the Jesuits, both of whom had tolerated him up until this point. He was tried by the Holy Office and found ‘vehemently suspect of heresy’, then forced to recant, and spent the rest of his life under house arrest.

At least Galileo did not suffer the cruel fate of the philosopher and cosmologist Giordano Bruno, who in 1600 was burned at the stake for heresy in Rome’s Campo de’ Fiori (a market square where there is now a statue of him).  Bruno had gone even further than the Copernican model, correctly proposing that the stars were just distant suns surrounded by their own exoplanets.  He suggested the possibility that these planets could even foster life of their own (a philosophical position known as cosmic pluralism).  Bruno also believed that the Universe is in fact infinite, thus having no celestial body at its ‘center’.

Johannes Kepler (1571- 1630 CE)

Johannes Kepler was a German mathematician, astronomer and astrologer (before these areas of study separated). A key figure in the second scientific revolution, he is best known for his three laws of planetary motion, which endure today. These laws also provided one of the foundations for Isaac Newton’s theory of universal gravitation.

Kepler was born in 1571 in Stuttgart area of Germany. At age six, he observed the Great Comet of 1577, and at age nine, the lunar eclipse of 1580.  These events inspired him to study philosophy, theology mathematics and astronomy at the University of Tübingen.  Here he learned both the Ptolemaic system and the Copernican system of planetary motion.  He later observed a bright supernova (exploding star) of 1604, which became known as Kepler’s Supernova.

After graduation, Kepler became a mathematics teacher at a seminary school in Graz, Austria. Later he became an assistant to astronomer Tycho Brahe, and eventually the imperial mathematician to Emperor Rudolf II and his two successors Matthias and Ferdinand II. He was also a mathematics teacher in Linz, Austria, and an adviser to General Wallenstein. Additionally, he did fundamental work in the field of optics, invented an improved version of the refracting telescope (the Keplerian Telescope).

Frontispiece to the Rudolphine Tables (Latin: Tabulae Rudolphinae) consisting of a star catalogue and planetary tables published by Johannes Kepler in 1627, using some observational data collected by Tycho Brahe

Frontispiece to the Rudolphine Tables consisting of a star catalogue and planetary tables published by Johannes Kepler in 1627, using observational data collected by Tycho Brahe

Kepler then set about calculating the entire orbit of Mars, using the geometrical rate law and assuming an egg-shaped ovoid orbit. After many failed attempts, in early 1605 he at last hit upon the idea of an ellipse, which he had previously assumed to be too simple a solution for earlier astronomers to have overlooked. Finding that an elliptical orbit fitted the Mars data, he immediately concluded that all planets move in ellipses, with the sun at one focus — which became Kepler’s first law of planetary motion.

He then formulated two more laws of planetary motion.  These are firstly, that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time; and secondly, that the square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.

Because of his religious beliefs, Kepler became convinced that God had created the universe according to perfectly harmonious geometrical shapes and patterns. He began by exploring regular polygons and regular solids, including the figures that would come to be known as Kepler’s solids.  Unfortunately, Kepler wasted a lot of his time fruitlessly searching for this underlying ‘harmony of the spheres’, drawing all sorts of weird and wonderful diagrams.  He even (unsuccessfully) tried to relate these geometric shapes to musical harmonies.

Keplers solids

Kepler’s solids

Concluding remarks

The great physicist Isaac Newton was later able to build upon the pioneering work of Galileo and Kepler, leading him to make his famous quotation ‘If I have seen further it is only by standing on the shoulders of giants’.

In contrast, it is perplexing to observe two great human failures. Firstly, how science was repeatedly led astray by fruitless searches for perfection in ‘God’s design of the cosmos’.  Secondly, that astronomical knowledge not only progressed very little during the 1400 years between Ptolemy and Copernicus, but in some areas it actually regressed.  The ancient Greeks had not only proposed a heliocentric model of the cosmos, but they had also calculated the diameters of the Sun and Moon, as well as their distances from the Earth.  They also knew that the tides were caused the gravitational effect of the Moon’s orbit around the Earth.  This valuable knowledge was either forgotten or rejected until the astronomical renaissance some 1800 years later. So much for the notion of inevitable human progress.


Koestler, A (1959) The Sleepwalkers. London: Hutchinson.

Kuhn, T.S. (1962) The Structure of Scientific Revolutions 3rd ed. Chicago: University of Chicago Press.

Toulmin, S. and Goodfield, J. (1961) The Fabric of the Heavens.  London: Hutchinson.

