The distance to heavenly bodies as well as the total size of the Universe has been commonly underestimated throughout the entire history of astronomy. From the time of the ancient Greeks and even in recent years, new discoveries have forced us to think bigger about just how vast and distant the Universe is. Currently we have no evidence to prove that the Universe is not infinite in size.
The Ancient Greeks
In his time, Aristotle (384-322 BC) lays down principles of the Universe that would go unchanged for 2000 years. He used philosophy and logic as the basis for his teachings of the natural world instead of experimentation. As such he believed that the Universe was finite, and bounded by a sphere containing the fixed stars.
Outside of the sphere there was nothing. Between this sphere and the moon's orbit was an intermediate region which contained the Sun and all of the planets. The Earth was stationary and at the center of the Universe. Within the Earth-Moon region existed everything that changed. This included thunderstorms, rainbows, comets, etc. Everything beyond the Moon remained the same forever. The stars were made of the fifth element, ether, which gave them their self-luminescence.
All of the planets and stars only stretched out to just beyond the orbit of Saturn. Aristotle's teachings of cosmology were to be the standard for 2000 years. For all this time, as far as most everyone was concerned, the entire Universe was within eyesight.
The Distance to the Sun and the Moon
Aristarchus (310-230 BC) was the first to determine a practical distance to the Moon. He did this by observing an eclipse of the Moon, during which the shadow cast by the Earth onto the Moon gave him an indication of the relative size of the two bodies. Since the angle that the Moon subtends to the Earth can be measured (it is about half a degree), its distance can then be estimated in Earth diameters. Aristarchus obtained a distance of 25 Earth diameters to the Moon, compared to a modern value of close to 30.
He then turned to the much more difficult task of determining the distance to the Sun. He pointed out that when the moon was exactly half illuminated, the angle between the Earth-Moon line and the Moon-Sun line was 90 degrees. So if he measured the angle between the Earth-Moon line and the Earth-Sun line, he could calculate the distance to the Sun in terms of Earth-moon distance. His method is geometrically correct but requires extremely precise instruments because of the great distance to the Sun. He obtains an angle of 87 degrees which meant the Sun was 20 times more distant than the moon. His results were grossly inaccurate. The actual angle is 89.9 degrees, implying that the Sun is more than 400 times more distant from the Earth than the Moon. Aristarchus underestimated the distance to the Sun by a factor of 20. But he had proven that the Sun was much more distant than the Moon, a considerable achievement for his time.
The Size of the Earth
Aristarchus' methods were all based on the then unknown diameter of the Earth. But in 240 BC, 10 years before Aristarchus' death, a young mathematician named Eratosthenes devised a simple way to determine the circumference of the Earth. He assumed that the Sun was very distant from the Earth and therefore its rays could be assumed to be parallel to each other. Measuring the angle of shadows cast at two different locations, and obtaining the distance between the two, he was able to calculate a remarkably accurate Earth circumference of about 25,000 miles. Compared to today's accepted measurement of 24,901 miles, Eratosthenes' calculation is off by less than 1%.
Determining that the Sun was much larger than the Earth, Aristarchus made the daring assumption that it was the Sun that was the center of the Universe. He accepted Aristotle's teachings of a bounded Universe of a sphere containing fixed stars at its outer limits. But with the Sun now at the center and the Earth revolving around it, Aristarchus realized that he could use his same methods to now determine the distance to the fixed stars by observing stellar parallax. Parallax is the effect of the stars appearing slightly shifted as the Earth moves around the Sun over the course of a year.
Unfortunately, no stellar parallax could be detected. This led Aristarchus to conclude that the size of the Universe, which was then the distance to the visible stars, was so great that, in his words, if you drew a very large circle, the Earth's orbit would appear only as a point. Aristarchus did not know it then, but even the closest stars only have a parallax of less than one second of arc. It would not be until the 19th century that stellar parallax would be detected.
In the mean time, another great Greek observational astronomer named Hipparchus (194-120 BC) improved on Aristarchus' methods and determined an Earth-Moon distance of 30 Earth diameters. And using Eratosthenes' calculation of Earth's diameter, he arrived at an Earth-Moon distance of 237,000 miles (382,000 kilometers), accurate within 1 percent.
