Authors: Kitty Ferguson
Cassini went on attempting to measure parallaxes and to tease fresh results out of the data from the Cayenne expedition. His work continued to fascinate the King, the court (especially the faithful Colbert) and the public. He became, for a while,
the
dominant figure in astronomy in Europe. Like Galileo, Cassini was astute when it came to self-promotion. More than anyone else in his time, he used the publication of papers in scientific periodicals as a way of establishing priority and of letting the educated world hear of his successes.
In 1676, Jupiter’s moons made possible another measurement that would be essential to later astronomy. Ole Roemer, a Danish astronomer also working at the Royal Observatory in Paris, studied the eclipses of Jupiter’s moons and noticed that the time that elapsed between their disappearances behind Jupiter varied with the distance between Jupiter and the Earth, a distance that changes as the two planets move in their orbits. Roemer speculated that the velocity of light was responsible for what looked like delays in the eclipses. When Jupiter was further from the Earth, it took longer for the picture of the eclipse to reach eyes and telescopes on the Earth. Timing the delays, Roemer proceeded to calculate the speed of light at
about
140,000 miles per second. That figure fell short of the 186,282 miles per second that we assign to the speed of light today. The discrepancy in the measurement was due in part to Roemer’s less-than-precise knowledge of the distance to Jupiter. The modern calculation is made with an atomic clock and a laser beam. (This book uses rounded-off figures of 186,000 miles or 300,000 kilometres per second for the speed of light.)
The Royal Observatory in England was established somewhat later than the Paris Observatory, and the impetus for its founding came from an unlikely source. In 1674, Louise de Kéroualle – a Bretonne who had recently been made Duchess of Portsmouth and was one of King Charles II’s mistresses – brought a Frenchman named Sieur de St Pierre to the King’s attention. St Pierre had discovered, so he said, a secret method for finding longitudes. Determining longitude requires having some form of universal clock – such as Jupiter’s moons were for Cassini and Richer – that will allow comparison of celestial phenomena as seen from different locations. If the Sun is directly overhead in New York, what is its position in Greenwich, England? Answering such questions is one way of finding longitude.
Flamsteed and others thought that St Pierre’s ‘secret method’ must involve using the Moon as a time-keeper. Who needed St Pierre? King Charles told the Royal Society, then known as the ‘Royal Society of London for Improving Natural Knowledge’, to collect whatever lunar data were necessary to determine whether the Moon could serve as a universal clock. Flamsteed soon reported that lunar and stellar positions were not known sufficiently well to make the method reliable. Nevertheless, the bee was in the King’s bonnet and he founded the Observatory, designating Flamsteed as ‘astronomical observator’, a position that would later become ‘astronomer royal’. A new building, designed by Sir Christopher Wren, was ready for occupancy in July 1676, and Flamsteed and his associates began the task of producing correct star positions and tables for the Sun, Moon
and
planets – for the express purpose, as those who governed England saw it, of aiding navigation, but also for the furthering of astronomy.
So things stood in the last quarter of the 17th century. Kings were footing the bill for observatories in Paris and at Greenwich. There was also royal patronage for such bodies as the French Academy and the Royal Society, where gentlemen – expert and not – got together and shared knowledge of the wonders of science. They had a fairly good idea of the dimensions of the solar system. Astronomy seemed poised and ready to measure much greater distances. But a base line from Paris to Cayenne isn’t long enough to measure the parallax shift of stars; in fact, no possible base line on the face of the Earth would suffice. Was there any way to make the parallax method work for stars?
The clue was there long before Ptolemy. One objection other Hellenistic scholars raised to Aristarchus’s suggestion that the Earth moves and orbits the Sun was that, if it does, we ought to be able to observe stellar parallax as we travel from one extreme of the orbit to the other. In other words, the stars ought to shift position relative to one another in the sky, just as the cactus and the mountain peak shifted. If we’re viewing the cactus and the mountains from a car window and they don’t seem to be changing positions relative to one another, either our car is standing still or both the cactus and the mountains are very far away. Likewise either the Earth does not move and orbit the Sun, or the stars are extremely far away – further away than most ancient scholars, except for Aristarchus, were willing to conceive.