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Ancient astronomy and astrology

by Tim Harding

(An edited version of this essay was published in The Skeptic magazine, December 2013, Vol 33 No 4. The essay is based on a talk presented to the Mordi Skeptics in October 2013).

Today, there are distinct boundaries between the modern science of astronomy and the pseudoscience known as astrology.  But in ancient times, these boundaries were not so clear.  Both fields of study used a common set of astronomical observations – but for different purposes.  The practical purposes of ancient astronomy were celestial navigation and the development of calendars of seasonal dates and events (such as the flooding of rivers) for the planting of crops.  In contrast, the purpose of astrology was to interpret celestial phenomena as signs of divine communications.

Long before the invention of the telescope, ancient observations and predictions could only be of celestial objects visible to the naked eye.  This restricted astronomical and astrological studies to the stars, the Sun, the Moon and five planets – Mercury, Venus, Mars, Jupiter and Saturn.  (The Earth was not counted as a planet until much later).

Prehistoric stone observatories

In some locations, early cultures assembled stone structures that are thought to have astronomical observations as one of their purposes.  The most well-known of these structures is Stonehenge in Wiltshire, England, which commenced construction around 3100BCE and went through several building phases.  As there are no written records to go by, there are several theories as to various religious, mystical and other purposes of Stonehenge.  One of these theories has been proposed by well-known Victorian skeptic Dr. Lynne Kelly. Lynne’s PhD thesis was about the use of structures like Stonehenge as mnemonic aids, to ensure that the oral knowledge of the culture is retained and passed on to succeeding generations. The layout of Stonehenge also includes a celestial observatory function, which would have allowed the prediction of eclipse, solstice, equinox and other celestial events important to a contemporary religion.


Drawing of Stonehenge in midsummer (Source: Wikimedia Commons)

One of the world’s earliest known archeo-astronomical devices is a stone circle at Nabta Playa, in southern Egypt on the Tropic of Capricorn.  The site is between 6,000 and 6,500 years old, or about 1,000 years older than Stonehenge.  Two pairs of upright stones stand directly across the circle from each other, defining a view that would have marked sunrise at the summer solstice, this providing the beginnings of a prehistoric calendar.

Early Egyptian astronomy and astrology

The Ancient Egyptian calendar year was 365 days long, divided into 12 months of 30 days each, plus five extra days at the end of the year.  This was one quarter of a day shorter than solar year, leading to the problem of a ‘wandering year’ requiring frequent astronomical correction.  Observation of stars was important in predicting the annual flooding of the Nile, for the allocation of resources to the planting of irrigated crops. Early Egyptian astronomy was intertwined with astrology.  The Sun was believed to be a major god named Ra, representing light, warmth, and growth.  Ra was thought to travel on two solar boats – one on his journey through the sky during the day and the other in a river flowing underneath the flat Earth from west to east at night.


Ra, the Egyptian sun god (Source: Wikimedia Commons)

Most Egyptologists believe that the Great Pyramid of Giza was built as a tomb for fourth dynasty Egyptian Pharaoh Khufu (Cheops in Greek) over a 10 to 20-year period concluding around 2560 BCE, although other dates have been suggested.  One theory is that this pyramid was carefully aligned towards the northern pole star, which at the time was Thuban, but is now Polaris due precession of the Earth’s rotational axis.

Ancient Mesopotamia

The ancient region known as Mesopotamia comprised the plains of the Tigris and Euphrates rivers, in what is now Iraq, plus parts of Syria, Turkey and Iran.  The lower part between the rivers was known as Sumer, with Babylon, Uruk and Ur as its major cities.  The significance of this region is that it was the cradle of astronomy and astrology as organised fields of study.


The ancient region known as Mesopotamia (in light shading) Source: Wikimedia Commons

Sumer was also the birthplace of writing, in the form of cuneiform clay tablets dating from the mid 4th millennium BCE.  These tablets provide us with the first written evidence of astronomy and astrology in the West, albeit in a fragmentary state. From these tablets we know that the Babylonians developed a sexagesimal (base 60) numerical system, resulting in our current 60 minute hour, 24 hour day and 360 degree circle.  The Babylonians were the first to recognize that astronomical phenomena are periodic and to apply mathematics to their predictions.  They developed the idea of a 7 day week and a 12-month calendar based on cycles of the Moon; together with the seasons of summer and winter.  The Babylonians also measured the variation in day length over a year. At around 1800BCE, the first star catalogues were compiled.

