A method of determining star distances based on a change in angle (parallax) from seasonal observations of star positions was suspected for many years, dating back millennia to the Phoenicians. It was well known that the positions of a number of stars seemed to oscillate in synch with the seasons on earth, and one explanation was that they might be a lot closer than the distant stars in the background. However, due to lack of imaging technology and precise telescopes (not to mention the risk of offending the gods), no one had accurately measured the distance to any stars, except the sun, before the nineteenth century.
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For 13 months, from April 1832 to May 1833, Thomas Henderson, the Astronomer Royal of Scotland, cataloged the positions of many southern stars while working at the Cape of Good Hope in southern Africa. He observed the exact position of the bright double star Alpha Centauri with respect to the surrounding stars. He chose this star because a fellow astronomer had pointed out to him that it had an unusually high amount of movement against the sky background and Henderson believed that it might be a close star. In mid-1834, he calculated the distance to Alpha Centauri as 2.6-3.1 light-years. However, even though he was the first person to ever properly utilize parallax to measure star distances, his equipment was of poor quality, and he did not trust his measurements. Fearing embarrassment, he did not publish his calculations for several years. Turns out his estimate was too low by more than 25%. Nevertheless, his timidity robbed him of his chance for immortality.
The first to actually announce and publish calculations of a star distance was Friedrich Bessel in 1838. (Interestingly, Bessel is far better known as the namesake of the Bessel functions, which were actually discovered by Daniel Bernoulli.) Bessel selected the star known as 61 Cygni for his calculations because it had the largest known seasonal motion. Working from his observatory in Konigsberg, Prussia, now part of Russia, he announced the distance to 61 Cygni to be 10.4 light-years, which is within 10% of the value of 11.2 light-years accepted today. Soon after his announcement, Henderson published his calculation, and Friedrich von Struve of Russia also published his calculation of the distance to the star Vega as 25.0 light-years in 1840.
The calculation of star distances is based on the method of trigonometric parallax. A star is selected for observation at two different times of year, usually six months apart. At each interval, a measurement of the angle to the star is taken. Stars in the background are used as a point of reference. Using the diameter of the Earth’s orbit around the sun as a base, a triangle is generated based on the shift in angle between the two measurements. With this triangle, simple trigonometry may be used to calculate the distance. The same principle is used by our brains every day in normal depth perception allowed by stereo vision to estimate near objects against a distant background.
It is impossible to ascertain any information about the distances of the farthest stars using this method. One limitation is the resolution of the telescopes and the imaging technology. Another limitation is the distortion of light caused by the Earth’s atmosphere. Because of distortion, Earth telescopes have a resolution of only about 0.2 arc-seconds, so only a few hundred stars can be measured from Earth. A satellite known as Hipparcos was launched by the European Space Agency in 1989 in order to measure star distances more accurately. From space, the resolution of the Hipparcos telescope improved to 1 millisecond of arc, so over 118,000 stars were measured.
For the three stars, 61 Cygni, Alpha Centauri, and Vega, that were announced by Bessel, Henderson, and von Struve in the early nineteenth century, the distances in light-yrs to the same stars calculated by the Hipparcos telescope are shown below.
61-Cygni Hipparcos: 11.395±0.0730 l-y Bessel (1838): 10.4 l-y
Alpha Centauri Hipparcos: 4.3955±0.0083 l-y Henderson (1839): 2.9 l-y
Vega Hipparcos: 25.301±0.0540 l-y von Struve (1840): 25.0 l-y
The early measurements were remarkably accurate considering the poor quality of the instruments that were available to the early astronomers.
Although modern day technology allows more precision for a wider range of star distance measurements than previously, the true innovation came about in ancient times with the development of trigonometry, which makes it all possible.