By 1700, nearly all astronomers agreed that the Earth rotates on its axis and orbits the Sun. They also recognized the potential of this orbit for a base line. Even so, at that time and even much later, no one was able to detect an annual shift in a star’s position. That discovery had to wait for considerable improvement in telescopes and the precision instruments used with
them
– advances that would eventually come with the Industrial Revolution. But there was also meanwhile more to be learned from a theoretical point of view, in order to be able to recognize stellar parallax and not confuse it with other effects.
Parallax wasn’t the only hope for measuring the distance to the stars. According to the ‘inverse square law’, the brightness of a light falls off with distance in a mathematically dependable way. The measured intensity of light diminishes by the square of the distance to its source. Imagine that you have two 100-watt lightbulbs. Place one of them twice as far away as the other. The further bulb will appear to be only a fourth as bright as the nearer. It will seem to you that it must be a 25-watt bulb. Turning that exercise around: suppose you keep one of the 100-watt bulbs nearby and ask an assistant to carry the second to an unknown distance. If the more distant bulb appears to be a 25-watt bulb, then you can be sure it’s twice as far away as the first bulb. Comparing their
apparent
brightness gives the distance of the second light. How does this apply to stars? If stars all have the same close-up brightness and we know the distance to one star, then in principle we can find the distance to any other star by comparing its
apparent
brightness (how it looks to us from the Earth) with the brightness of the first star.
The reasons why measuring the distance of stars has turned out to be far more complicated than that become clearer if we come in out of the dark and note that the same inverse square law that works with the brightness of light works with the size of objects. Even without knowing the mathematics, you and I use the method instinctively, if imprecisely. Suppose you are overlooking a vast expanse of land with a great number of elephants grazing on it. Some of the elephants look tiny, but because you have previous experience of elephants and know how large an elephant would be if you were standing near it, you make an educated guess that these aren’t really tiny at all, just far away. From the difference between their apparent sizes
and
the normal close-up size of an elephant, you judge how far away.
Your success relies upon: (1) having some way of knowing that elephants are all approximately the same size – some reason for assuming there aren’t elephants that are pygmies and others that are giants; and (2) having experience of what that size actually is – that is, how big an elephant looks when it’s standing a known distance away.
With a light seen at night at an unknown distance, on the Earth or in the sky, we lack those essential ingredients. Experience tells us that lights can’t be depended on all to have approximately the same close-up brightness, so knowing the close-up brightness of one light is of no use when studying the brightness of a distant light. A comparison is meaningless. We’re left with such questions as: Is it a dim bicycle headlamp over there, just a few yards up the road, or is it the high-beam headlight of a car a mile away? Is it a meteor suffering a fiery death in the upper atmosphere, or is it a firefly no further away than the treetops?
The situation is puzzling but not completely hopeless, nor did it seem so at the end of the 17th century. Astronomers did know how far it is to one star – the Sun. Stars
might
all be equally bright, and it
might
be safe to assume the Sun is a typical star. It would seem highly desirable to know the brightness or the distance of at least one star other than the Sun, but failing that, the Sun would have to serve as a standard. On the assumption that it could, Englishman Isaac Newton set out to measure the distances to the nearest stars.
Newton, born in 1642, the year that Galileo died, was 30 years old when Cassini and Flamsteed measured the distance to Mars. Except for his
Principia Mathematica
, which appeared in 1687, unarguably one of the most important achievements in the history of human knowledge, Newton published almost nothing. However, he obsessively researched an astounding variety of subjects including optics, theology, alchemy and
calculus
, and was responsible for significant advances in many of the fields he investigated. He contributed to the development of a new type of telescope that used a mirror rather than a lens to focus incoming light. (See
Figure 4.5
on here
.)