The Babylonian astronomers noticed that a few ‘stars’ (later called planets) wandered in relation to other fixed stars and even retrograded in their motions.  These movements were confined to a narrow belt at an angle of about 23 degrees to the equator.  This belt – the Zodiac – was divided into 12 sections, and each section was named after a constellation of fixed stars in the neighbourhood.  The Zodiac also became one of the important features of western astrology. In this early period astronomy consisted of observations, calculations and predictions of events such as solstices and eclipses.  As such, astronomy at this stage was like a branch of applied mathematics plus a database of observations.  There were no cosmological theories to tie all the observations and calculations together and to try and rationally explain them.  This explanation vacuum was instead filled by astrology, which claimed to interpret celestial events as religious or mystical omens.

The Enuma Anu Enlil (c.1600BCE) is a major series of 68 or 70 tablets dealing with Babylonian astrology.  Substantial collection of omens, estimated to number between 6500 and 7000, interpret a wide variety of celestial and atmospheric phenomena in terms relevant to the king and state (known as ‘mundane astrology’).  For example, a typical astrological report to the king reads:

‘If the moon becomes visible on the first day: reliable speech; the land will be happy. If the day reaches its normal length: a reign of long days. If the moon at its appearance wears a crown: the king will reach the highest rank.’

Movements of the Sun, Moon and five planets were regarded as representing the activity of the gods in question.  Evil celestial omens attached to any particular planet were therefore seen as indications of dissatisfaction or disturbance of the god that planet represented. The Venus tablet of Ammisaduqa (Enuma Anu Enlil Tablet 63) refers to the record of astronomical observations of Venus, as preserved in numerous cuneiform tablets dating from the first millennium BCE.

Venus Tablet of Ammisaduqa

Venus tablet

Source: Wikimedia commons

During the 8th and 7th centuries BCE, Babylonian astronomers developed a new theoretical approach to astronomy.  They began to develop an internal logic within their observational data systems to improve their predictive power.  This was an important contribution towards the development of astronomy from a database to a science.  Some scholars have thus referred to this new approach as the first scientific revolution. The new scientific approach to astronomy was adopted and further developed in Greek astronomy.  This process was considerably helped by the conquest of Babylon by Alexander the Great in 331 BCE.  According to the late classical philosopher Simplicius of Cilicia (c.490CE – c.560CE), Alexander ordered the translation of the Babylonian historical astronomical records under supervision of his chronicler Callisthenes of Olynthus, who sent them to his uncle Aristotle in Athens.  Aristotle was also the teacher of Alexander until the age of 16 – what a small world!

Ancient Greece

The name ‘planet’ comes from the Greek term planētēs, meaning ‘wanderer’.  The names of individual planets (within our solar system) are all drawn from Greek mythology, although they have Romanised names outside of Greece. References to identifiable stars and constellations appear in the writings of Homer and Hesiod, in the 7th or 8th centuries BCE.  However, the first Greek attempts to rationally explain the structure and behaviour of the cosmos date from the period 600-450BCE.  The anomalies in the motions of the planets bothered the early Greeks, who were culturally inclined to try to find rational physical explanations for them.

Pythagoras of Samos (c. 570 BCE – c. 495 BCE) was an Ionian Greek philosopher and mathematician who founded a philosophical movement known as the Pythagoreans.  Amongst other things, Pythagoras was the first to think that the Earth was spherical rather than flat; and that the Morning Star and the Evening Star are identical (they are both the planet Venus). Astronomy was listed by the Pythagoreans among the four mathematical arts (along with arithmetic, geometry, and music). One of these Pythagoreans was Anaxagoras (c. 510 – 428 BCE), who discovered that the Moon shines by reflected light from the Sun and gave the correct theory of lunar eclipses (i.e. the Earth is blocking the light from the Sun to the Moon). These eclipses provided the conclusive arguments in favour of the Earth being spherical.  The Pythagoreans also regarded the Earth as one of the planets.

Herakleides of Pontus was a Pythagorean who lived in the 4th century BCE and studied under Plato.  Herakleides discovered that Venus and Mercury revolve around the Sun. He also held that the Earth rotated on its own axis every 24 hours, which accounted for the apparent procession of the stars across the night sky, but did not explain the retrograde motion of the planets.  By now, these anomalous planetary motions had become the central problem of astronomy and cosmology. Plato encouraged Eudoxus of Cnidus (c. 410 BCE – c. 347 BCE) to develop a two-sphere model with the Earth at the centre, and the planets occupying a separate sphere to the stars, similar to that shown by the following diagram. two sphere model

