B00B7H7M2E EBOK (13 page)

Kepler’s second law, then, accounted for the way a planet varies in speed and made it possible to predict those variations. While one can’t make sense of the system by saying ‘this planet always travels thus-and-so-many miles per hour’, one
can
make sense of it by saying ‘this planet’s imaginary line to the Sun always sweeps out an area of thus-and-so-many square miles per hour’. This was another of Kepler’s crazy ideas, a ‘connection’ he found between astronomy and geometry, arising from his belief in the intrinsic harmony of a universe created by God. We still today think he got this one right.

Kepler’s
Astronomia Nova
contained more than these two laws. He was well on track towards our modern understanding of gravity, previewing Newton’s later discoveries about the tides and understanding them a great deal better than Galileo did. Kepler had discerned that the more massive a body, the
stronger
its attractive effect. He also wrote that it couldn’t be the Sun’s light that provided the ‘whirling force’, for the Earth didn’t screech to a halt during a solar eclipse.

Kepler finished
Astronomia Nova
in 1606 but didn’t publish it until 1609. That was the same year Galileo first looked through a telescope.

In 1611, after the death of Kepler’s wife and son, and with difficulties for Protestants mounting in Prague with the counter-reformation as they had done earlier in Graz, Kepler moved to Linz. He lived there for 14 years, marrying a second time. It was in Linz that he published, in 1619, a book called
Harmonices Mundi (Harmonies of the World)
, relating the orbital speeds of the planets to melodic lines. He speculated that it might be possible to discover the moment of Creation by calculating backwards in time and determining the moment when the orbits of the planets would have produced the equivalent of the most perfect musical harmony.

Much more significant,
Harmonices Mundi
also contained Kepler’s third law of planetary motion, which establishes a relationship between the lengths of time the planets take to complete their orbits and their distances from the Sun. Those not conversant in the language of mathematical equations may skip the following paragraph.

The equation is (T
_A
/T
_B
)
²
= (R
_A
/R
_B
)
³
. T
_A
is the time it takes planet A to complete its orbit (its ‘orbital period’). T
_B
is the time it takes planet B to complete its orbit. R
_A
is the average distance from planet A to the Sun. R
_B
is the average distance from planet B to the Sun. The ratio of the squares of the orbital periods of the two planets is equal to the ratio of the cubes of their average distances from the Sun.

This equation makes it possible to build a scale model of the solar system. The question remains, however: What is the scale? For even though the orbital periods could be timed and were known, Kepler’s law didn’t provide the means to calculate any
actual measurement
for the distance from any planet to the Sun.
The
third law was an equation waiting for just one absolute, known distance to plug in.

Kepler’s discovery of his first and second laws allowed him to put together far more accurate tables for calculating the planets’ positions for any time in the past or future. When he published his third law, he had already begun the laborious task of producing these, but the completed tables were still slow in coming. Kepler’s preface explains that this was partly because of difficulties finding financial backing (he finally paid for the publication out of his own pocket) and also because of ‘the novelty of my discoveries and the unexpected transfer of the whole of astronomy from fictitious circles to natural causes’. He went on to point out that no one had ever attempted anything of this kind before. It required intense study of Tycho’s astronomical observations. Kepler tried orbit after orbit, leaving one after another behind when, after prodigious computation, they didn’t match his data. He was not particularly happy doing this work. It must have been very pedantic for so imaginative and creative a mind. It wasn’t until 1627 that he finally published his
Rudolphine Tables
, and they were a triumph for Copernican astronomy.

Kepler spent his last years at Sagan, in Silesia. He died at Regensburg on a trip seeking a new job and trying to collect back salary, in November 1630, just a year short of seeing that his prediction, in accordance with the Rudolphine tables, that Mercury would cross the disc of the Sun on 7 November 1631 was correct. He had composed his own epitaph:

I measured the skies, now the shadows I measure

Skybound was the mind, Earthbound the body rests.

Compared with Kepler’s bleak childhood, Galileo’s apparently was a pleasant one in a family that valued intellectual pursuits. He was born seven years before Kepler, in 1564, in the north Italian city of Pisa, and attended school both there and in
Florence
. At the age of 17, honouring his father’s wishes, he entered the University of Pisa as a medical student. Two years later, when it was clear that mathematics and mechanics, not medicine, were Galileo’s forte, his father allowed him to change his course of study.

One of Galileo’s important discoveries took place during his student years. Good Catholic he may have been, but evidently he was not always completely attentive at services. A lamp swinging on a long cord in the cathedral caught his eye. He noticed that regardless of whether the length (in space) of each swing was long or short, it seemed that the time it took to complete the swing remained the same. Curious, he experimented on his own and found that the length of time it takes a pendulum to complete one swing depends not on how big the swing is but only on the length of the cord by which it hangs.

In 1585, Galileo’s formal education ended when his father ran short of money to pay university costs. Galileo came home to Florence, where his family was now living. Undeterred, he studied on his own and with scholars among his father’s acquaintances and was soon making a local reputation with several inventions and discoveries, circulating his own short book on measuring the specific gravities of bodies, and brashly voicing suspicions about Aristotle’s mental capacities. One bizarre undertaking during these years was a series of public lectures he delivered about the shape, size and location of Dante’s hell – a topic that might draw a considerable audience even today.

In 1589, when Galileo was 25, four years after he had left the University of Pisa without a degree, he returned there as a lecturer. Pisa, like Tübingen, still taught Ptolemaic astronomy. Whatever Galileo may have been thinking privately, that was what he taught. It isn’t clear just when he became a convinced Copernican.

