Within a century of the death of Aristotle, mathematicians were attempting to make geometrical models to account for the actual motions of the heavenly bodies. In so doing they were violating the principle that all motion in the heavens was perfectly circular and centred on the Earth, but ultimately they were partially successful in describing the observed motions. The most successful of these mathematical astronomers was Claudius Ptolemy, who lived and worked in Alexandria in Egypt around 150 AD. In his book The Almagest, he presented a complete system of geometrical constructions which accounted for the motion of each heavenly body, including the retrograde or backwards motion of the planets, by breaking down the complex motions into components with perfectly circular motions. Ptolemy, using the observations of Hipparchos and other Greek astronomers, used a complex system of circles within circles or epicycles, to describe the observed motions. True, he did move the centres of rotation away from the exact centre of the Earth, but his efforts at 'saving the appearances' of perfectly circular motion in the heavens resulted in a masterpiece which became the basis of mathematical astronomy until the seventeenth century and was used by both Copernicus and Kepler in their formulation of the heliocentric theory ( see later ). He also wrote books on sundials, geography and astrology, which he regarded as a physical effect produced by the celestial bodies on humankind, as well as on optics.
Ptolemy's books survived the ravages of the Dark Ages, being rescued from the great library at Alexandria, before it was burned in 415 AD, by scholars who fled to Edessa in southern Turkey. Here a college was established for Syrians and Nestorian ( early ) Christians who translated the Greek texts into Syriac and later Arabic. When these scholars moved to Iran in 489 AD, the knowledge of the ancient world passed for safe-keeping into the Islamic world. In the 9th century, Indian astronomy, with its system of numerals including the figure 0, was introduced into Arabia, from whence they reached Europe in the 12th century as the 'Arabic' numerals we use today. At this time, European scholars began translating Arabic works into Latin and the works of Aristotle and Ptolemy reached the newly-founded universities in Oxford and Paris. By this time, Islamic astronomers had contributed their own observations and had named most of the stars; we still use the Arabic names for the brightest ones. Also by the time the Ptolemaic system became known in Europe, it was apparent that it did not fit with observations of planetary motions to the required degree of accuracy, a fact that Islamic scholars had already noticed and had attempted to correct, without great success.
The trouble with the Ptolemaic system was that although it correctly accounted for the retrograde motions of the planets, at least qualitatively, it was out-of-step with the actual positions of the planets after 1000 years of use. It was a Polish clergyman, Nicholas Copernicus who in 1504 developed the heliocentric or sun-centred model which bears his name. Although not the first to suggest that the planets might revolve around the Sun rather than the Earth, Copernicus was first to formulate a complete cosmology based on this theory. On the surface, it provided a more accurate means of predicting the positions of the planets, hence 'saving the appearances' better than the complex Ptolemaic system, but it also put the planets in their correct order of distance from the Sun, based on their periods and it stated that the sphere of the fixed stars was stationary, rather than spinning around the Earth at some ridiculous speed. The fact that the Earth had to be rotating was not easily accepted by most scholars, as there was no sensible proof of this fact; no sensation of motion is readily apparent, but this is because we are also rotating at the same speed as the surface.( The proof of the Earth's rotation came in 1851 when French physicist Jean Foucault demonstrated that the plane of oscillation of a pendulum changes slowly over a period of 24 hours as the Earth spins beneath it.)
Copernicus saw that there were major problems with the Universe of Ptolemy and Aristotle. Other scholars agreed that the tables of planetary positions and eclipses were increasingly at variance with observations and they began computing corrections to the Ptolemaic tables as well as preparing new ones, such as the eclipse tables of Georg Peuerbach and those of his pupil Johannes Regiomontanus, who pointed out , in 1496, that Ptolemy's system of epicycles would require the Moon's apparent diameter to change by a factor two as it approached and receded from the Earth each month - clearly nonsense. Nicholas of Cusa ( born at Kues, Germany in 1401 ) held the view that the Sun was the centre of the solar system and that other stars also had inhabited worlds revolving around them - an idea that Giordano Bruno, burned at the stake in Rome in 1601, also held to be absolutely true. Copernicus learned of these ideas during his studies at university in Cracow in Poland and at Padua in Italy, where Galileo would later become a teacher. When he returned to Poland in 1505, he set about making observations with which to test his own theory. A small hand-written pamphlet was circulated by Copernicus in 1507 in which he stated, " All heavenly bodies revolve about the Sun which is close to the centre of the world" ( meaning the Universe ). The detailed calculations to support the new theory would follow in his later work, but the seeds of the 'Copernican Revolution' had been sown and they did not fall on deaf ears.