It would be thousands of years until the next shocking revelation as to the enormous extent of the Universe would occur. While professor of mathematics in Padua, near Venice, Italy, Galileo Galilei heard of a recent Flemish invention of a device that could increase the power of the human eye. It was called a telescope, and quickly working out its design, he built one himself. He would improve on its design until he constructed one which gave a magnification power of 33. With an aperture of nearly 5 centimeters, his telescope effectively increased the power of the human eye by a factor of 100.
Instead of using his telescope for commercial or military advantages, Galileo pointed his new device towards the heavens. He saw mountains and craters on the Moon, Saturn's rings, as well as moons orbiting the other planets. He described the wonders revealed by his telescope in a book titled Siderius Nuncias (The Starry Messenger), published in 1610.
The greater implications resulted from the fact that wherever in the sky Galileo pointed his telescope, he saw countless stars that were not visible with the naked eye. Towards the Milky Way, stars appeared in countless numbers. The teachings of Aristotle that the stars were fixed on a sphere that marked the boundary of the Universe were appearing less likely. This was the first breach of the idea of a small, nearby, shell-like Universe.
The Size of Our Solar System
Giovanni Cassini and Jean Richer established the basic size of our solar system later in the 17th century. They first measured the distance to Mars in 1673 by taking observations of the planet from two very distant locations on Earth: Paris and French Guiana. They both observed the position of Mars against the background of fixed stars.
The different angular position of Mars allowed them to calculate a distance of 87 million miles (140 million kilometers). They were within 7 percent of the correct value of 93 million miles (150 million kilometers). The true scale of the solar system had now been established and it was staggeringly large.
Heinrich Wilhelm Olbers was the first to place any real scientific constraints on the size of the Universe. He did this by making one simple and profound observation, that it gets dark at night! In 1826 he pointed out that in an infinite Universe composed of stars, any line of sight would intersect a star and the sky would be constantly bright. Olbers then concluded that we must be living in a Universe that was finite in either space or time. His question was based on a static Universe, an assumption that had been in place since ancient times and would remain in place for another 100 years.
The Distance to the Stars
It would not be until 1838 that observational equipment was built that was finally precise enough to detect stellar parallax, that is the apparent wobble of stars as the Earth revolves around the Sun. In that one year it was observed for three different stars by three different astronomers. The first was Friedrich Bessel in Germany who measured the parallax of the star 61 Cygni to be 0.3 seconds of arc. The second was Thomas Henderson who measured a parallax of 0.8 seconds of arc from the British observatory at the Cape of Good Hope. The third person to detect stellar parallax was the Russian astronomer Friedrich Struve, who measured 0.1 seconds of arc for the star Alpha Lyrai (Vega).
Using the angles observed 6 months apart, the distances to these stars was determined. But the distances were so vast that to express them in Astronomical Units (the distance from the Earth to the Sun) would make them incomprehensible. A new standard unit of measurement was needed. The astronomers used a unit that came naturally from their methods, the parsec. Parsec is a contraction of parallax second, the distance at which a star would have a parallax of one arc second. Even the stars closest to Earth have parallax of less than one arc second, implying that they all are a distance from Earth of greater than one parsec.
These enormous distances to even the nearest stars were greeted by many with amazement. It was incredibly difficult for most to comprehend how vast the visible Universe was. But the measurement of stellar parallax was only a small step in determining the huge scale of the Universe.
The Size of the Milky Way Galaxy
By the beginning of the 20th century, the mainstream belief was that all of the observable stars lie within the Milky Way galaxy, and therefore our galaxy encompassed the entire Universe. Beyond our galaxy was an empty void, thus fulfilling Olbers' paradox. But the size of our galaxy was not yet know.
At Harvard College Observatory, an astronomer named Henrietta Leavitt conducted a major study of a specific type of star, a cepheid variable. This is a type of star whose brightness varies regularly as gravity loses control of its nuclear burning during the late stages of its life. She measured the period of variation in brightness, which gave the luminosity, and then calculated their average apparent brightness. This relationship is know as the period-luminosity law.
But one important step was needed to turn this into a powerful tool for measuring distance. The method had to be calibrated so that relative luminosities could be converted into absolute luminosities. This could be achieved by determining the distance of any one cepheid.