Newton probably wouldn’t even have published the
Principia
had his friend Edmund Halley not goaded him sufficiently. Publication meant public notice, and contact and correspondence with other scholars. It meant he would be expected to take part in the discussions at the Royal Society. There would be invitations to perform experiments for that body and to watch others do the same. Though honours were tempting and sometimes Newton succumbed, those distractions more often seemed anathema to him. They took precious time away from his research. It is surprising therefore that he agreed to become head of the Royal Society. Unfortunately, he used the position of power in an extremely unpleasant, autocratic manner, bringing misery to other fine scientists (including the elderly Flamsteed). Newton also eventually accepted the job as Master of the Mint and thoroughly enjoyed his rather pedestrian duties there.
Whatever his personal failings, it was Newton who capped the Copernican revolution with his discovery of laws of gravity. In Newton’s description, each body in the universe is attracted towards every other body by the force called gravity. How much bodies are influenced by one another’s gravitational attraction depends on how massive the bodies are and how near they are to one another. For instance, any change in the mass of the Earth or the Moon, or in their distance from one another, would change the strength of the gravitational attraction between them. If the mass of the Earth were doubled, the attraction between the Earth and the Moon would double. If the Moon were twice as far from the Earth as it is, the attraction of gravity between the Earth and the Moon would be only a quarter as strong.
Here at last in this simple description were the dynamics that
cause
the planets to move as they do rather than in some other way, the physical reasons behind Kepler’s laws. The answer that eluded Ptolemy, Copernicus, Galileo and Kepler – but to which Kepler’s laws point – was summed up in one sentence: the gravitational force between any two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. It took Newton’s genius to see that it is this same force – gravity – that keeps us from flying off the ground, dictates the path of a ball thrown on the Earth, underlies the motions of the planets, and governed the way Galileo’s two objects landed at the foot of the Tower of Pisa (if they did).
Newton’s ‘laws of motion’ could be tested by experiments as well as by astronomical observations, and this was an era that rejoiced in such testing. The scientific rigour that had made Galileo exceptional was beginning to be considered essential for any scientific activity. It became clear that Newton’s formulae did indeed describe the way things happen. Nature was law-abiding and she was following these laws! It’s difficult for us, who take for granted that science is able to predict reality and that simple, dependable mathematical and scientific rules underlie the apparent complications of nature, to appreciate how awe-inspiring it must have been for the many men and women who were realizing this in the 17th century for the first time. Not only did such laws exist, but human minds could discover them and understand them. The concept was not a complete novelty to scientists, although to see it demonstrated as beautifully as it was in Newton’s
Principia was
a novelty. To the non-scientific public Newton’s revelation was sensational, miraculous. The fame of his book spread quickly throughout Europe, and his ideas were popularized in many forms. There was a publication called
Newton for Ladies
in France.
Principia
did encounter some hostility on philosophical grounds, uneasiness with the notion that gravitation could act through empty space. ‘Action at a distance’ suggested the occult.
Newton’s attempt to estimate the distances to the nearest stars by assuming that all stars, including the Sun, have approximately the same brightness, is one of his less celebrated efforts. In the analogy with the elephants, you and I assumed that all elephants are about the same size, but suppose we had seen only one elephant close up. It would be risky to jump to the conclusion that all elephants are the same size – that our local elephant is a typical elephant – based on such limited experience. The difference in apparent size between the local elephant and other elephants whose distance we don’t know might actually be due to differences in size, not an indication of their distance at all. Newton’s situation was even more ambiguous than that. Elephants look pretty much alike, but the Sun, as seen from Earth, doesn’t resemble the other stars. Most experts in Newton’s time did think that the Sun was a star. But was it a
typical
star? It wasn’t unreasonable to decide to assume that it was, and see where that would lead.