The Copernican Theory was in direct contradiction of the established knowledge about the Universe, handed down through the ages from the Greek philosophers. However, as it was written by a clergyman, with the express intention of providing an alternative 'mechanism' for calculating the motions of the heavens rather than describing how they actually moved, it was acceptable to the Church, which had the ultimate authority in matters to do with Heaven. Although Copernicus himself believed that the planets went round the Sun, it was not necessary that anyone elso should do so to make use of his revised system - it was merely an improved method for calculations. Copernicus still retained the idea of perfect circular orbits however, and for this reason, some of his calculations are actually more involved than those of Ptolemy. It would be nearly seventy years before another significant change would lead to the correct description of the orbits of the planets.
Copernicus died in 1543 but on his death bed he was handed the first printed copy of his book De Revolutionibus Orbium Coelestium ( On the Revolutions of the Celestial Spheres). This book was placed on the Index of banned works by the Inquisition in 1616, by which time its revolutionary ideas had spread throughout Europe. Copernicus awakened astronomy from its dark age. In the years after his death three major figures contributed to the reshaping of the Universe.
Tyge
'Tycho' Brahe (1546-1601) was a Danish nobleman who, from his observatory
on the island of Hven, without the use of a telescope ( not invented until
1608) made very precise measurements of the positions of the 'fixed' stars
and also, the motion of the planets, particularly the planet Mars. He discovered
a new star or supernova in 1572 and a bright comet in 1577, just twelve
months after being given the island of Hven by the Danish King, Frederick
II. Here Tycho built enormous sextants and quadrants for measuring the
positions of the planets with greater accuracy than ever before. He even
calculated the errors associated with each instrument and corrected for
them in all his observations. This recognition of the fact that no measurement,
however carefully made, could ever be perfect was a vital innovation and
it has been appreciated by scientists ever since. However, Tycho was arrogant,
haughty and neglectful of the welfare of his tenants and when King Frederick
died in 1588, his income was cut off. He was forced to leave his observatory
in 1597 for a position in Prague. Here he published his book Instruments
for the Restored
Astronomy and he took an assistant to help
him analyse his data. When Tycho died in 1601 as the result of a drinking
bout, his observations passed to his assistant , Johannes Kepler.
Johannes
Kepler ( 1571-1630) was born in Wurttemberg in SW Germany. He attended
the University of Tubingen where he learned the principles of the Copernican
system. In 1600, when he was forced to leave his post as a mathematics
teacher at Graz in Austria, he took up the position of assistant to Tycho
Brahe in Prague. In 1597 Kepler had published his first important work
The Cosmographic Mystery in which he attempted to explain the distances
of the planets from the Sun, according to the Copernican system, by reference
to the five regular solids. Except for Mercury,
Kepler's construction produced remarkably
accurate results and Tycho was so impressed that he invited this able mathematician
to join him in his attempts to extract the true planetary motions from
his observations. Tycho had devised his own alternative to the Ptolemaic
system; he did not believe in the Copernican theory and, on his deathbed,
he urged Kepler to prepare a new set of tables of planetary motion - the
Rudolphine Tables - which he believed would validate his theory. In 1609,
Kepler published the results of his work on the orbit of Mars under the
appropriate title
The New Astronomy. In this he conclusively
showed not only that Mars orbited the Sun, but also that it did so in an
ellipse; he had tried for several years to fit various combinations of
circular motions to Tycho's data, at one time achieving agreement to within
8 arcminutes ( 1 degree = 60 arcmin) but such was his faith in Tycho's
observations that he refused to believe they could have been in error by
even this much. Kepler also showed that the planets moved faster when nearer
to the Sun and slower when farther away. In 1619, in Harmony of the World
Kepler published his final result relating the periods of the planets in
their orbits to their average distances from the Sun. True, he did wrap
it up in musical terms which today do not have any scientific value, but
it was the final vindication of the Copernican theory that Kepler was able,
from his mathematical relationship, to predict the future positions of
the planets with greater accuracy than had ever been possible using the
Ptolemaic system. In 1627, three years before his death, the Rudolphine
Tables, dedicated to Tycho's patron, the Holy Roman Emperor Rudolph II,
were published in Ulm in Germany.
