If the Universe only consisted of the solar system,
the problem of its size would have been solved in 1700.
But the solar system is not the universe, we lack the stars.
In 1700 it was still possible to believe that a vault limited the universe and that the stars were fixed as little lights, and also that this vault was far beyond the end of the solar system. That’s what Kepler thought.
The measures of parallaxes that had been used to calculate the scale of the solar system in the seventeenth century were not good for the stars. The separation between two nearby stars hardly varied at all, however widely separated were the terrestrial observatories from which they were measured. Even placing the two observatories at opposite ends of the Earth, no change in the position of the stars was noticed. This should not surprise us, because although the stars were a little beyond Saturn, this distance is too large for the parallax could be measured with the means available in 1700.
But the surface of the Earth was not the astronomer’s only resource for solving this problem. Although the diameter of the Earth does not measure more than about 12,000 kilometers, in its movement around the Sun the entire planet moves through space and between the two extremes of the average orbit a distance of 299,000,000 kilometers. So if the position of the stars was recorded one night and it was recorded again another night, but half a year later, the astronomer would have made two observations from two positions separated by a distance equivalent to 23,600 times the diameter of the Earth. The angular distance between the edge and the center of the ellipse would be the stellar parallax .
This method can not be applied to planets because they describe such a complicated trajectory in space that any displacement caused by the movement of the Earth is masked. Trying to separate the own movement of the planet from the other one that it has by virtue of the movement of the Earth would be a very complicated work, and it would give inaccurate results that those that can be obtained by the parallax method. As the stars remain practically fixed throughout the year, with them you can use that method.
During the ten years that elapsed between 1800 and 1809, astronomers could not detect the parallax of any star. The reasons for this were very varied.
It could happen that Copernicus and Kepler were wrong and that the Earth did not revolve around the Sun, but that it was the immobile center of the Universe. If it had been like that, it would have been impossible to observe any parallax. When Copernicus first exposed the heliocentric theory , one of the strongest arguments against him was that no parallax could be performed. But there were too many reasons in favor of the heliocentric theory , so, although no stellar parallax had been observed, that theory ended up steadily in astronomical thought. The Earth does move, so the absence of parallaxes had to be explained by other causes.
Although the Earth moves, no parallax could be observed if all the stars were at the same distance, because the parallax can only be measured when observing the position that a nearby object occupies with respect to another one farther away. If the celestial vault were rigid, all the stars would have an identical displacement even if the observer’s position changed and no parallax could be observed.
There were several arguments that led to think that the distances between the Earth and the stars could be variable. It could happen that the stars were distributed in a very wide space, and the Universe did not have a rigid border.
The brightness of the stars changes, made evident to anyone who has looked at the night sky. Hipparchus was the one who tried for the first time to systematize these differences in brightness, for which he divided the stars into six classes or magnitudes. The brightest ones classified them in the first magnitude, those that shone a little less in the second magnitude, and thus until arriving at the sixth, within which the weakest stars were included that could be observed with the naked eye.
At present, astronomers measure the brightness of stars with instruments that, of course, did not exist in antiquity, and specify the different magnitudes with great mathematical precision. A difference of 5 magnitudes translates into a quotient of 100 measured in brightness, which means that a star of magnitude 1 is 100 times brighter than another of magnitude 6. So a difference of a single magnitude represents, in brightness, a quotient of 2,512, since 2,512 X 2,512 X 2,512 X 2,512 X 2,512 is equal to 100.
There are currently very precise measurement methods that allow you to define the magnitude of a star up to tenths of a magnitude. The star Aldebaran, for example, has a magnitude of 1.1, while Regulus is of magnitude 1.3, which is somewhat dimmer. The magnitude of the Polar Star is 2.1.
There are many brighter stars than Aldebaran, of magnitude greater than 1.0. Procyon has magnitude of 0.5, and Vega, still brighter, of 0.1. The stars that shine the most are assigned negative magnitudes. Sirius has a magnitude of -1.4.