A discovery Galileo made while he was a lecturer at Pisa caused his already low opinion of Aristotle to sink even further.
Though
Aristotle had in truth been rather ambiguous on the subject, at least in those writings that survive, most scholars of Galileo’s time, including Galileo, thought that Aristotle had said that if two objects were dropped simultaneously from the same height, the heavier would strike the ground first. Galileo either dropped weights on numerous occasions from the Tower of Pisa, as his earliest biographer reported, or rolled them down a ramp, or perhaps he tried both. But he established to his satisfaction that the heavier and the lighter hit the ground at the same time. This was, of course, an experiment that he couldn’t perform in the absence of air resistance, and science historian Thomas Kuhn has quipped that it probably wasn’t Galileo who carried out the legendary public demonstration from the Leaning Tower but a defender of Aristotle, who thereby proved quite decisively for all present that Galileo was wrong and Aristotle was right. In the 20th century, astronauts performed the experiment in the airless environment of the Moon. Galileo was right.

Never a tactful man, Galileo somewhat incautiously proceeded to debunk the still highly venerated Aristotle. Aristotle ‘wrote the opposite of truth’ . . . was ‘ignorant’. Galileo also showed a lack of judgement when he bluntly advised the Grand Duke of Tuscany, Ferdinand I (who had granted him his professorship), that a dredging machine designed by the Grand Duke’s brother-in-law wasn’t going to work. The machine was built nevertheless and
didn’t
work, which made Galileo even less popular. When his father died in 1591, leaving him as eldest son responsible for the family, Galileo’s salary at Pisa was far from sufficient and, thanks to the dredging machine incident, not likely to rise. He looked for a new job and found one at the University of Padua, where Copernicus had studied medicine 90 years earlier. The Venetian Republic, the source of funding for Padua, was liberal and tolerant compared with Tuscany, and Padua and Venice were much more sympathetic venues for someone with ideas as radical and speech as imprudent as Galileo’s.

Though his financial difficulties didn’t end, Galileo was happy and influential in the intellectual milieu of Padua and Venice. On the personal front, he fathered three children by Marina Gamba, though he never married her. Their relationship seems to have ended amicably when he finally moved back to Florence, for he remained good friends with her and with the man she later married. Galileo’s two daughters both became nuns, and one of them was a source of great comfort and help to him when he was elderly.

At Padua, Galileo still taught Ptolemaic astronomy. However, though he lacked observational evidence to support a change of allegiance – and he was almost always careful about waiting for that before making announcements or going into print – by the mid-1590s he was personally convinced that Copernican astronomy was correct. In 1597 (12 years before he first looked through a telescope) he wrote a letter to that effect to a friend at Pisa, and it was also at this time that the exchange of letters with Kepler took place concerning Kepler’s book
Mysterium
. Galileo had joined the Copernican camp, but he declined to say so publicly.

In the late spring of 1609, the same year that Kepler published
Astronomia Nova
with his first and second laws, Galileo, in Padua, heard of an invention from Holland currently on view nearby in Venice – a tube with lenses arranged in it so that it made objects in the distance look closer. Apparently Galileo didn’t hurry off to examine this wonder in person. A few days later he heard a report of another such instrument from a friend in Paris. His interest aroused, Galileo started pondering what arrangement of lenses would produce the reputed effect. Venice and its nearby islands were centres of expert glass-making, so there was no difficulty obtaining the lenses he needed to build his own improved ‘perspicillum’.

The use of lenses for eye-glasses was nothing new. That had begun as early as the 13th century. There were probably also telescopic devices before the 17th century. However, one of the
first
pieces of documentable evidence of such an instrument identifies the maker as Jän Lippershey, a lens-grinder from the Dutch island of Walcheren. He presented it to Dutch authorities in October of 1608, eight or nine months before it came to Galileo’s attention.

It was obvious that such an instrument would be useful for sighting ships and distant features of the landscape. One brochure in the autumn of 1608 also pointed out its advantage for ‘seeing stars which are not ordinarily in view, because of their smallness’. Sir William Lower, a Welshman, looked at the Moon through a telescope earlier than Galileo did and thought it looked similar to a tart: ‘here some bright stuff, there some dark, and so confusedly all over’.

Clearly, the familiar story that Galileo invented the telescope is untrue. By the time he knew of its existence it had already been on sale in Paris and probably elsewhere for several months. A second piece of fiction is that he tried to pass it off as his own invention. However, Galileo did proceed immediately to make better capital out of it than anyone else was doing. On this occasion, and perhaps several others (it isn’t always clear precisely where he got his ideas), Galileo displayed a talent for seeing the unrealized potential of another person’s thought or invention and carrying it forward so rapidly and enthusiastically that he was halfway over the horizon before its originator had left the starting line. That isn’t plagiarism, but it did, in the case of the telescope at least, result in Galileo getting the popular credit while (his letters show) he was actually giving fair credit to others.

Galileo, a master of self-promotion, presented his own improved version of the tube with lenses to the Senate in Venice, hustled some of them up to the top of the Campanile, and showed them that it was possible to look out to sea and spot ships that wouldn’t be visible to the naked eye until two hours later. The military and commercial advantages of such an instrument were obvious to rulers of a major city-state whose
prosperity
rested on trade by sea. Galileo received a permanent appointment at the University of Padua and a hefty increase in salary.