Galileo
Galilei ( 1564-1642 ) If Kepler was subjected to religious persecution
during his working life, then Religion had an even greater impact on the
life of Galileo, who tried to overturn 1000 years of dogma almost overnight
with his telescopic observations of the Heavens.
Only in 1992 did the Roman Catholic Church
admit that their treatment of the famous scientist had been erroneous.
Born in Pisa in 1564, Galileo was eight years
older than Kepler. Son of the composer and musicologist Vincenzo Galilei,
who was himself no stranger to controversy and innovative change, Galileo
could as easily have become an artist or a musician, as did his brother
Michelangelo. Just as his father saw that rigid theory stifled new forms
in music, so Galileo came to see Aristotelian physical theology as an obstacle
to scientific inquiry. Vincenzo was a member of a Florentine family, prominent
in medicine and public affairs. When the family moved to Florence, Galileo
was sent to the Jesuit monastery school at Vallombrosa, 20 km away. When
in 1578, at the age of fourteen, Galileo became a Jesuit novice, his father
promptly removed him and, three years later, he was enrolled as a medical
student at Pisa university.
Galileo was more interested in mathematics than medicine; he discovered the isochronous swing of a pendulum by observing the swings of a chandelier during Church services, using his pulse to time the period of the swing. He left Pisa without a degree in 1585 and tutored privately whilst engaged in the study of mathematics, mechanics and hydrostatics.
In 1588 he gave a mathematical lecture to the
Florentine Academy on the geography of Dante's Inferno which earned him
considerable praise and the support of Guidobaldo del Monte, through whose
influence he obtained the Chair of mathematics at Pisa. He was 35 years
of age.
Galileo became increasingly critical of Aristotle's
teaching about motion. He wrote a short article in which he demolished
Aristotle's distinction between 'forced' and 'natural' motion. According
to classical theories, a force was always necessary to generate 'forced'
motion, the velocity being proportional to this force, whereas 'natural'
motion resulted when an object fell to the ground because of its 'gravity'
or rose like smoke due to its 'levity'. This caused great difficulties
when it came to explaining the motion of projectiles for example and Galileo
recognised that an altogether different way of tackling the problem was
needed - mathematics.
While at Pisa, he is said to have dropped different weights from the leaning tower. He proved that, contrary to Aristotelian theory, however light or heavy, the weights took equal times to fall the same distance. ( The effects of air-resistance make this experiment difficult to do in practice.) He also discussed the motion of balls rolling down inclined planes and came very close to deducing what was later known as Newton's First Law of Motion - that a body will remain either at rest, or in a state of uniform motion in a straight line unless it is acted upon by a resultant external force, in which case it will accelerate. (This means that in a vacuum, a body subjected to a constant force will accelerate indefinitely, ultimately achieving an infinitely high velocity. This was taken to be absurd by Aristotle, who therefore believed that it was impossible to have such a thing as a vacuum. It does lead to another important realisation, by Albert Einstein in the Twentieth Century, that the maximum speed attainable by any massive body is that of the Speed of Light - but that's another story.)
Galileo broke with tradition in that he used mathematics to analyse his experimental results. He abandoned vague speculative theorising in favour of precise physical measurements, which could be confirmed by repetition. This became the hallmark of the new physics which developed in the 17th and 18th centuries and which remains the basis of the scientific method of today. For this reason, Galileo is justly called the Father of Mathematical Physics. Following the death of his father in 1591, Galileo's contract at Pisa was not renewed, probably because of his continued contradiction of his fellow Aristotelian professors, and he sought a new appointment which would enable him to support his family. With Guidobaldo's help, he obtained the chair of mathematics at Padua where Copernicus had studied in 1501. Galileo found the atmosphere here more to his liking; there was freedom of academic thought because the university came under the jurisdiction of the powerful Venetian government, which brooked no external interference in its affairs.