Source: Wikimedia Commons

Aristarchus of Samos (310 BCE – ca. 230 BCE) has been called ‘the Greek Copernicus’ because he proposed a heliocentric model of the cosmos, with the Sun at the centre instead of the Earth, about 1800 years before Copernicus did.  Aristarchus also calculated the sizes of the Sun and Moon, as well as their distances from the Earth in Earth radii.   Aristarchus’s working drawings of the relative sizes of the Sun, Earth and the Moon are shown below. Aristarchus drawing

Source: Wikipedia Commons

The radius and circumference of the Earth were first calculated (but slightly underestimated) by Eratosthenes of Cyrene – c.276-c.194 BCE.  He was a mathematician, poet, music theorist and inventor of the  discipline of geography, including the terminology used today.  Unfortunately, Aristarchus was unable to persuade his contemporary colleagues of the merits of his theory, which was largely forgotten until rediscovered by Copernicus in the 16th century CE.  Seleucus of Seleucia (b.190BCE) was the only Greek Babylonian philosopher to support heliocentric model of planetary motion. He also correctly theorized that tides were caused by the Moon, a theory that was overlooked by Galileo 1700 years later.

Hipparchos of Nicaea (c. 190 BCE – c. 120 BCE) was a Greek astronomer, geographer, and mathematician of the Hellenistic period.  He is considered the founder of trigonometry but is most famous for his incidental discovery of precession of the equinoxes.  He compiled a star catalogue recording the position and brightness of the stars, which was used by astronomers for centuries afterwards. As a result of the non-acceptance of Aristarchus’s heliocentric model, subsequent Greek astronomers persisted with trying to reconcile the anomalous movements of the planets with a geocentric model of the cosmos.

Apollonius of Perga (c. 262 BCE–c. 190 BCE) introduced two new mechanisms: the eccentric deferent and the epicycle, which are illustrated in the diagram below. Claudius Ptolemy of Alexandria (c. 90CE – c. 168CE) was a Greco-Roman mathematician, also known as an astronomer, geographer and astrologer.  Ptolemy explained how to predict the behavior of the planets by introducing the equant. Below is a simple illustration showing the basic elements of Ptolemaic cosmology.  It shows a planet rotating on an epicycle which is itself rotating around a deferent inside a crystalline sphere. The center of the system is marked with an X, and the earth is slightly off of the center.  Opposite the earth is the equant point, which is what the planetary deferent would actually rotate around.

Ptolemy model

Illustration showing the basic elements of Ptolemaic cosmology (Source: Wikimedia Commons)

Ultimately, these attempts at retrofitting cosmological theory to seemingly endless observational anomalies became too much.  Dislike of the equant, on top of the deferent and the epicycle, was a major motivation for Copernicus to construct his heliocentric system after the scientific renaissance some 1500 years later. Although astrology was not as popular in ancient Greece as it was in Egypt and Mesopotamia, belief in astrology continued through the Roman period and the Middle Ages.  Through most of its history, astrology was considered a scholarly tradition. It was accepted in political and academic contexts, and was connected with other studies, such as astronomy, alchemy, meteorology, and medicine.  At the end of the 17th century, new scientific concepts in astronomy and physics (such as heliocentrism and Newtonian mechanics) called astrology into question.[1] Astrology thus lost its academic and theoretical standing, and common belief in astrology has since largely declined.


Brown, D (2000) Mesopotamian Planetary Astronomy-Astrology Bandhagen: Styx Publications.

Evans, James (1998). The History and Practice of Ancient Astronomy. Oxford: Oxford University Press.

Hermann Hunger, ed. (1992). Astrological reports to Assyrian kings. State Archives of Assyria 8. Helsinki: Helsinki University Press

Koestler, A (1959) The Sleepwalkers (Danube Edition 1968) London: Hutchinson.

Kuhn, T.S. (1962) The Structure of Scientific Revolutions (3rd ed. 1996) Chicago: University of Chicago Press.

Leverington, D. (2003). Babylon to Voyager and beyond: a history of planetary astronomy. Cambridge: Cambridge University Press.

Russell, B. (1946) History of Western Philosophy (2nd edition 1961). London: George Allen & Unwin.

Toulmin, S. and Goodfield, J. (1961) The Fabric of the Heavens: The Development of Astronomy and Dynamics Chicago: University of Chicago Press.

Wightman, W.P.D. (1951, 1953) The Growth of Scientific Ideas, Yale University Press.

Endnotes [1] Rational arguments that the claims of astrology are false include firstly, because they are incompatible with science; secondly, because there is no credible causal mechanism by which they could possibly be true; thirdly, because there is no empirical evidence that they are true despite objective testing; and fourthly, because the star signs used by astrologers are all out of kilter with the times of the year and have been so for the last two or three thousand years.

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