This problem was solved by Harlow Shapley, the director of Harvard College Observatory. Since there is no cepheid close enough to Earth to measure its parallax, Shapley had the brilliant idea of using the motion of the Sun as a baseline instead of the Earth to measure stellar parallax. Relative to the background of stars, and over a period of 10 years, the Sun moves 20 times farther than the diameter of Earth's orbit. This allowed measuring distances of stars which were 20 times more distant, which now included cepheids. This method would only work if the background stars were stationary, which they are not. Shapley overcame this problem by taking the average parallax of groups of stars which included a cepheid and were perpendicular to the Sun's motion. This method achieved a great distance measurement at the expense of accuracy. Nevertheless Shapley's method provided the most powerful tool then available for determining distance.
Shapley applied this technique to his great passion, determining the size and shape of the Milky Way galaxy, which was then believed to contain the entire Universe. He concluded that the Sun did not lie at the center of the galaxy, but instead lie two thirds of the distance from the center to the edge. He determined that our galaxy was roughly 100,000 light years across and a few thousand light years thick. He publishes his findings in 1917.
The Existence of and Distance to Other Galaxies
photo credit: NASA
Edwin Hubble had an unconventional background, as many great scientists do. He was born in Missouri in 1889, took a degree in physics at the University of Chicago, then switched fields and took a degree in law at Oxford. After a few months practicing law, he abandons his career path and returns to Chicago where he is granted a doctorate in astronomy in 1917. After spending two years in the army he is granted a position at the Mount Wilson Observatory in 1919 at the age of 30, when most scientists would have already made their mark.
He uses the observatory's 100-inch telescope to study the brightest spiral nebula which lie in the constellation of Andromeda. He was able to resolve and observe its individual stars and he detected some that had regular variations in brightness, marking them as cepheids. Using Shapley's calibration of Leavitt's period-luminosity law, he was able to determine the distance to the great Andromeda nebula. He obtains a shocking distance, 1 million light years! This put Andromeda well outside of the Milky Way Galaxy. The Milky Way was not the whole Universe but only one of many galaxies. The year was 1924 and the Universe had once again increased in size by an enormous factor. Current estimates put the Andromeda Galaxy at 2.5 million light years from the Milky Way.
Hubble would go on to make a catalog of all the galaxies within view of the 100-inch telescope. He observes galaxies that range from one tenth of the diameter of the Milky Way to 10 times its diameter. Their Doppler effect was determined by observing the resonance of ionized calcium, and was observed to always be shifted towards the red. That is, all galaxies in the observable Universe are moving away from our Milky Way Galaxy. Furthermore, he found that galaxies were moving away at a faster rate the more distant they were. He therefore proved that the Universe was expanding. Centuries of belief in a static Universe had been shattered once and for all.
photo credit: NASA
In September of 2015, the Hubble Space Telescope captured the most distant galaxy observed to date, EGS8p7, at roughly 13.2 billion light years away. The telescope looks for infrared light waves, invisible to the human eye, because the more distant a galaxy is from Earth, the faster away it is moving from us, causing its light to be shifted to the red. That is, visible light emitted from a far away galaxy is shifted more and more toward redder wavelengths.
Very recently it was believed that the Universe contains approximately 200 billion galaxies, but new research has shown that this estimate is probably 10 times too low. Currently at least 90 percent of galaxies have yet to be studied.
The Earth currently appears at the center of a large sphere containing billions of galaxies. In any direction, the edge of the observable Universe is 13.8 billion light years away, making the Earth appear to be at the center. Accounting for the speed at which these distant objects are moving, along with the time it has taken their light to reach us, the most distant observable reaches of our Universe are calculated to actually be 46 billion light years away. This makes the diameter of the known Universe to be 92 billion light years.
Olbers' Paradox Revisited
Olbers argued that, because the sky is dark at night, the Universe must be finite in space or time, but he based this on a static Universe. An expanding Universe would be infinite in space but finite in time, namely the time since its creation. But in an infinite Universe the Earth would appear to be at the center. However, the sky will still appear dark at night because of the high redshift of its most distant parts, since the human eye cannot see infrared light waves. Olbers' question, "Why does it get dark at night?" had finally been answered by Edwin Hubble, but in a way he could not have imagined.
It is interesting to apply all of this hindsight to our own current understanding of the Universe. If everyone who came before us drastically underestimated its size and nature, who is to say that we are not also doing the same? It makes one wonder what the true size of the Universe really is, or if we will ever really know or understand the extent of creation.
Originally published February 21, 2017
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