At Padua Galileo lectured and did research on motion, explaining the parabolic path of projectiles in terms which were more acceptable than the straight lines demanded by Aristotle. He manufactured a calculating device which he called a Geometrical and Military Compass, with an eye to selling it to supplement his income. At this time he showed little interest in astronomy, but as his letter to Kepler reveals, he preferred the Copernican theory, mainly because it supported his own theories on the origin of the tides, which he ( erroneously ) supposed to be due to the motion of the earth.
In the Spring of 1609, Galileo heard a report concerning a new kind of optical instrument which had been invented in the Netherlands. It is not certain who deserves the credit for producing the first telescope, the name was coined in Italy in 1611, but a spectacle maker from Middelburg by the name of Hans Lipperhey applied for a patent for an optical device for seeing at a distance in September of 1608. Galileo used his own knowledge of optics ( or 'perspective' as he called it ) to design a similar instrument of his own. His first telescope was constructed in a day and had a magnifying power of three. He continued to make improvements by grinding his own lenses and eventually produced one with a power of 33 and a diameter of 4.4 cm.
Galileo was not the only astronomer to turn this new invention towards the heavens; by April 1609 similar instruments could be purchased on the streets of Paris and, later that year appeared in Germany, various Italian cities and in London. The English astronomer Thomas Harriot used a 6-power instrument to observe the Moon in August 1609, but he did not publish his results. The reason that Galileo is usually associated with the first astronomical use of the telescope is that he published his findings within a few short months of his first observations and the effect it had was enormous.
In Sidereus Nuncius, the Starry Messenger, published in March 1610, Galileo revealed that the Moon had a rough, irregular surface featuring mountains whose heights he estimated from the lengths of their shadows, he saw that the Milky Way was composed of myriads of individial stars, too faint to be seen by the naked eye, and, most important of all, that Jupiter was attended by four bright stars, which followed the planet as it moved, and which themselves revolved around Jupiter as the centre of their motion. Always with a view to enhancing his own position, Galileo had presented an eight-powered telescope to the Doge of Venice in August 1609. On discovering the satellites ( a word coined by Kepler ) of Jupiter on 7th January 1610, he named them the Medicean Stars, in honour of the Grand Duke of Tuscany, Cosimo de Medici. This was an astute move, because he was soon to become "first philosopher and mathematician" to this powerful young man. Although the Venetian senate had granted him a lifetime appointment as professor at Padua because of his findings with the telescope, Galileo's social climbing caused him to leave the university in the summer of 1610 to take up this new position which would allow him more time for his researches. It would also lead him into direct conflict with the Holy Roman Inquisition.
The Sidereal Messenger drew the attention of
the western world to what the telescope could do. In his book Galileo explained
how he had observed many more stars than could be seen with the unaided
eye - more than were seen by the ancient astronomers. This argued eloquently
against the presumed perfection of ancient science, so dear to his Aristotelian
antagonists. Later in 1610, Galileo observed the phases of Venus, hitherto
unpredicted by the Ptolemaic theory, although not prohibited by Tycho's
arrangement of it, a fact that Galileo overlooked, to his eventual cost.
He reported the 'triple' nature of the planet Saturn, whose rings remained
unresolved by his crude instrument. It was to continue to puzzle him for
many years. Sometime between 1610 and 1611 he also observed sunspots, although
it was one of his former students, Benedetto Castelli, who devised a safer
way of observing the Sun's disk by projecting its image on to paper. This
discovery also led to an acrimonious dispute with the Jesuit astronomer
Christoph Scheiner who claimed to have discovered them before Galileo.
The manner in which Galileo dismissed both his claim and his explanation
of the effect did much to earn him Scheiner's unmitigated hatred - this
may also have contributed to Galileo's eventual treatment by the Inquisition.