Besides the stars, the planets, the Moon and the Sun are also included. Venus, Mars and Jupiter, sometimes have a higher brightness than the brightest stars: Jupiter can reach a magnitude of – 2.5, Mars of -2.8 and Venus of -4.3. The full Moon has a magnitude of -12.6 and the Sun of -26.9.
At the opposite extreme, there are stars with magnitude less than the sixth and are invisible to the naked eye. When Galileo focused his telescope for the first time towards the sky, in the year 1609, he saw hundreds of stars impossible to detect until then. Today you can see stars of magnitude 7, 8, 9 and much more up and down the scale of brightness. The most powerful telescopes that exist today can distinguish thousands of stars of magnitudes greater than 23.
If all stars had the same brightness, we might think that the difference in apparent brightness was due only to distance. The closest stars appear brighter than the farther ones, just as the nearby streetlamps seem to shine more brightly than the more distant ones.
In 1700 there was nothing to suggest that all stars had an identical brightness. If all the stars were at the same distance from the Earth, it could be because there was a real difference in the brightness and not an apparent difference, that is, there were simply brighter and dimmer stars, just as some light bulbs give more light than others
The Greeks had recorded the relative positions of the stars. The first to do so were Aristilos and Timocares de Alejandría, in the 3rd century BC. C. Hipparchus worked in a more systematic way, and in the year 134 a. C. had registered the position of more than 800 stars. He also made the first star map, which was enriched by Ptolemy with some two hundred more stars.
Halley studied the position of the stars, and in 1718 he realized that there were at least three stars, Sirius, Procyon and Arthur, who were not in the place the Greeks said. There was a difference so great that the possibility that he or the Greeks had made a mistake was very remote. Halley found that Arthur had moved a degree with respect to the position assigned to him by the Greeks, so he thought that those stars had moved. This meant that those stars were not totally fixed, but had a much slower own motion compared to that of the planets, so it was impossible to detect it in a day or even a year.
The existence of stars with own movement supposed a tremendous blow against the hypothesis of a fixed celestial vault. It seemed that some stars were not subject to the vault, and began to think that perhaps none of them was, is more, perhaps there was no vault .
Although the stars were not fixed to the celestial vault, it did not mean that they were all located at the same distance. You could think that, without being fixed to anything, they were distributed along a strip of space.
This was very unlikely since only a small part of the stars showed visible movement of their own. Of course, a star could move without that movement being visible, even with the passage of many years, since its trajectory could be parallel to the line of sight.
But if the stars moved in random directions, the number of those that moved more or less at right angles to the line of sight should at least be the same as those moving in a direction parallel to it. And if the stars had their own movement, at least half of them should be able to be seen. However, after thorough investigations it was shown that visible own movements were the exception.
But if not all stars are at the same distance, but are at very variable distances, and if all move at the same speed more or less, and do so in random directions, you can reach some conclusions.
No star that moves in a direction parallel to the line of sight will have a visible movement of its own, either distant or close. Of those that move in a direction perpendicular to the line of sight, those closest to Earth will have their own movement greater than that of the farthest ones. This is so because it is precisely the bright stars that most frequently have a more similar self-movement. The three stars in which a movement of their own was detected for the first time, Sirius, Procyon and Arthur, are among the eight brightest stars in the sky. Obviously, a nearby star will present an intense brightness and its own movement will be measurable. According to this, it is logical that the number of stars with measurable own movement is very small, since only the closest ones are sufficiently close so that a proper movement is visible, however small it may be. There are millions of stars that are too far away to show visible movement, even if centuries pass.
In the middle of the 18th century, it was already assumed that there was no rigid celestial vault, nor a strip through which the stars moved. On the contrary, the stars were distributed throughout a huge and indefinite space. In fact, it was the German philosopher Nicolás de Cusa who first suggested this idea, but at that time it was a mere speculation, and now it is a result obtained from meticulous observations.